TSTP Solution File: SWW257+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW257+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:37 EDT 2022
% Result : Theorem 26.01s 26.37s
% Output : Refutation 26.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWW257+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Sat Jun 4 14:14:52 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.00/1.60 *** allocated 10000 integers for termspace/termends
% 1.00/1.60 *** allocated 10000 integers for clauses
% 1.00/1.60 *** allocated 10000 integers for justifications
% 1.00/1.60 *** allocated 15000 integers for termspace/termends
% 1.00/1.60 *** allocated 22500 integers for termspace/termends
% 1.00/1.60 *** allocated 33750 integers for termspace/termends
% 1.00/1.60 Bliksem 1.12
% 1.00/1.60
% 1.00/1.60
% 1.00/1.60 Automatic Strategy Selection
% 1.00/1.60
% 1.00/1.60 *** allocated 50625 integers for termspace/termends
% 1.00/1.60 *** allocated 75937 integers for termspace/termends
% 1.00/1.60 *** allocated 113905 integers for termspace/termends
% 1.00/1.60
% 1.00/1.60 Clauses:
% 1.00/1.60
% 1.00/1.60 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.00/1.60 { ! v_a____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.00/1.60 { ! v_k____ = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.60 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.00/1.60 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.00/1.60 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.00/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.00/1.60 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.00/1.60 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.00/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 1.00/1.60 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.00/1.60 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.00/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 1.00/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 1.00/1.60 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.00/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.60 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.00/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 1.00/1.60 ) }.
% 1.00/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.60 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.00/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.00/1.60 ) }.
% 1.00/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.00/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.00/1.60 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.00/1.60 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.00/1.60 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), skol2 ), hAPP( hAPP
% 1.00/1.60 ( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_a____ ), hAPP(
% 1.00/1.60 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol2 ),
% 1.00/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 1.00/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ) ) =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.00/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.00/1.60 = c_Groups_Oone__class_Oone( X ) }.
% 1.00/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.00/1.60 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.00/1.60 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.00/1.60 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.00/1.60 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.00/1.60 .
% 1.00/1.60 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.00/1.60 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.00/1.60 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.00/1.60 tc_Nat_Onat ) }.
% 1.00/1.60 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.00/1.60 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.00/1.60 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.00/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.00/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.00/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.00/1.60 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 1.00/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.00/1.60 ( tc_Nat_Onat ) ) ) ) }.
% 1.00/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.60 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.00/1.60 ( tc_Nat_Onat ) ) ), X ) ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.00/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.00/1.60 tc_Nat_Onat ) ) = Y }.
% 1.00/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.00/1.60 tc_Nat_Onat ) ) = Y }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.00/1.60 tc_Nat_Onat, Z, Y ) ) }.
% 1.00/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.00/1.60 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.00/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.00/1.60 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.00/1.60 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.00/1.60 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.00/1.60 c_Groups_Oone__class_Oone( X ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.00/1.60 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 1.00/1.60 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.00/1.60 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.00/1.60 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.00/1.60 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.00/1.60 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.00/1.60 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.00/1.60 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.00/1.60 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.00/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.00/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.00/1.60 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.00/1.60 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.00/1.60 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.00/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.00/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.00/1.60 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.00/1.60 ), U = Z, T = Y }.
% 1.00/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.00/1.60 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.00/1.60 ) }.
% 1.00/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.00/1.60 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.00/1.60 ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.00/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 1.00/1.60 ) ), Z ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.00/1.60 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.00/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.00/1.60 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.00/1.60 ) }.
% 1.00/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.00/1.60 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.00/1.60 ), ! U = T }.
% 1.00/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.00/1.60 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.00/1.60 ), ! Z = Y }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.00/1.60 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.00/1.60 = Y }.
% 1.00/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.00/1.60 = Y }.
% 1.00/1.60 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.00/1.60 ( X ) }.
% 1.00/1.60 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.00/1.60 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.00/1.60 c_Groups_Oone__class_Oone( X ) }.
% 1.00/1.60 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.00/1.60 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.00/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.00/1.60 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.00/1.60 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.00/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.00/1.60 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.00/1.60 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.00/1.60 .
% 1.00/1.60 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.60 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.00/1.60 Z ) ), U ), T ) = Y }.
% 1.00/1.60 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.00/1.60 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.60 ( X ), Z ), U ), Y ) }.
% 1.00/1.60 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.60 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.00/1.60 W ) ), U ), Y ) }.
% 1.00/1.60 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.00/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.00/1.60 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.60 ( X ), Z ), U ), Y ) }.
% 1.00/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.00/1.60 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.00/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.00/1.60 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.00/1.60 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.00/1.60 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.00/1.60 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.60 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.00/1.60 Z ) ), Y ) ) }.
% 1.00/1.60 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.00/1.60 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.00/1.60 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.00/1.60 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.00/1.60 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.60 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.00/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 1.00/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.00/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.00/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.00/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 1.00/1.60 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.00/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.00/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.00/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.00/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.60 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.00/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.00/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.00/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.00/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.00/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 1.00/1.60 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 1.00/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 1.00/1.60 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.00/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.00/1.60 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.00/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.00/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.00/1.60 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.60 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.00/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.00/1.60 .
% 1.00/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.00/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.00/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.00/1.60 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.60 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.00/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.00/1.60 .
% 1.00/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.00/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.00/1.60 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 1.00/1.60 ( tc_Nat_Onat ) ) = X }.
% 1.00/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.60 tc_Nat_Onat ), X ) = X }.
% 1.00/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.60 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 1.00/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 1.00/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.60 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 1.00/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.00/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.00/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.00/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.00/1.60 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.00/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 1.00/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.00/1.60 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.00/1.60 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.00/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.60 tc_Nat_Onat, Y, X ), Y ) = X }.
% 1.00/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.60 tc_Nat_Onat, Y, X ), X ) = Y }.
% 1.00/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.00/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.00/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.00/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.00/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.00/1.60 tc_Nat_Onat ) }.
% 1.00/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.00/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.00/1.60 tc_Nat_Onat ) }.
% 1.00/1.60 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.00/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.00/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.00/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.00/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.00/1.60 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.00/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.00/1.60 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.00/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.00/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.00/1.60 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.00/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.00/1.60 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.00/1.60 , Y ), X ) }.
% 1.00/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.00/1.60 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.60 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.00/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.00/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.00/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.61 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.61 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.61 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.61 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.61 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.61 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.00/1.61 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.61 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.61 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.61 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.00/1.61 c_Groups_Oone__class_Oone( X ) }.
% 1.00/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.00/1.61 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.00/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.00/1.61 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.00/1.61 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.00/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.00/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.00/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.00/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.00/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.00/1.61 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 1.00/1.61 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.61 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 1.00/1.61 ) ), T ), Y ) }.
% 1.00/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.00/1.61 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.00/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.00/1.61 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.00/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.00/1.61 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.00/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.00/1.61 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.00/1.61 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.00/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.00/1.61 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.00/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.00/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.00/1.61 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.00/1.61 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.00/1.61 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.00/1.61 .
% 1.00/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 1.00/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 1.00/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.00/1.61 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 1.00/1.61 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 1.00/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.00/1.61 = Y }.
% 1.00/1.61 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.00/1.61 = Y }.
% 1.00/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.00/1.61 = Y }.
% 1.00/1.61 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.00/1.61 = Y }.
% 1.00/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.00/1.61 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.61 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.00/1.61 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.00/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 1.00/1.61 Y, T ), Z = Y }.
% 1.00/1.61 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.00/1.61 T, Y ), Z = Y }.
% 1.00/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.00/1.61 T, Y ), Z = Y }.
% 1.00/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.00/1.61 Y, Z ), T = Y }.
% 1.00/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.00/1.61 Y, Z ) }.
% 1.00/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.00/1.61 T, Y ), Z = Y }.
% 1.00/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.00/1.61 T, Y ) }.
% 1.00/1.61 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.00/1.61 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.00/1.61 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.00/1.61 c_Groups_Oone__class_Oone( X ) }.
% 1.00/1.61 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.00/1.61 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.00/1.61 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.00/1.61 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.00/1.61 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.00/1.61 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.00/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.00/1.61 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.00/1.61 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.00/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.00/1.61 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.00/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.00/1.61 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.00/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.00/1.61 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.00/1.61 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.00/1.61 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.61 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.00/1.61 ) }.
% 1.00/1.61 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.00/1.61 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.00/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.00/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.00/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.61 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex
% 1.00/1.61 , v_pa____ ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 1.00/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.00/1.61 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.00/1.61 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.00/1.61 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 1.00/1.61 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 1.00/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.00/1.61 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 1.00/1.61 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.00/1.61 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.00/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 1.00/1.61 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.00/1.61 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 1.00/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 1.00/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 1.00/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.00/1.61 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 1.00/1.61 tc_Complex_Ocomplex ), c_Polynomial_Omonom( tc_Complex_Ocomplex, v_a____
% 1.00/1.61 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 1.00/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semiring__1( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 1.00/1.61 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.61 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 1.00/1.61 ), Y ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.00/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.00/1.61 c_Fact_Ofact__class_Ofact( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, Y, X ) ) = c_Fact_Ofact__class_Ofact( tc_Nat_Onat, X ) }.
% 1.00/1.61 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Fact_Ofact__class_Ofact
% 1.00/1.61 ( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP
% 1.00/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.00/1.61 c_Fact_Ofact__class_Ofact( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 1.00/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 1.00/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.00/1.61 v_pa____ ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.00/1.61 X ) ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 1.00/1.61 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.00/1.61 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 1.00/1.61 , Y, T ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha1( X, Y ) }.
% 1.00/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.00/1.61 { ! alpha1( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.00/1.61 c_Nat_OSuc( X ) ) }.
% 1.00/1.61 { ! alpha1( X, Y ), Y = c_Nat_OSuc( skol3( Z, Y ) ) }.
% 1.00/1.61 { ! alpha1( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol3( X, Y
% 1.00/1.61 ), X ) }.
% 1.00/1.61 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.00/1.61 ), alpha1( X, Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol4( X ) ) }.
% 1.00/1.61 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol5( X, Y ) ) ) }.
% 1.00/1.61 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.00/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.00/1.61 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.00/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.00/1.61 ), X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.00/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.00/1.61 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.00/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.00/1.61 ), X ) ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.00/1.61 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 1.00/1.61 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.00/1.61 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.00/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.00/1.61 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.00/1.61 ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.00/1.61 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 1.00/1.61 ) }.
% 1.00/1.61 { ! c_Fact_Ofact__class_Ofact( tc_Nat_Onat, X ) =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ), c_Fact_Ofact__class_Ofact( tc_Nat_Onat, X ) ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 1.00/1.61 ( tc_Nat_Onat ), c_Fact_Ofact__class_Ofact( tc_Nat_Onat, X ) ) }.
% 1.00/1.61 { c_Fact_Ofact__class_Ofact( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ) ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.00/1.61 ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), c_Fact_Ofact__class_Ofact(
% 1.00/1.61 tc_Nat_Onat, X ) ) }.
% 1.00/1.61 { c_Fact_Ofact__class_Ofact( tc_Nat_Onat, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.00/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Fact_Ofact__class_Ofact
% 1.00/1.61 ( tc_Nat_Onat, X ), c_Fact_Ofact__class_Ofact( tc_Nat_Onat, Y ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Fact_Ofact__class_Ofact
% 1.00/1.61 ( tc_Nat_Onat, Y ), c_Fact_Ofact__class_Ofact( tc_Nat_Onat, X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.00/1.61 { ! X = c_Nat_OSuc( X ) }.
% 1.00/1.61 { ! c_Nat_OSuc( X ) = X }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 1.00/1.61 .
% 1.00/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.00/1.61 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 1.00/1.61 }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.00/1.61 ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.00/1.61 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.00/1.61 , c_Nat_OSuc( X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.00/1.61 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.00/1.61 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.00/1.61 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.00/1.61 X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.00/1.61 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 1.00/1.61 }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.00/1.61 c_Nat_OSuc( X ) ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 1.00/1.61 .
% 1.00/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 1.00/1.61 .
% 1.00/1.61 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.00/1.61 X, Y, Z ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 1.00/1.61 .
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 1.00/1.61 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.00/1.61 ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.00/1.61 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.00/1.61 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.00/1.61 { alpha23( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.00/1.61 ( X, Y ), Z ) ) }.
% 1.00/1.61 { ! alpha23( X, Y, Z ), alpha24( X, Y, Z ), Z = Y }.
% 1.00/1.61 { ! alpha23( X, Y, Z ), alpha24( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.00/1.61 ) ) }.
% 1.00/1.61 { ! alpha24( X, Y, Z ), alpha23( X, Y, Z ) }.
% 1.00/1.61 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha23( X, Y, Z ) }.
% 1.00/1.61 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.00/1.61 }.
% 1.00/1.61 { ! alpha24( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.00/1.61 X, Y ), Z ) ), alpha24( X, Y, Z ) }.
% 1.00/1.61 { c_Fact_Ofact__class_Ofact( tc_Nat_Onat, c_Nat_OSuc( X ) ) = hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( X ) ),
% 1.00/1.61 c_Fact_Ofact__class_Ofact( tc_Nat_Onat, X ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.00/1.61 { c_Fact_Ofact__class_Ofact( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.00/1.61 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 1.00/1.61 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.00/1.61 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.00/1.61 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.00/1.61 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.00/1.61 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.00/1.61 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.00/1.61 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.00/1.61 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.00/1.61 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.00/1.61 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.00/1.61 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.00/1.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.00/1.61 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.00/1.61 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.00/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.00/1.61 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.00/1.61 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.00/1.61 ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.00/1.61 ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.00/1.61 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.00/1.61 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.00/1.61 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.00/1.61 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.00/1.61 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 X ), Y ), Z = Y }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 1.00/1.61 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.00/1.61 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.00/1.61 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.00/1.61 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.00/1.61 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.00/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 1.00/1.61 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.00/1.61 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 1.00/1.61 ) ) = X }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.00/1.61 ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.00/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.00/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 1.00/1.61 ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.00/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.00/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 1.00/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 1.00/1.61 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.00/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, T, Y ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.00/1.61 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.00/1.61 , Y, Z ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.00/1.61 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, Z, Y ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.00/1.61 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.00/1.61 , T, Y ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.00/1.61 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 1.00/1.61 , Y, T ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.00/1.61 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.00/1.61 , T, Y ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 1.00/1.61 , T ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 1.00/1.61 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, Z, Y ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.00/1.61 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, Z, Y ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.00/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.00/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.00/1.61 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.00/1.61 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.00/1.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.00/1.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.00/1.61 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.00/1.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.00/1.61 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.00/1.61 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.00/1.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.00/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.00/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.00/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.00/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.00/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 1.00/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.00/1.61 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.00/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.00/1.61 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.00/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.00/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ), X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.00/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ), X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.00/1.61 .
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.00/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.00/1.61 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.61 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 1.00/1.61 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.61 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.00/1.61 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 1.00/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.00/1.61 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.00/1.61 ( tc_Nat_Onat, Z, Y ), X ) }.
% 1.00/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.00/1.61 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.00/1.61 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.00/1.61 ( tc_Nat_Onat, Y, X ), X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.00/1.61 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 1.00/1.61 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 1.00/1.61 .
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.00/1.61 .
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.00/1.61 .
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.00/1.61 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.00/1.61 , X ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol6( X, Y ) ) }.
% 1.00/1.61 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.00/1.61 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.00/1.61 ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.00/1.61 ( tc_Nat_Onat, Y, Z ), X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.00/1.61 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.00/1.61 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.00/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.00/1.61 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 1.00/1.61 ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.00/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.00/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.00/1.61 ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 1.00/1.61 c_Groups_Oone__class_Oone( X ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 1.00/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.00/1.61 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.00/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 1.00/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.00/1.61 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.00/1.61 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.00/1.61 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 1.00/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 1.00/1.61 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.00/1.61 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.00/1.61 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.00/1.61 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.00/1.61 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.00/1.61 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.00/1.61 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), X ), c_Fact_Ofact__class_Ofact( tc_Nat_Onat, X ) = hAPP
% 1.00/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.00/1.61 c_Fact_Ofact__class_Ofact( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.00/1.61 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.00/1.61 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.00/1.61 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.00/1.61 ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), U ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 1.00/1.61 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 1.00/1.61 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 1.00/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.00/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha2( X, Y, Z, T ),
% 1.00/1.61 alpha14( X, Y, Z, T ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z, T ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha14( X, Y, Z, T ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.00/1.61 { ! alpha14( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.61 { ! alpha14( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.00/1.61 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha14( X, Y, Z, T ) }.
% 1.00/1.61 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.00/1.61 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.00/1.61 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha2( X, Y, Z, T ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha3( X, Y, Z, T ),
% 1.00/1.61 alpha15( X, Y, Z, T ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z, T ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha15( X, Y, Z, T ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.00/1.61 { ! alpha15( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.61 { ! alpha15( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.00/1.61 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha15( X, Y, Z, T ) }.
% 1.00/1.61 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.00/1.61 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.00/1.61 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha3( X, Y, Z, T ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.00/1.61 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.00/1.61 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.00/1.61 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.00/1.61 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.00/1.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.00/1.61 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.00/1.61 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( X ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.00/1.61 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.00/1.61 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( X ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.00/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.00/1.61 .
% 1.00/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.00/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.00/1.61 .
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.00/1.61 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.00/1.61 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.00/1.61 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.00/1.61 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.00/1.61 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( X ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.00/1.61 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.00/1.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.00/1.61 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.00/1.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.00/1.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.00/1.61 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.00/1.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.00/1.61 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.00/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 1.00/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.00/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.00/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.00/1.61 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 1.00/1.61 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.00/1.61 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.00/1.61 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.00/1.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.00/1.61 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.00/1.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.00/1.61 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.00/1.61 .
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.00/1.61 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.00/1.61 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( X ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.00/1.61 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.00/1.61 , Z, Y ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.00/1.61 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha4( X, Y
% 1.00/1.61 , Z ), alpha16( X, Y, Z ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.00/1.61 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.61 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.00/1.61 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ), alpha16( X, Y, Z ) }.
% 1.00/1.61 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.00/1.61 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), alpha4( X, Y, Z ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( X ) ), alpha5( X, Y, Z ), alpha17( X, Y, Z ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( X ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha17( X, Y, Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( X ) ) }.
% 1.00/1.61 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.61 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.00/1.61 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( X ), Y ), alpha17( X, Y, Z ) }.
% 1.00/1.61 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.00/1.61 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ), alpha5( X, Y, Z ) }.
% 1.00/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( X ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.00/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__semiring( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.00/1.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__semiring( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.00/1.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__comm__semiring( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.00/1.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__semiring( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__semiring( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.61 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.00/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.61 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.00/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( X ) ) }.
% 1.00/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.00/1.61 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 ) }.
% 1.00/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.00/1.61 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.00/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 1.00/1.61 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 ) }.
% 1.00/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 1.00/1.61 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.00/1.61 ) }.
% 1.00/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.00/1.61 .
% 1.00/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.00/1.61 .
% 1.00/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.00/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.00/1.61 Y, Z ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.00/1.61 Z, Y ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 1.00/1.61 ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.00/1.61 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.61 c_Groups_Oone__class_Oone( X ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.00/1.61 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.00/1.61 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.00/1.61 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.00/1.61 ) }.
% 1.00/1.61 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.00/1.61 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.00/1.61 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.00/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.00/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.00/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.00/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.00/1.61 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.00/1.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.00/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha6( X, Y ), alpha18( X
% 1.00/1.61 , Y ) }.
% 1.00/1.61 { ! alpha6( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.00/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.00/1.61 { ! alpha18( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.00/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.00/1.61 { ! alpha18( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.61 { ! alpha18( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ) ) }.
% 1.00/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha18( X, Y ) }.
% 1.00/1.61 { ! alpha6( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ) ) }.
% 1.00/1.61 { ! alpha6( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha6( X, Y ) }.
% 1.00/1.61 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha7( X, Y ), alpha19
% 1.00/1.61 ( X, Y ) }.
% 1.00/1.61 { ! alpha7( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.00/1.61 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! alpha19( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.00/1.61 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! alpha19( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.61 { ! alpha19( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ) ) }.
% 1.00/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha19( X, Y ) }.
% 1.00/1.61 { ! alpha7( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ) ) }.
% 1.00/1.61 { ! alpha7( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha7( X, Y ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.00/1.61 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.00/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.00/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.00/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 1.00/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.00/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.00/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 1.00/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.00/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.00/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.00/1.61 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.00/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 1.00/1.61 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.00/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.00/1.61 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.00/1.61 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.00/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.00/1.61 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, Y, X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, Y, X ) ) }.
% 1.00/1.61 { c_Fact_Ofact__class_Ofact( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = hAPP( hAPP
% 1.00/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 1.00/1.61 tc_Nat_Onat ) ) ), c_Fact_Ofact__class_Ofact( tc_Nat_Onat, X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.00/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.00/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.00/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.00/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ), Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.00/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ), Z ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.00/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.00/1.61 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.00/1.61 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.61 Y ), X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.00/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.00/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.00/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.00/1.61 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.00/1.61 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.61 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.00/1.61 tc_Nat_Onat ), X ), Y ) }.
% 1.00/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.00/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.00/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.00/1.61 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.00/1.61 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.61 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, Z, X ), Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.00/1.61 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.00/1.61 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.00/1.61 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.00/1.61 tc_Nat_Onat, X, Y ), Y ) = X }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, Z, X ), Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, X, Z ), Y ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, Z, Y ), X ) }.
% 1.00/1.61 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.00/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.00/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.00/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.00/1.61 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 1.00/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.00/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.00/1.61 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.00/1.61 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.00/1.61 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.61 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.00/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.00/1.61 ), X ) ) }.
% 1.00/1.61 { ! class_Groups_Ozero( X ), !
% 1.00/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.61 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Polynomial_Opoly( X ) ),
% 1.00/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.00/1.61 c_Fact_Ofact__class_Ofact( tc_Nat_Onat, X ) = c_Groups_Oone__class_Oone(
% 1.00/1.61 tc_Nat_Onat ) }.
% 1.00/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Fact_Ofact__class_Ofact
% 1.00/1.61 ( tc_Nat_Onat, X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.00/1.61 tc_Nat_Onat ), X ), c_Fact_Ofact__class_Ofact( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Groups_Oone__class_Oone
% 1.00/1.61 ( tc_Nat_Onat ) ) ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.00/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.61 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.00/1.61 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.00/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.00/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.00/1.61 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.00/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.00/1.61 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.00/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.00/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.00/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 }.
% 1.00/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.00/1.61 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.00/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.00/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.00/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.00/1.61 ( X, Z, W ) ), U ), Y ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.00/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.00/1.61 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.00/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.00/1.61 X, W, Z ) ), U ), T ), Y ) }.
% 1.00/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.61 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.00/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.00/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.61 ( X ), Z ), U ), Y ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.00/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.00/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.00/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.00/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.00/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.00/1.61 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.00/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.00/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.00/1.61 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.00/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.61 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.61 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.61 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.00/1.61 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.00/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.61 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.61 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 1.00/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.00/1.61 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.00/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.00/1.61 , alpha8( X, Y, Z ) }.
% 1.00/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.00/1.61 , alpha20( X, Y, Z ) }.
% 1.00/1.61 { ! alpha8( X, Y, Z ), ! alpha20( X, Y, Z ), hBOOL( hAPP( Z,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.00/1.61 { ! alpha20( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.00/1.61 T ), hBOOL( hAPP( Z, T ) ) }.
% 1.00/1.61 { ! hBOOL( hAPP( Z, skol7( T, U, Z ) ) ), alpha20( X, Y, Z ) }.
% 1.00/1.61 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol7( X, Y, Z ) ),
% 1.00/1.61 alpha20( X, Y, Z ) }.
% 1.00/1.61 { ! alpha8( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.00/1.61 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.00/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha8( X, Y, Z ) }.
% 1.00/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha8
% 1.00/1.61 ( X, Y, Z ) }.
% 1.00/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.00/1.61 , ! alpha9( X, Y, Z ) }.
% 1.00/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.00/1.61 , ! alpha21( X, Y, Z ) }.
% 1.00/1.61 { alpha9( X, Y, Z ), alpha21( X, Y, Z ), hBOOL( hAPP( Z,
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.00/1.61 { ! alpha21( X, Y, Z ), ! hBOOL( hAPP( Z, skol8( T, U, Z ) ) ) }.
% 1.00/1.61 { ! alpha21( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.00/1.61 skol8( X, Y, Z ) ) }.
% 1.00/1.61 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 1.00/1.61 ) ), alpha21( X, Y, Z ) }.
% 1.00/1.61 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 1.00/1.61 .
% 1.00/1.61 { ! alpha9( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.00/1.61 tc_Nat_Onat ) ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 1.00/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha9( X, Y, Z ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.00/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.00/1.61 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.00/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 1.00/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.00/1.62 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 1.00/1.62 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.00/1.62 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.00/1.62 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.00/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Fact_Ofact__class_Ofact(
% 1.00/1.62 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.00/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Fact_Ofact__class_Ofact(
% 1.00/1.62 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP(
% 1.00/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.00/1.62 c_Fact_Ofact__class_Ofact( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.00/1.62 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ),
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.00/1.62 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.00/1.62 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.00/1.62 tc_Complex_Ocomplex, v_pa____ ) }.
% 1.00/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 1.00/1.62 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.62 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 1.00/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 1.00/1.62 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.00/1.62 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.00/1.62 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 1.00/1.62 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.00/1.62 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Nat_Onat ), Y ) }.
% 1.00/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.00/1.62 ), X ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.62 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.00/1.62 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.00/1.62 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.00/1.62 tc_Complex_Ocomplex, c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), c_Polynomial_Omonom(
% 1.00/1.62 tc_Complex_Ocomplex, v_a____, c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 1.00/1.62 , v_k____, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.00/1.62 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 1.00/1.62 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 1.00/1.62 c_Polynomial_Omonom( tc_Complex_Ocomplex, v_a____,
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ), skol9 ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.00/1.62 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.00/1.62 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.00/1.62 tc_Complex_Ocomplex, v_p ) ) }.
% 1.00/1.62 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.00/1.62 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.00/1.62 tc_Complex_Ocomplex, v_pa____ ) ) }.
% 1.00/1.62 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.00/1.62 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.00/1.62 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.00/1.62 tc_Complex_Ocomplex, v_q____ ) ) }.
% 1.00/1.62 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.00/1.62 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.00/1.62 tc_Complex_Ocomplex, v_q____ ) ) }.
% 1.00/1.62 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.00/1.62 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 1.00/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 1.00/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 1.00/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 1.00/1.62 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.00/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.00/1.62 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.00/1.62 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.00/1.62 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.00/1.62 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.00/1.62 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.00/1.62 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.00/1.62 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.00/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.00/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.00/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.00/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.00/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.00/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.00/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.00/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.00/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.00/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.00/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.00/1.62 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.00/1.62 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.00/1.62 ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.00/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.00/1.62 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.00/1.62 c_Groups_Oone__class_Oone( X ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.00/1.62 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.00/1.62 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.00/1.62 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.00/1.62 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.00/1.62 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.00/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 1.00/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.00/1.62 ) ) }.
% 1.00/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.00/1.62 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 1.00/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 1.00/1.62 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 1.00/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.00/1.62 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.00/1.62 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.62 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 1.00/1.62 X, T ) = hAPP( X, U ) }.
% 1.00/1.62 { ! hAPP( X, skol10( X ) ) = hAPP( X, skol27( X ) ),
% 1.00/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.00/1.62 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 1.00/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 1.00/1.62 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.00/1.62 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.00/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.00/1.62 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 1.00/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.00/1.62 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 1.00/1.62 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 1.00/1.62 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 1.00/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 1.00/1.62 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 1.00/1.62 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 1.00/1.62 c_Polynomial_Omonom( X, Y, Z ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 1.00/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.00/1.62 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 1.00/1.62 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 1.00/1.62 X, Z ), Y ) ) }.
% 1.00/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.62 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.00/1.62 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.00/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 1.00/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ) ) }.
% 1.00/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.00/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.00/1.62 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.00/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.62 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.62 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.00/1.62 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.00/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.00/1.62 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.00/1.62 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 1.00/1.62 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 1.00/1.62 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.00/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex, X
% 1.00/1.62 ), c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.00/1.62 tc_Complex_Ocomplex, v_pa____ ) ),
% 1.00/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 1.00/1.62 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex, X ) ),
% 1.00/1.62 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol11( X ) ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.00/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.00/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.00/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) }.
% 1.00/1.62 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.00/1.62 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.00/1.62 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.00/1.62 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.00/1.62 v_q____ ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, hAPP
% 1.00/1.62 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.00/1.62 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.00/1.62 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.00/1.62 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.00/1.62 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ), hAPP(
% 1.00/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), v_k____ ) ),
% 1.00/1.62 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 1.00/1.62 tc_Complex_Ocomplex, v_a____, v_s____ ) ), X ) ) ) }.
% 1.00/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.00/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.00/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.00/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.00/1.62 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.00/1.62 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.00/1.62 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.00/1.62 v_q____ ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.00/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.00/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.00/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.00/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.00/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.00/1.62 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.00/1.62 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.00/1.62 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.00/1.62 v_q____ ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.00/1.62 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) = hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.00/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.00/1.62 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.00/1.62 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.00/1.62 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.00/1.62 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), hAPP
% 1.00/1.62 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 1.00/1.62 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 1.00/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.00/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.00/1.62 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.00/1.62 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.00/1.62 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.00/1.62 v_q____ ) ), X ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.00/1.62 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 1.00/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.00/1.62 tc_Complex_Ocomplex, v_s____ ), v_k____ ), c_Groups_Oone__class_Oone(
% 1.00/1.62 tc_Nat_Onat ) ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.00/1.62 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.00/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 1.00/1.62 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.00/1.62 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.00/1.62 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.00/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 1.00/1.62 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.00/1.62 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.00/1.62 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.00/1.62 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.00/1.62 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.00/1.62 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.00/1.62 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.00/1.62 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.00/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) ) }.
% 1.00/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.00/1.62 ( tc_Int_Oint ) }.
% 1.00/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Int_Oint ), X ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.00/1.62 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.00/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 1.00/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.00/1.62 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.00/1.62 .
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.00/1.62 tc_Int_Oint ) ), X ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.00/1.62 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.00/1.62 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 1.00/1.62 }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.00/1.62 tc_Int_Oint ) ), X ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.00/1.62 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.00/1.62 .
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.00/1.62 ( tc_Int_Oint ) ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.00/1.62 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 1.00/1.62 }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.00/1.62 tc_Int_Oint ) ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 1.00/1.62 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.00/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.00/1.62 ( tc_Int_Oint ) ) = X }.
% 1.00/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Int_Oint ), X ) = X }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.00/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_RealDef_Oreal ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.00/1.62 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 1.00/1.62 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 1.00/1.62 .
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 1.00/1.62 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.00/1.62 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.00/1.62 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 1.00/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 1.00/1.62 ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__div__algebra( X ), Y =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ) =
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.00/1.62 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.00/1.62 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 1.00/1.62 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.00/1.62 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.00/1.62 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.00/1.62 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.00/1.62 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.00/1.62 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 1.00/1.62 = Y }.
% 1.00/1.62 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.00/1.62 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.00/1.62 ( X ) }.
% 1.00/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.00/1.62 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 1.00/1.62 X, Y ) ) = Y }.
% 1.00/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.00/1.62 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.62 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.00/1.62 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.62 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.00/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.62 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.62 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.00/1.62 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 1.00/1.62 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 1.00/1.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 1.00/1.62 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.00/1.62 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 1.00/1.62 ) ), Y ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.00/1.62 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.00/1.62 ( X, Y ) ) ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.00/1.62 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 1.00/1.62 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.00/1.62 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 1.00/1.62 ( X, Y, Z ) ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.00/1.62 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.00/1.62 ( X, Y ) ) ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.00/1.62 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.00/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 1.00/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 1.00/1.62 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 1.00/1.62 , Y ) ) = Y }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 1.00/1.62 class_Rings_Odivision__ring__inverse__zero( X ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 1.00/1.62 Y ) ) = c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.00/1.62 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.00/1.62 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 1.00/1.62 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.00/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.00/1.62 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.00/1.62 = X }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.00/1.62 tc_Int_Oint ) ) ) }.
% 1.00/1.62 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.00/1.62 tc_Int_Oint ) ) ) }.
% 1.00/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.00/1.62 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.00/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.00/1.62 .
% 1.00/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.00/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.00/1.62 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 1.00/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 1.00/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.00/1.62 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 1.00/1.62 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 1.00/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.00/1.62 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.00/1.62 ) ), Z ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.00/1.62 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.00/1.62 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 1.00/1.62 ( X, T, Y ) ) ) ) }.
% 1.00/1.62 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.62 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.62 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.62 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.00/1.62 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.00/1.62 , Y ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.00/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 1.00/1.62 Y ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.00/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 1.00/1.62 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.00/1.62 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.00/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.00/1.62 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.00/1.62 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.00/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.00/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 1.00/1.62 ) }.
% 1.00/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.00/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.00/1.62 c_Groups_Oone__class_Oone( X ) }.
% 1.00/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.00/1.62 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 1.00/1.62 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.00/1.62 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.00/1.62 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.00/1.62 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 1.00/1.62 .
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.00/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 1.00/1.62 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 1.00/1.62 .
% 1.00/1.62 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex
% 1.00/1.62 , v_pa____ ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), c_Orderings_Oord__class_Oless
% 1.00/1.62 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 1.00/1.62 , hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.00/1.62 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.00/1.62 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.00/1.62 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.00/1.62 v_q____ ) ), skol12 ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.00/1.62 }.
% 1.00/1.62 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.00/1.62 skol13 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.00/1.62 tc_Complex_Ocomplex, v_pa____ ) }.
% 1.00/1.62 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol13 ), X ) = hAPP(
% 1.00/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 1.00/1.62 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.00/1.62 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.00/1.62 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.00/1.62 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.00/1.62 v_q____ ) ), skol14 ) = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.00/1.62 c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.00/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ),
% 1.00/1.62 skol28 ) }.
% 1.00/1.62 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 1.00/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), skol15 ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 1.00/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 1.00/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), T ), hAPP(
% 1.00/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ), Z ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.00/1.62 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.00/1.62 { c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.00/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 1.00/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.00/1.62 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.00/1.62 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.00/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.00/1.62 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), X ) =
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.00/1.62 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 1.00/1.62 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 1.00/1.62 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.00/1.62 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 1.00/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 1.00/1.62 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 1.00/1.62 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 1.00/1.62 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.00/1.62 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 1.00/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 1.00/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 1.00/1.62 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 1.00/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 1.00/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.00/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 1.00/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 1.00/1.62 }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 1.00/1.62 Y ) ), c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Z ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.00/1.62 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.00/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.00/1.62 ( tc_Int_Oint ), Y ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.00/1.62 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.00/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.00/1.62 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.00/1.62 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.00/1.62 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 1.00/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.00/1.62 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.00/1.62 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 1.00/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.00/1.62 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.00/1.62 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.00/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.00/1.62 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.00/1.62 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.00/1.62 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.00/1.62 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.62 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 1.00/1.62 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.00/1.62 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.00/1.62 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.62 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.00/1.62 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.00/1.62 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 1.00/1.62 , Y = c_Groups_Oone__class_Oone( X ) }.
% 1.00/1.62 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 1.00/1.62 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 1.00/1.62 = c_Groups_Oone__class_Oone( X ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol16( X, Y ) ) }.
% 1.00/1.62 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.62 ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.00/1.62 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.00/1.62 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.62 ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.62 ), c_Orderings_Oord__class_Oless__eq( X,
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.00/1.62 ) ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.00/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.00/1.62 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.00/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.00/1.62 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.00/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.00/1.62 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 1.00/1.62 , Y ) ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.00/1.62 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 1.00/1.62 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.00/1.62 .
% 1.00/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.00/1.62 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.00/1.62 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 1.00/1.62 ( X ) ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.00/1.62 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.00/1.62 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.00/1.62 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 1.00/1.62 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.00/1.62 .
% 1.00/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.00/1.62 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.00/1.62 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.00/1.62 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.00/1.62 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.00/1.62 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.00/1.62 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.00/1.62 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 1.00/1.62 , Y ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.62 ), c_Orderings_Oord__class_Oless__eq( X,
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 1.00/1.62 ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.00/1.62 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 1.00/1.62 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.00/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.00/1.62 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.00/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.00/1.62 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 1.00/1.62 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.00/1.62 ) ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.00/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.00/1.62 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.00/1.62 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.00/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.00/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.00/1.62 c_Groups_Oone__class_Oone( X ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.00/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.00/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.00/1.62 }.
% 1.00/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.00/1.62 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 1.00/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 1.00/1.62 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.00/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 1.00/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 1.00/1.62 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 1.00/1.62 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol17( X, Y ) ), Y
% 1.00/1.62 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 1.00/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Int_Oint ) ) }.
% 1.00/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.00/1.62 tc_Int_Oint ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Int_Oint, X, Y ) ) }.
% 1.00/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.00/1.62 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.00/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.00/1.62 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.00/1.62 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 1.00/1.62 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.62 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.62 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 1.00/1.62 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.00/1.62 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 1.00/1.62 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.00/1.62 { ! skol18 = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.00/1.62 { ! skol29 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.00/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.00/1.62 tc_Complex_Ocomplex, skol31 ), skol29 ), c_Groups_Oone__class_Oone(
% 1.00/1.62 tc_Nat_Onat ) ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.00/1.62 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.00/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 1.00/1.62 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.00/1.62 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.00/1.62 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.00/1.62 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.00/1.62 v_q____ ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, hAPP
% 1.00/1.62 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.00/1.62 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.00/1.62 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.00/1.62 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.00/1.62 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ), hAPP(
% 1.00/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), skol29 ) ),
% 1.00/1.62 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 1.00/1.62 tc_Complex_Ocomplex, skol18, skol31 ) ), X ) ) ) }.
% 1.00/1.62 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 1.00/1.62 , Y ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 1.00/1.62 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 1.00/1.62 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 1.00/1.62 , Y ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.00/1.62 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.00/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.00/1.62 hAPP( Y, U ) ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.00/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.00/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.00/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.00/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.00/1.62 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.00/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 1.00/1.62 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.00/1.62 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.00/1.62 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.00/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.00/1.62 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.00/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.00/1.62 hAPP( Y, U ) ) }.
% 1.00/1.62 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.00/1.62 ( X, Z, Y ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.00/1.62 ( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.00/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.00/1.62 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.00/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.00/1.62 hAPP( Y, U ) ) }.
% 1.00/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 1.00/1.62 ( Z, skol19( X, Y, Z ) ), hAPP( Y, skol19( X, Y, Z ) ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.00/1.62 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.00/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.00/1.62 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.00/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.00/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.00/1.62 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.00/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.00/1.62 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.00/1.62 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.00/1.62 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.00/1.62 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.00/1.62 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.00/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.00/1.62 , ! Y = Z }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.00/1.62 , ! Z = Y }.
% 1.00/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.00/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.00/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.00/1.62 , ! Z = Y }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.00/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.00/1.62 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.00/1.62 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.00/1.62 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.00/1.62 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.00/1.62 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.00/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.00/1.62 Y ), ! Z = Y }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.00/1.62 Z ), ! Z = Y }.
% 1.00/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.00/1.62 Y ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.00/1.62 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 1.00/1.62 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 1.00/1.62 ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.00/1.62 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.00/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.00/1.62 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.00/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.00/1.62 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.00/1.62 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.00/1.62 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.00/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.62 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.00/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.00/1.62 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.00/1.62 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.00/1.62 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.00/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.00/1.62 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.00/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.00/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.00/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.00/1.62 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.00/1.62 ( X, Z, Y ) }.
% 1.00/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.00/1.62 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.00/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.00/1.62 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.62 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.00/1.62 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.00/1.62 , ! Z = Y }.
% 1.00/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.00/1.62 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.00/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.00/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.00/1.62 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.00/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.00/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.00/1.62 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.00/1.62 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 1.00/1.62 }.
% 1.00/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.00/1.62 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 1.00/1.62 ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.00/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 1.00/1.62 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.00/1.62 ), c_Orderings_Oord__class_Oless__eq( X, T, skol20( X, U, W, T ) ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.00/1.62 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 1.00/1.62 ) ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.00/1.62 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 1.00/1.62 hAPP( Z, T ), hAPP( Z, skol20( X, Y, Z, T ) ) ) ),
% 1.00/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.00/1.62 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 1.00/1.62 ) ) }.
% 1.00/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.00/1.62 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 1.00/1.62 .
% 1.00/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.00/1.62 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 1.00/1.62 }.
% 1.00/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.00/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 1.00/1.62 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 1.00/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 1.00/1.62 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) =
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) ) }.
% 1.00/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.00/1.62 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.00/1.62 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 1.00/1.62 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.00/1.62 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 1.00/1.62 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.00/1.62 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.00/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.00/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 1.00/1.62 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 1.00/1.62 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 1.00/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 1.00/1.62 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 1.00/1.62 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 1.00/1.62 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.00/1.62 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.62 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.00/1.62 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.00/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 1.00/1.62 c_Groups_Oone__class_Oone( X ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 1.00/1.62 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 1.00/1.62 ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.00/1.62 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 1.00/1.62 X, Y ) ) }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.00/1.62 X, Z, Y ) }.
% 1.00/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 1.00/1.62 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 1.00/1.62 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 1.00/1.62 , Y ) ) }.
% 1.00/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.00/1.62 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 1.00/1.62 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.00/1.62 ) }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.00/1.62 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 1.00/1.62 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.00/1.62 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.00/1.62 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.00/1.62 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.00/1.62 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.00/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.00/1.62 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.00/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.00/1.62 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.00/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.00/1.62 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.00/1.62 X, Y ) }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.00/1.62 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 1.00/1.62 ( X, Z ) }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.00/1.62 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.00/1.62 X ) }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.00/1.62 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.00/1.62 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 1.00/1.62 ( X, Y ) }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.00/1.62 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.00/1.62 Z ) = Y }.
% 1.00/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.00/1.62 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.62 , Y ) }.
% 1.00/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.00/1.62 , Y ) }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.00/1.62 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.00/1.62 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.00/1.62 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.00/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.00/1.62 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.00/1.62 .
% 1.00/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.00/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.00/1.62 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.00/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.00/1.62 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.00/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.00/1.62 ( X, Y ), Y ) }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.00/1.62 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.62 ) }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.00/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.00/1.62 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.00/1.62 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.62 ) }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.00/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.00/1.62 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.00/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.00/1.62 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.00/1.62 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.00/1.62 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.00/1.62 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.00/1.62 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.00/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.00/1.62 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.00/1.62 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.00/1.62 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.00/1.62 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.00/1.62 ( X, Y ) ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.00/1.62 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.00/1.62 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.00/1.62 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.00/1.62 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.00/1.62 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.00/1.62 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.00/1.62 ) ), Y ) }.
% 1.00/1.62 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.00/1.62 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.00/1.62 ( X, Y ) ) }.
% 1.00/1.62 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.00/1.62 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.00/1.62 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 1.00/1.62 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.00/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.00/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.00/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 1.00/1.62 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 1.00/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.00/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 1.00/1.62 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 1.00/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.00/1.62 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.00/1.62 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 1.00/1.62 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.00/1.62 Y ) ) = Y }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 1.00/1.62 Z, Y ) ) = Y }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 1.00/1.62 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 1.00/1.62 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.00/1.62 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.00/1.62 ( X, Y ), Z ) }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.00/1.62 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.00/1.62 ( X, Z ), Y ) }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.00/1.62 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 1.00/1.62 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 1.00/1.62 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.00/1.62 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.00/1.62 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.00/1.62 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.00/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.00/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.00/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.00/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.00/1.62 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 1.00/1.62 = Y }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 1.00/1.62 ) }.
% 1.00/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 1.00/1.62 ( X ) }.
% 1.00/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 1.00/1.62 , Y ) }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.00/1.62 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.00/1.62 ) }.
% 1.00/1.62 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.00/1.62 ) }.
% 1.00/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.00/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.00/1.62 = Y }.
% 1.00/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.00/1.62 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.00/1.62 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.00/1.62 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.00/1.62 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.00/1.62 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.00/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 1.00/1.62 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 1.00/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.00/1.62 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.00/1.62 tc_Polynomial_Opoly( X ), Y ) }.
% 1.00/1.62 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.00/1.62 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.00/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.00/1.62 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.00/1.62 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.00/1.62 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.00/1.62 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 1.00/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 1.00/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.00/1.62 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.00/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.00/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 1.00/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.00/1.63 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.00/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 1.00/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 1.00/1.63 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.00/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 1.00/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.00/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 1.00/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 1.00/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.00/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.00/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.00/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 1.00/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.00/1.63 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 1.00/1.63 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.00/1.63 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.00/1.63 Y ) ), c_Groups_Ominus__class_Ominus( X, Y, Z ) ) ),
% 1.00/1.63 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 1.00/1.63 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.00/1.63 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 1.00/1.63 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.00/1.63 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.00/1.63 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.00/1.63 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.00/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.00/1.63 Y ) ) ), Y ) }.
% 1.00/1.63 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.00/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.00/1.63 Y ) ) ), Y ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.00/1.63 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 1.00/1.63 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 1.00/1.63 , Z, Y ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.00/1.63 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 1.00/1.63 ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.00/1.63 , Y ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.00/1.63 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.00/1.63 ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), !
% 1.00/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.00/1.63 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 1.00/1.63 .
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.00/1.63 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.00/1.63 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 1.00/1.63 .
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.00/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 1.00/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.00/1.63 ), T ), U ), Y ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 1.00/1.63 ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.00/1.63 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 1.00/1.63 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 1.00/1.63 c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.00/1.63 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.00/1.63 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.00/1.63 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.00/1.63 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.00/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.00/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.00/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.00/1.63 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.00/1.63 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.00/1.63 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 1.00/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.00/1.63 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.00/1.63 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.00/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.00/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.00/1.63 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 1.00/1.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.00/1.63 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.00/1.63 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.00/1.63 }.
% 1.00/1.63 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.00/1.63 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.00/1.63 }.
% 1.00/1.63 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 1.00/1.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 1.00/1.63 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.00/1.63 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.00/1.63 }.
% 1.00/1.63 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.00/1.63 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.00/1.63 }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 1.00/1.63 ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.00/1.63 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 1.00/1.63 Z, T ) }.
% 1.00/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 1.00/1.63 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.00/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 1.00/1.63 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 1.00/1.63 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 1.00/1.63 X, T, Z ), Y ) }.
% 1.00/1.63 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 1.00/1.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Polynomial_Opoly( X ), T, Y ) }.
% 1.00/1.63 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha10( X
% 1.00/1.63 , Y, T ) }.
% 1.00/1.63 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha22( X
% 1.00/1.63 , Y, Z, T ) }.
% 1.00/1.63 { ! class_Fields_Ofield( X ), ! alpha10( X, Y, T ), ! alpha22( X, Y, Z, T )
% 1.00/1.63 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 1.00/1.63 ( X, T, Z ), Y ) }.
% 1.00/1.63 { ! alpha22( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.00/1.63 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha22( X, Y, Z, T ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha22( X
% 1.00/1.63 , Y, Z, T ) }.
% 1.00/1.63 { ! alpha10( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { Z = c_Groups_Ozero__class_Ozero( X ), alpha10( X, Y, Z ) }.
% 1.00/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha10( X
% 1.00/1.63 , Y, Z ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 1.00/1.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 1.00/1.63 ( X ), Y ), Z ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 1.00/1.63 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 1.00/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.00/1.63 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.00/1.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 1.00/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 1.00/1.63 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.00/1.63 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.00/1.63 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 1.00/1.63 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.00/1.63 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.00/1.63 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.00/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.00/1.63 X ) }.
% 1.00/1.63 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.00/1.63 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 1.00/1.63 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.00/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 1.00/1.63 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.00/1.63 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 1.00/1.63 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.00/1.63 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.00/1.63 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.00/1.63 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.00/1.63 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.00/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.00/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.00/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.00/1.63 }.
% 1.00/1.63 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.00/1.63 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.00/1.63 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.00/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.00/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.00/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.00/1.63 }.
% 1.00/1.63 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 1.00/1.63 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 1.00/1.63 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 1.00/1.63 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 1.00/1.63 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.00/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Int_Oint, Y, X ), X = Y }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.00/1.63 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 1.00/1.63 .
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Fact_Ofact__class_Ofact(
% 1.00/1.63 tc_Nat_Onat, Y ), c_Fact_Ofact__class_Ofact( tc_Nat_Onat, X ) ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 1.00/1.63 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.00/1.63 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 1.00/1.63 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.00/1.63 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.00/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.00/1.63 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.00/1.63 , Z ), X ) ), T ) ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.00/1.63 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.00/1.63 tc_Int_Oint, U, T ) ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.00/1.63 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.00/1.63 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.00/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 1.00/1.63 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 1.00/1.63 ) ) }.
% 1.00/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 1.00/1.63 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 1.00/1.63 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.00/1.63 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 1.00/1.63 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 1.00/1.63 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Int_Oint, Y, X ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.00/1.63 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 1.00/1.63 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Nat_Onat, Y, X ) }.
% 1.00/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.00/1.63 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.00/1.63 X ) ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.00/1.63 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 1.00/1.63 ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.63 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.00/1.63 ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.63 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.00/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.63 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.63 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.00/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ), !
% 1.00/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Fact_Ofact__class_Ofact(
% 1.00/1.63 tc_Nat_Onat, Y ) ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.63 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.00/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 1.00/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.63 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.63 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.00/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 1.00/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.63 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.00/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.00/1.63 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.00/1.63 ) }.
% 1.00/1.63 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.00/1.63 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.00/1.63 hAPP( Z, skol21( U, W, Z ) ) ) }.
% 1.00/1.63 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.00/1.63 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol21( X
% 1.00/1.63 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.00/1.63 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 1.00/1.63 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol30( X,
% 1.00/1.63 Y, Z ) ) ) ) }.
% 1.00/1.63 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 1.00/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.00/1.63 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X,
% 1.00/1.63 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 1.00/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.00/1.63 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 1.00/1.63 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 1.00/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.00/1.63 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X, c_Complex_Oii ) ),
% 1.00/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.00/1.63 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 1.00/1.63 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.00/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.00/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.00/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 1.00/1.63 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 1.00/1.63 ) }.
% 1.00/1.63 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 1.00/1.63 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.00/1.63 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha11( X, Y ), Y = X }
% 1.00/1.63 .
% 1.00/1.63 { ! alpha11( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.00/1.63 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.00/1.63 { ! alpha11( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.00/1.63 { ! alpha11( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, X, Y ), alpha11( X, Y ) }.
% 1.00/1.63 { ! alpha12( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.00/1.63 { ! alpha12( X, Y ), ! Y = X }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha12( X, Y ) }
% 1.00/1.63 .
% 1.00/1.63 { ! alpha12( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.00/1.63 { ! alpha12( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, X, Y ), alpha12( X, Y ) }.
% 1.00/1.63 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.00/1.63 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.00/1.63 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, Y, X ), Y = X }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.00/1.63 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Nat_Onat, Y, Z ) }.
% 1.00/1.63 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Nat_Onat, Y, Z ) }.
% 1.00/1.63 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, Z, Y ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 1.00/1.63 , Z ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 1.00/1.63 Z, Y ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Nat_Onat, Y, Z ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, Z, Y ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.00/1.63 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.00/1.63 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 1.00/1.63 tc_Nat_Onat ) ) }.
% 1.00/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.00/1.63 c_Complex_Oii ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.00/1.63 tc_Complex_Ocomplex ), c_Complex_Oii ), X ) ) =
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) }.
% 1.00/1.63 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.00/1.63 tc_Nat_Onat ), X ) }.
% 1.00/1.63 { c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, c_Complex_Oii ) =
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, c_Complex_Oii ) }.
% 1.00/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.00/1.63 c_Complex_Oii ), c_Complex_Oii ) = c_Groups_Ouminus__class_Ouminus(
% 1.00/1.63 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }
% 1.00/1.63 .
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.63 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.00/1.63 tc_Nat_Onat ), Y ) }.
% 1.00/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.00/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.00/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.00/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.00/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 1.00/1.63 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 1.00/1.63 ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.00/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.00/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Int_Oint, Z, X ) }.
% 1.00/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.00/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.00/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.00/1.63 tc_Nat_Onat, Z, X ) }.
% 1.00/1.63 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.00/1.63 skol22 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.00/1.63 tc_Complex_Ocomplex, v_pa____ ) }.
% 1.00/1.63 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol22 ), X ) = hAPP(
% 1.00/1.63 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 1.00/1.63 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 1.00/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol23( Z, T ) ) }.
% 1.00/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.00/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.00/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol23( X, Y ) ) ) }.
% 1.00/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol24( Y ) ) }.
% 1.00/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.00/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.00/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.00/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol24( X ) ) ) }.
% 1.00/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol25( Z, T ) ) }.
% 1.00/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.00/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.00/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.00/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol25( X, Y ) ) ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.00/1.63 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.00/1.63 tc_Int_Oint, X, Y ) }.
% 1.00/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.00/1.63 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 1.00/1.63 ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.00/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.00/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.00/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 1.00/1.63 ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.00/1.63 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.00/1.63 tc_Int_Oint, X, Y ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.00/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.00/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.00/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.00/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.00/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.00/1.63 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.00/1.63 alpha13( X, Y, Z ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.00/1.63 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), ! alpha13( X, Y, Z ),
% 1.00/1.63 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.00/1.63 { ! alpha13( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.00/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 1.00/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.00/1.63 alpha13( X, Y, Z ) }.
% 1.00/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.00/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 1.00/1.63 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.00/1.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.00/1.63 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 1.00/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.00/1.63 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.00/1.63 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.00/1.63 .
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.00/1.63 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 1.00/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 1.00/1.63 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.00/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.00/1.63 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 1.00/1.63 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 1.00/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.00/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.00/1.63 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 1.00/1.63 tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol26( T, U, W ) ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.00/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.00/1.63 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, T, Z ) ) ), !
% 1.00/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.00/1.63 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, T, Z ) ), skol26( X,
% 1.00/1.63 Y, Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.00/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.00/1.63 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, hAPP(
% 1.00/1.63 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), T ), hAPP(
% 1.00/1.63 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), Z ) ) ), X ) }.
% 1.00/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.00/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.00/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.00/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 1.00/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 1.00/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.00/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.00/1.63 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.00/1.63 c_Divides_Odiv__class_Odiv( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z
% 1.00/1.63 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 1.00/1.63 , Z ) ) }.
% 1.00/1.63 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.00/1.63 c_Divides_Odiv__class_Odiv( X, Y, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.00/1.63 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 1.00/1.63 , Z ) ) }.
% 1.00/1.63 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.00/1.63 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.00/1.63 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.00/1.63 ) ) }.
% 1.00/1.63 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.00/1.63 .
% 1.00/1.63 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.00/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.00/1.63 tc_Int_Oint ) }.
% 1.00/1.63 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.00/1.63 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.00/1.63 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.00/1.63 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.00/1.63 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.00/1.63 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.00/1.63 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.00/1.63 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.00/1.63 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.00/1.63 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.00/1.63 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.00/1.63 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.00/1.63 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.00/1.63 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.00/1.63 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.00/1.63 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.00/1.63 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.00/1.63 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.00/1.63 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.00/1.63 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.00/1.63 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.00/1.63 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.00/1.63 { class_Power_Opower( tc_Int_Oint ) }.
% 1.00/1.63 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.00/1.63 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.00/1.63 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.00/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.00/1.63 tc_Nat_Onat ) }.
% 1.00/1.63 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.00/1.63 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.00/1.63 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.00/1.63 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.00/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.00/1.63 tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 1.00/1.63 .
% 1.00/1.63 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Rings_Odvd( tc_RealDef_Oreal ) }.
% 1.00/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.00/1.63 tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 1.00/1.63 { ! class_Rings_Oidom( X ),
% 1.00/1.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.00/1.63 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.00/1.63 ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.00/1.63 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.00/1.63 X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.00/1.63 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.00/1.63 ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.00/1.63 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.00/1.63 }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.00/1.63 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.00/1.63 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.00/1.63 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.00/1.63 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.00/1.63 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.00/1.63 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.00/1.63 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.00/1.63 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.00/1.63 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.00/1.63 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.00/1.63 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.00/1.63 ( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.00/1.63 ( tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 1.00/1.63 ( X ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.00/1.63 }.
% 1.00/1.63 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.00/1.63 ) ) }.
% 1.00/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.00/1.63 .
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.00/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.00/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.00/1.63 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.00/1.63 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.00/1.63 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), v_k____ ) ),
% 1.00/1.63 v_a____ ) ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 1.00/1.63 v_thesis____ }.
% 1.00/1.63 { ! v_thesis____ }.
% 1.00/1.63
% 1.00/1.63 *** allocated 15000 integers for clauses
% 1.00/1.63 *** allocated 22500 integers for clauses
% 1.00/1.63 *** allocated 33750 integers for clauses
% 1.00/1.63 *** allocated 50625 integers for clauses
% 1.00/1.63 *** allocated 75937 integers for clauses
% 1.00/1.63 percentage equality = 0.261217, percentage horn = 0.917283
% 1.00/1.63 This is a problem with some equality
% 1.00/1.63
% 1.00/1.63
% 1.00/1.63
% 1.00/1.63 Options Used:
% 1.00/1.63
% 1.00/1.63 useres = 1
% 1.00/1.63 useparamod = 1
% 1.00/1.63 useeqrefl = 1
% 1.00/1.63 useeqfact = 1
% 1.00/1.63 usefactor = 1
% 1.00/1.63 usesimpsplitting = 0
% 1.00/1.63 usesimpdemod = 5
% 1.00/1.63 usesimpres = 3
% 1.00/1.63
% 1.00/1.63 resimpinuse = 1000
% 1.00/1.63 resimpclauses = 20000
% 1.00/1.63 substype = eqrewr
% 1.00/1.63 backwardsubs = 1
% 1.00/1.63 selectoldest = 5
% 1.00/1.63
% 1.00/1.63 litorderings [0] = split
% 1.00/1.63 litorderings [1] = extend the termordering, first sorting on arguments
% 1.00/1.63
% 1.00/1.63 termordering = kbo
% 1.00/1.63
% 1.00/1.63 litapriori = 0
% 1.00/1.63 termapriori = 1
% 1.00/1.63 litaposteriori = 0
% 1.00/1.63 termaposteriori = 0
% 1.00/1.63 demodaposteriori = 0
% 1.00/1.63 ordereqreflfact = 0
% 1.00/1.63
% 1.00/1.63 litselect = negord
% 1.00/1.63
% 1.00/1.63 maxweight = 15
% 1.00/1.63 maxdepth = 30000
% 1.00/1.63 maxlength = 115
% 1.00/1.63 maxnrvars = 195
% 1.00/1.63 excuselevel = 1
% 1.00/1.63 increasemaxweight = 1
% 1.00/1.63
% 1.00/1.63 maxselected = 10000000
% 1.00/1.63 maxnrclauses = 10000000
% 1.00/1.63
% 1.00/1.63 showgenerated = 0
% 1.00/1.63 showkept = 0
% 1.00/1.63 showselected = 0
% 1.00/1.63 showdeleted = 0
% 1.00/1.63 showresimp = 1
% 1.00/1.63 showstatus = 2000
% 1.00/1.63
% 1.00/1.63 prologoutput = 0
% 1.00/1.63 nrgoals = 5000000
% 1.00/1.63 totalproof = 1
% 1.00/1.63
% 1.00/1.63 Symbols occurring in the translation:
% 1.00/1.63
% 1.00/1.63 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.00/1.63 . [1, 2] (w:1, o:201, a:1, s:1, b:0),
% 1.00/1.63 ! [4, 1] (w:0, o:118, a:1, s:1, b:0),
% 1.00/1.63 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.00/1.63 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.00/1.63 hAPP [38, 2] (w:1, o:225, a:1, s:1, b:0),
% 1.00/1.63 v_a____ [39, 0] (w:1, o:12, a:1, s:1, b:0),
% 1.00/1.63 tc_Complex_Ocomplex [40, 0] (w:1, o:24, a:1, s:1, b:0),
% 1.00/1.63 c_Groups_Ozero__class_Ozero [41, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.00/1.63 v_k____ [42, 0] (w:1, o:25, a:1, s:1, b:0),
% 1.00/1.63 tc_Nat_Onat [43, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.00/1.63 class_Power_Opower [46, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.00/1.63 class_Rings_Osemiring__0 [47, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.00/1.63 c_Power_Opower__class_Opower [48, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.00/1.63 c_Groups_Oone__class_Oone [49, 1] (w:1, o:135, a:1, s:1, b:0),
% 1.00/1.63 class_Rings_Ocomm__semiring__1 [51, 1] (w:1, o:139, a:1, s:1, b:0),
% 1.00/1.63 c_Groups_Oplus__class_Oplus [52, 3] (w:1, o:251, a:1, s:1, b:0),
% 1.00/1.63 c_Groups_Otimes__class_Otimes [53, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.00/1.63 class_Rings_Olinordered__ring__strict [57, 1] (w:1, o:141, a:1, s:1
% 1.00/1.63 , b:0),
% 1.00/1.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [62
% 1.00/1.63 , 1] (w:1, o:167, a:1, s:1, b:0),
% 1.00/1.63 c_Groups_Ominus__class_Ominus [64, 3] (w:1, o:252, a:1, s:1, b:0),
% 1.00/1.63 class_Groups_Omonoid__mult [65, 1] (w:1, o:173, a:1, s:1, b:0),
% 1.00/1.63 class_Groups_Ocomm__monoid__mult [66, 1] (w:1, o:174, a:1, s:1, b:0)
% 1.00/1.63 ,
% 1.00/1.63 class_Rings_Omult__zero [72, 1] (w:1, o:150, a:1, s:1, b:0),
% 1.00/1.63 class_Rings_Ono__zero__divisors [73, 1] (w:1, o:151, a:1, s:1, b:0),
% 1.00/1.63
% 1.00/1.63 class_Rings_Ozero__neq__one [74, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.00/1.63 class_Rings_Oring__1__no__zero__divisors [86, 1] (w:1, o:129, a:1, s:
% 1.00/1.63 1, b:0),
% 1.00/1.63 class_Rings_Oring__1 [87, 1] (w:1, o:130, a:1, s:1, b:0),
% 1.00/1.63 class_Rings_Oring [89, 1] (w:1, o:131, a:1, s:1, b:0),
% 1.00/1.63 class_RealVector_Oreal__normed__algebra [90, 1] (w:1, o:153, a:1, s:1
% 1.00/1.63 , b:0),
% 1.00/1.63 c_Power_Opower_Opower [91, 3] (w:1, o:255, a:1, s:1, b:0),
% 1.00/1.63 class_Rings_Oring__no__zero__divisors [99, 1] (w:1, o:132, a:1, s:1
% 1.00/1.63 , b:0),
% 1.00/1.63 class_Rings_Ocomm__semiring [102, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.00/1.63 class_Rings_Osemiring [106, 1] (w:1, o:155, a:1, s:1, b:0),
% 1.00/1.63 class_Groups_Ogroup__add [108, 1] (w:1, o:175, a:1, s:1, b:0),
% 1.00/1.63 class_Groups_Oab__group__add [109, 1] (w:1, o:176, a:1, s:1, b:0),
% 1.00/1.63 class_Groups_Ozero [110, 1] (w:1, o:177, a:1, s:1, b:0),
% 1.00/1.63 class_Groups_Oab__semigroup__mult [111, 1] (w:1, o:178, a:1, s:1, b:0
% 1.00/1.63 ),
% 1.00/1.63 class_Groups_Ocancel__semigroup__add [112, 1] (w:1, o:179, a:1, s:1
% 1.00/1.63 , b:0),
% 1.00/1.63 class_Groups_Ocancel__ab__semigroup__add [113, 1] (w:1, o:180, a:1
% 1.00/1.63 , s:1, b:0),
% 1.00/1.63 class_Groups_Oab__semigroup__add [114, 1] (w:1, o:181, a:1, s:1, b:0)
% 1.00/1.63 ,
% 1.00/1.63 class_Groups_Oone [115, 1] (w:1, o:182, a:1, s:1, b:0),
% 1.00/1.63 class_Groups_Ocomm__monoid__add [116, 1] (w:1, o:183, a:1, s:1, b:0)
% 1.00/1.63 ,
% 1.00/1.63 class_Groups_Omonoid__add [117, 1] (w:1, o:184, a:1, s:1, b:0),
% 1.00/1.63 class_Groups_Olinordered__ab__group__add [118, 1] (w:1, o:172, a:1
% 1.00/1.63 , s:1, b:0),
% 1.00/1.63 v_pa____ [119, 0] (w:1, o:87, a:1, s:1, b:0),
% 1.00/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [120, 2] (w:1, o:
% 1.00/1.63 226, a:1, s:1, b:0),
% 1.00/1.63 c_Orderings_Oord__class_Oless [121, 3] (w:1, o:253, a:1, s:1, b:0),
% 1.00/1.63 class_Rings_Ocomm__ring__1 [122, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.00/1.63 c_Nat_OSuc [123, 1] (w:1, o:185, a:1, s:1, b:0),
% 1.00/1.63 c_Polynomial_Omonom [124, 3] (w:1, o:256, a:1, s:1, b:0),
% 1.00/1.63 c_Polynomial_OpCons [125, 3] (w:1, o:258, a:1, s:1, b:0),
% 1.00/1.63 class_Rings_Olinordered__semiring__1 [127, 1] (w:1, o:143, a:1, s:1
% 1.00/1.63 , b:0),
% 1.00/1.63 c_Orderings_Oord__class_Oless__eq [128, 3] (w:1, o:254, a:1, s:1, b:0
% 1.00/1.63 ),
% 1.00/1.63 class_Rings_Olinordered__semidom [129, 1] (w:1, o:144, a:1, s:1, b:0)
% 1.00/1.63 ,
% 1.00/1.63 c_Fact_Ofact__class_Ofact [130, 2] (w:1, o:227, a:1, s:1, b:0),
% 1.00/1.63 class_Groups_Oordered__cancel__ab__semigroup__add [131, 1] (w:1, o:
% 1.00/1.63 186, a:1, s:1, b:0),
% 1.00/1.63 class_Rings_Olinordered__idom [137, 1] (w:1, o:145, a:1, s:1, b:0),
% 1.00/1.63 hBOOL [141, 1] (w:1, o:187, a:1, s:1, b:0),
% 1.00/1.63 class_Rings_Olinordered__semiring__strict [142, 1] (w:1, o:146, a:1
% 1.00/1.63 , s:1, b:0),
% 1.00/1.63 class_Rings_Olinordered__semiring [143, 1] (w:1, o:147, a:1, s:1, b:0
% 1.00/1.63 ),
% 1.00/1.63 class_Groups_Oordered__comm__monoid__add [144, 1] (w:1, o:188, a:1
% 1.00/1.63 , s:1, b:0),
% 1.00/1.63 class_Groups_Oordered__ab__semigroup__add__imp__le [146, 1] (w:1, o:
% 1.00/1.63 189, a:1, s:1, b:0),
% 1.00/1.63 class_Groups_Oordered__ab__group__add [147, 1] (w:1, o:190, a:1, s:1
% 1.00/1.63 , b:0),
% 1.00/1.63 class_Groups_Oordered__ab__semigroup__add [148, 1] (w:1, o:191, a:1
% 1.00/1.63 , s:1, b:0),
% 1.00/1.63 class_Rings_Olinordered__semiring__1__strict [155, 1] (w:1, o:148, a:
% 1.00/1.63 1, s:1, b:0),
% 1.00/1.63 class_Rings_Olinordered__ring [156, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.00/1.63 class_Rings_Olinordered__comm__semiring__strict [157, 1] (w:1, o:149
% 1.00/1.63 , a:1, s:1, b:0),
% 1.00/1.63 class_Rings_Oordered__cancel__semiring [158, 1] (w:1, o:156, a:1, s:1
% 1.00/1.63 , b:0),
% 1.00/1.63 class_Rings_Oordered__ring [159, 1] (w:1, o:157, a:1, s:1, b:0),
% 1.00/1.63 class_Rings_Oordered__semiring [160, 1] (w:1, o:158, a:1, s:1, b:0),
% 1.00/1.63
% 1.00/1.63 class_Rings_Oordered__comm__semiring [161, 1] (w:1, o:159, a:1, s:1
% 1.00/1.63 , b:0),
% 1.00/1.63 tc_Polynomial_Opoly [163, 1] (w:1, o:197, a:1, s:1, b:0),
% 1.00/1.63 tc_Int_Oint [165, 0] (w:1, o:96, a:1, s:1, b:0),
% 1.00/1.64 v_q____ [166, 0] (w:1, o:98, a:1, s:1, b:0),
% 1.00/1.64 class_Rings_Ocomm__semiring__0 [167, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.00/1.64
% 1.00/1.64 c_Polynomial_Opoly [168, 2] (w:1, o:228, a:1, s:1, b:0),
% 1.00/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [169, 3] (w:1
% 1.00/1.64 , o:250, a:1, s:1, b:0),
% 1.00/1.64 v_p [170, 0] (w:1, o:97, a:1, s:1, b:0),
% 1.00/1.64 v_c____ [171, 0] (w:1, o:99, a:1, s:1, b:0),
% 1.00/1.64 class_Rings_Ocomm__ring [176, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.00/1.64 class_Int_Oring__char__0 [178, 1] (w:1, o:198, a:1, s:1, b:0),
% 1.00/1.64 class_Rings_Oidom [179, 1] (w:1, o:160, a:1, s:1, b:0),
% 1.00/1.64 tc_RealDef_Oreal [183, 0] (w:1, o:104, a:1, s:1, b:0),
% 1.00/1.64 c_RealVector_Onorm__class_Onorm [184, 2] (w:1, o:229, a:1, s:1, b:0)
% 1.00/1.64 ,
% 1.00/1.64 c_Rings_Oinverse__class_Oinverse [185, 2] (w:1, o:230, a:1, s:1, b:0)
% 1.00/1.64 ,
% 1.00/1.64 c_Polynomial_Osmult [186, 3] (w:1, o:259, a:1, s:1, b:0),
% 1.00/1.64 v_s____ [187, 0] (w:1, o:105, a:1, s:1, b:0),
% 1.00/1.64 class_RealVector_Oreal__normed__vector [191, 1] (w:1, o:161, a:1, s:1
% 9.50/9.87 , b:0),
% 9.50/9.87 class_RealVector_Oreal__normed__div__algebra [192, 1] (w:1, o:162, a:
% 9.50/9.87 1, s:1, b:0),
% 9.50/9.87 class_Rings_Odivision__ring [193, 1] (w:1, o:163, a:1, s:1, b:0),
% 9.50/9.87 class_Rings_Odivision__ring__inverse__zero [194, 1] (w:1, o:164, a:1
% 9.50/9.87 , s:1, b:0),
% 9.50/9.87 class_RealVector_Oreal__normed__algebra__1 [195, 1] (w:1, o:165, a:1
% 9.50/9.87 , s:1, b:0),
% 9.50/9.87 class_Fields_Olinordered__field [200, 1] (w:1, o:168, a:1, s:1, b:0)
% 9.50/9.87 ,
% 9.50/9.87 class_Fields_Olinordered__field__inverse__zero [201, 1] (w:1, o:169
% 9.50/9.87 , a:1, s:1, b:0),
% 9.50/9.87 class_Fields_Ofield__inverse__zero [202, 1] (w:1, o:170, a:1, s:1, b:
% 9.50/9.87 0),
% 9.50/9.87 class_Fields_Ofield [204, 1] (w:1, o:171, a:1, s:1, b:0),
% 9.50/9.87 c_Polynomial_Opcompose [205, 3] (w:1, o:260, a:1, s:1, b:0),
% 9.50/9.87 c_Polynomial_Oorder [206, 3] (w:1, o:257, a:1, s:1, b:0),
% 9.50/9.87 class_Orderings_Opreorder [208, 1] (w:1, o:126, a:1, s:1, b:0),
% 9.50/9.87 c_Polynomial_Osynthetic__div [209, 3] (w:1, o:261, a:1, s:1, b:0),
% 9.50/9.87 class_Orderings_Olinorder [210, 1] (w:1, o:127, a:1, s:1, b:0),
% 9.50/9.87 class_Orderings_Oord [211, 1] (w:1, o:124, a:1, s:1, b:0),
% 9.50/9.87 tc_fun [212, 2] (w:1, o:239, a:1, s:1, b:0),
% 9.50/9.87 class_Orderings_Oorder [213, 1] (w:1, o:125, a:1, s:1, b:0),
% 9.50/9.87 c_Groups_Ouminus__class_Ouminus [214, 2] (w:1, o:240, a:1, s:1, b:0)
% 9.50/9.87 ,
% 9.50/9.87 c_Rings_Odvd__class_Odvd [217, 3] (w:1, o:262, a:1, s:1, b:0),
% 9.50/9.87 class_Rings_Odvd [218, 1] (w:1, o:166, a:1, s:1, b:0),
% 9.50/9.87 c_Complex_Oii [221, 0] (w:1, o:112, a:1, s:1, b:0),
% 9.50/9.87 c_Nat__Transfer_Otsub [224, 2] (w:1, o:241, a:1, s:1, b:0),
% 9.50/9.87 c_Polynomial_Opos__poly [225, 2] (w:1, o:242, a:1, s:1, b:0),
% 9.50/9.87 c_Divides_Odiv__class_Odiv [226, 3] (w:1, o:263, a:1, s:1, b:0),
% 9.50/9.87 class_Divides_Oring__div [227, 1] (w:1, o:199, a:1, s:1, b:0),
% 9.50/9.87 class_Groups_Ocancel__comm__monoid__add [229, 1] (w:1, o:200, a:1, s:
% 9.50/9.87 1, b:0),
% 9.50/9.87 tc_HOL_Obool [231, 0] (w:1, o:95, a:1, s:1, b:0),
% 9.50/9.87 v_thesis____ [232, 0] (w:1, o:117, a:1, s:1, b:0),
% 9.50/9.87 alpha1 [233, 2] (w:1, o:243, a:1, s:1, b:1),
% 9.50/9.87 alpha2 [234, 4] (w:1, o:284, a:1, s:1, b:1),
% 9.50/9.87 alpha3 [235, 4] (w:1, o:286, a:1, s:1, b:1),
% 9.50/9.87 alpha4 [236, 3] (w:1, o:264, a:1, s:1, b:1),
% 9.50/9.87 alpha5 [237, 3] (w:1, o:265, a:1, s:1, b:1),
% 9.50/9.87 alpha6 [238, 2] (w:1, o:244, a:1, s:1, b:1),
% 9.50/9.87 alpha7 [239, 2] (w:1, o:245, a:1, s:1, b:1),
% 9.50/9.87 alpha8 [240, 3] (w:1, o:266, a:1, s:1, b:1),
% 9.50/9.87 alpha9 [241, 3] (w:1, o:267, a:1, s:1, b:1),
% 9.50/9.87 alpha10 [242, 3] (w:1, o:268, a:1, s:1, b:1),
% 9.50/9.87 alpha11 [243, 2] (w:1, o:246, a:1, s:1, b:1),
% 9.50/9.87 alpha12 [244, 2] (w:1, o:247, a:1, s:1, b:1),
% 9.50/9.87 alpha13 [245, 3] (w:1, o:269, a:1, s:1, b:1),
% 9.50/9.87 alpha14 [246, 4] (w:1, o:282, a:1, s:1, b:1),
% 9.50/9.87 alpha15 [247, 4] (w:1, o:283, a:1, s:1, b:1),
% 9.50/9.87 alpha16 [248, 3] (w:1, o:270, a:1, s:1, b:1),
% 9.50/9.87 alpha17 [249, 3] (w:1, o:271, a:1, s:1, b:1),
% 9.50/9.87 alpha18 [250, 2] (w:1, o:248, a:1, s:1, b:1),
% 9.50/9.87 alpha19 [251, 2] (w:1, o:249, a:1, s:1, b:1),
% 9.50/9.87 alpha20 [252, 3] (w:1, o:272, a:1, s:1, b:1),
% 9.50/9.87 alpha21 [253, 3] (w:1, o:273, a:1, s:1, b:1),
% 9.50/9.87 alpha22 [254, 4] (w:1, o:285, a:1, s:1, b:1),
% 9.50/9.87 alpha23 [255, 3] (w:1, o:274, a:1, s:1, b:1),
% 9.50/9.87 alpha24 [256, 3] (w:1, o:275, a:1, s:1, b:1),
% 9.50/9.87 skol1 [257, 2] (w:1, o:231, a:1, s:1, b:1),
% 9.50/9.87 skol2 [258, 0] (w:1, o:18, a:1, s:1, b:1),
% 9.50/9.87 skol3 [259, 2] (w:1, o:234, a:1, s:1, b:1),
% 9.50/9.87 skol4 [260, 1] (w:1, o:192, a:1, s:1, b:1),
% 9.50/9.87 skol5 [261, 2] (w:1, o:235, a:1, s:1, b:1),
% 9.50/9.87 skol6 [262, 2] (w:1, o:236, a:1, s:1, b:1),
% 9.50/9.87 skol7 [263, 3] (w:1, o:276, a:1, s:1, b:1),
% 9.50/9.87 skol8 [264, 3] (w:1, o:277, a:1, s:1, b:1),
% 9.50/9.87 skol9 [265, 0] (w:1, o:19, a:1, s:1, b:1),
% 9.50/9.87 skol10 [266, 1] (w:1, o:193, a:1, s:1, b:1),
% 9.50/9.87 skol11 [267, 1] (w:1, o:194, a:1, s:1, b:1),
% 9.50/9.87 skol12 [268, 0] (w:1, o:13, a:1, s:1, b:1),
% 9.50/9.87 skol13 [269, 0] (w:1, o:14, a:1, s:1, b:1),
% 9.50/9.87 skol14 [270, 0] (w:1, o:15, a:1, s:1, b:1),
% 9.50/9.87 skol15 [271, 0] (w:1, o:16, a:1, s:1, b:1),
% 9.50/9.87 skol16 [272, 2] (w:1, o:237, a:1, s:1, b:1),
% 9.50/9.87 skol17 [273, 2] (w:1, o:238, a:1, s:1, b:1),
% 26.01/26.37 skol18 [274, 0] (w:1, o:17, a:1, s:1, b:1),
% 26.01/26.37 skol19 [275, 3] (w:1, o:278, a:1, s:1, b:1),
% 26.01/26.37 skol20 [276, 4] (w:1, o:287, a:1, s:1, b:1),
% 26.01/26.37 skol21 [277, 3] (w:1, o:279, a:1, s:1, b:1),
% 26.01/26.37 skol22 [278, 0] (w:1, o:20, a:1, s:1, b:1),
% 26.01/26.37 skol23 [279, 2] (w:1, o:232, a:1, s:1, b:1),
% 26.01/26.37 skol24 [280, 1] (w:1, o:195, a:1, s:1, b:1),
% 26.01/26.37 skol25 [281, 2] (w:1, o:233, a:1, s:1, b:1),
% 26.01/26.37 skol26 [282, 3] (w:1, o:280, a:1, s:1, b:1),
% 26.01/26.37 skol27 [283, 1] (w:1, o:196, a:1, s:1, b:1),
% 26.01/26.37 skol28 [284, 0] (w:1, o:21, a:1, s:1, b:1),
% 26.01/26.37 skol29 [285, 0] (w:1, o:22, a:1, s:1, b:1),
% 26.01/26.37 skol30 [286, 3] (w:1, o:281, a:1, s:1, b:1),
% 26.01/26.37 skol31 [287, 0] (w:1, o:23, a:1, s:1, b:1).
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Starting Search:
% 26.01/26.37
% 26.01/26.37 *** allocated 113905 integers for clauses
% 26.01/26.37 *** allocated 170857 integers for clauses
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 3134
% 26.01/26.37 Kept: 2050
% 26.01/26.37 Inuse: 45
% 26.01/26.37 Deleted: 1
% 26.01/26.37 Deletedinuse: 0
% 26.01/26.37
% 26.01/26.37 *** allocated 256285 integers for clauses
% 26.01/26.37 *** allocated 170857 integers for termspace/termends
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 *** allocated 384427 integers for clauses
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 *** allocated 256285 integers for termspace/termends
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 11525
% 26.01/26.37 Kept: 4058
% 26.01/26.37 Inuse: 120
% 26.01/26.37 Deleted: 5
% 26.01/26.37 Deletedinuse: 0
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 *** allocated 576640 integers for clauses
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 17476
% 26.01/26.37 Kept: 6245
% 26.01/26.37 Inuse: 226
% 26.01/26.37 Deleted: 10
% 26.01/26.37 Deletedinuse: 0
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 *** allocated 384427 integers for termspace/termends
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 30622
% 26.01/26.37 Kept: 8253
% 26.01/26.37 Inuse: 259
% 26.01/26.37 Deleted: 11
% 26.01/26.37 Deletedinuse: 1
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 *** allocated 864960 integers for clauses
% 26.01/26.37 *** allocated 576640 integers for termspace/termends
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 37781
% 26.01/26.37 Kept: 10332
% 26.01/26.37 Inuse: 300
% 26.01/26.37 Deleted: 13
% 26.01/26.37 Deletedinuse: 2
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 47831
% 26.01/26.37 Kept: 12332
% 26.01/26.37 Inuse: 347
% 26.01/26.37 Deleted: 15
% 26.01/26.37 Deletedinuse: 2
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 *** allocated 1297440 integers for clauses
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 59065
% 26.01/26.37 Kept: 14782
% 26.01/26.37 Inuse: 392
% 26.01/26.37 Deleted: 16
% 26.01/26.37 Deletedinuse: 2
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 *** allocated 864960 integers for termspace/termends
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 73248
% 26.01/26.37 Kept: 17196
% 26.01/26.37 Inuse: 412
% 26.01/26.37 Deleted: 16
% 26.01/26.37 Deletedinuse: 2
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 97034
% 26.01/26.37 Kept: 20327
% 26.01/26.37 Inuse: 436
% 26.01/26.37 Deleted: 17
% 26.01/26.37 Deletedinuse: 2
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying clauses:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 104061
% 26.01/26.37 Kept: 22604
% 26.01/26.37 Inuse: 451
% 26.01/26.37 Deleted: 905
% 26.01/26.37 Deletedinuse: 2
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 *** allocated 1946160 integers for clauses
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 116067
% 26.01/26.37 Kept: 25670
% 26.01/26.37 Inuse: 506
% 26.01/26.37 Deleted: 905
% 26.01/26.37 Deletedinuse: 2
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 *** allocated 1297440 integers for termspace/termends
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 122623
% 26.01/26.37 Kept: 27754
% 26.01/26.37 Inuse: 531
% 26.01/26.37 Deleted: 905
% 26.01/26.37 Deletedinuse: 2
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 135951
% 26.01/26.37 Kept: 29778
% 26.01/26.37 Inuse: 546
% 26.01/26.37 Deleted: 905
% 26.01/26.37 Deletedinuse: 2
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 150749
% 26.01/26.37 Kept: 31900
% 26.01/26.37 Inuse: 561
% 26.01/26.37 Deleted: 905
% 26.01/26.37 Deletedinuse: 2
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 159630
% 26.01/26.37 Kept: 33922
% 26.01/26.37 Inuse: 600
% 26.01/26.37 Deleted: 905
% 26.01/26.37 Deletedinuse: 2
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 169677
% 26.01/26.37 Kept: 35948
% 26.01/26.37 Inuse: 631
% 26.01/26.37 Deleted: 905
% 26.01/26.37 Deletedinuse: 2
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 178748
% 26.01/26.37 Kept: 38198
% 26.01/26.37 Inuse: 651
% 26.01/26.37 Deleted: 905
% 26.01/26.37 Deletedinuse: 2
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 *** allocated 2919240 integers for clauses
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 191382
% 26.01/26.37 Kept: 41422
% 26.01/26.37 Inuse: 661
% 26.01/26.37 Deleted: 905
% 26.01/26.37 Deletedinuse: 2
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying clauses:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 *** allocated 1946160 integers for termspace/termends
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 199874
% 26.01/26.37 Kept: 44153
% 26.01/26.37 Inuse: 691
% 26.01/26.37 Deleted: 1054
% 26.01/26.37 Deletedinuse: 2
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 208197
% 26.01/26.37 Kept: 48062
% 26.01/26.37 Inuse: 711
% 26.01/26.37 Deleted: 1054
% 26.01/26.37 Deletedinuse: 2
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 215443
% 26.01/26.37 Kept: 51869
% 26.01/26.37 Inuse: 726
% 26.01/26.37 Deleted: 1054
% 26.01/26.37 Deletedinuse: 2
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 230470
% 26.01/26.37 Kept: 54134
% 26.01/26.37 Inuse: 746
% 26.01/26.37 Deleted: 1055
% 26.01/26.37 Deletedinuse: 3
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 242717
% 26.01/26.37 Kept: 56155
% 26.01/26.37 Inuse: 758
% 26.01/26.37 Deleted: 1056
% 26.01/26.37 Deletedinuse: 4
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 251391
% 26.01/26.37 Kept: 59413
% 26.01/26.37 Inuse: 781
% 26.01/26.37 Deleted: 1056
% 26.01/26.37 Deletedinuse: 4
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 259580
% 26.01/26.37 Kept: 61448
% 26.01/26.37 Inuse: 818
% 26.01/26.37 Deleted: 1056
% 26.01/26.37 Deletedinuse: 4
% 26.01/26.37
% 26.01/26.37 Resimplifying clauses:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 *** allocated 4378860 integers for clauses
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 267598
% 26.01/26.37 Kept: 63494
% 26.01/26.37 Inuse: 845
% 26.01/26.37 Deleted: 1252
% 26.01/26.37 Deletedinuse: 4
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 275341
% 26.01/26.37 Kept: 65511
% 26.01/26.37 Inuse: 871
% 26.01/26.37 Deleted: 1252
% 26.01/26.37 Deletedinuse: 4
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 283592
% 26.01/26.37 Kept: 67536
% 26.01/26.37 Inuse: 901
% 26.01/26.37 Deleted: 1252
% 26.01/26.37 Deletedinuse: 4
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 295181
% 26.01/26.37 Kept: 70509
% 26.01/26.37 Inuse: 916
% 26.01/26.37 Deleted: 1252
% 26.01/26.37 Deletedinuse: 4
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 *** allocated 2919240 integers for termspace/termends
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 306127
% 26.01/26.37 Kept: 75731
% 26.01/26.37 Inuse: 941
% 26.01/26.37 Deleted: 1252
% 26.01/26.37 Deletedinuse: 4
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Intermediate Status:
% 26.01/26.37 Generated: 317867
% 26.01/26.37 Kept: 80979
% 26.01/26.37 Inuse: 961
% 26.01/26.37 Deleted: 1252
% 26.01/26.37 Deletedinuse: 4
% 26.01/26.37
% 26.01/26.37 Resimplifying inuse:
% 26.01/26.37 Done
% 26.01/26.37
% 26.01/26.37 Resimplifying clauses:
% 26.01/26.37
% 26.01/26.37 Bliksems!, er is een bewijs:
% 26.01/26.37 % SZS status Theorem
% 26.01/26.37 % SZS output start Refutation
% 26.01/26.37
% 26.01/26.37 (2) {G0,W4,D3,L1,V0,M1} I { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 26.01/26.37 ==> v_k____ }.
% 26.01/26.37 (12) {G0,W27,D8,L1,V0,M1} I { c_Groups_Oplus__class_Oplus(
% 26.01/26.37 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.01/26.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), skol2 )
% 26.01/26.37 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 26.01/26.37 v_a____ ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex
% 26.01/26.37 ), skol2 ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.01/26.37 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ) ) ==>
% 26.01/26.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 26.01/26.37 (36) {G0,W25,D7,L2,V4,M2} I { ! class_Rings_Ocomm__semiring__1( X ), hAPP(
% 26.01/26.37 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ==> hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 26.01/26.37 (38) {G0,W15,D5,L2,V3,M2} I { ! class_Rings_Ocomm__semiring__1( X ), hAPP(
% 26.01/26.37 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 26.01/26.37 (167) {G0,W5,D3,L1,V1,M1} I { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.37 , X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.37 (191) {G0,W15,D4,L2,V2,M2} I { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.37 tc_Nat_Onat, Y, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 26.01/26.37 c_Nat_OSuc( X ), Y ) ==> c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 26.01/26.37 tc_Nat_Onat, X, Y ) ) }.
% 26.01/26.37 (210) {G0,W11,D2,L3,V2,M3} I { Y = X, c_Orderings_Oord__class_Oless(
% 26.01/26.37 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y )
% 26.01/26.37 }.
% 26.01/26.37 (212) {G0,W9,D3,L2,V2,M2} I { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.37 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y )
% 26.01/26.37 , X ) }.
% 26.01/26.37 (464) {G0,W21,D6,L2,V3,M2} I { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.37 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( X ), Z ), Y ) ) ==> hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 26.01/26.37 (493) {G0,W6,D4,L1,V0,M1} I { c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 26.01/26.37 tc_Nat_Onat ) ) ==> c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 26.01/26.37 (509) {G0,W8,D4,L1,V1,M1} I { c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 26.01/26.37 c_Nat_OSuc( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ==> X }.
% 26.01/26.37 (1353) {G0,W2,D2,L1,V0,M1} I { class_Rings_Ocomm__semiring__1(
% 26.01/26.37 tc_Complex_Ocomplex ) }.
% 26.01/26.37 (1431) {G0,W19,D8,L2,V1,M2} I { ! c_Groups_Oplus__class_Oplus(
% 26.01/26.37 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.01/26.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 26.01/26.37 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), v_k____ )
% 26.01/26.37 ), v_a____ ) ) ==> c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 26.01/26.37 v_thesis____ }.
% 26.01/26.37 (1432) {G0,W1,D1,L1,V0,M1} I { ! v_thesis____ }.
% 26.01/26.37 (5299) {G1,W23,D9,L1,V0,M1} P(38,12);d(36);d(464);r(1353) {
% 26.01/26.37 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 26.01/26.37 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol2 ), c_Nat_OSuc
% 26.01/26.37 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.01/26.37 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ), v_a____ ) ) ==>
% 26.01/26.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 26.01/26.37 (20339) {G1,W18,D8,L1,V1,M1} S(1431);r(1432) { !
% 26.01/26.37 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 26.01/26.37 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), v_k____ ) ),
% 26.01/26.37 v_a____ ) ) ==> c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 26.01/26.37 (70472) {G1,W8,D3,L2,V1,M2} P(210,2);r(167) { ! X = v_k____,
% 26.01/26.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 26.01/26.37 tc_Nat_Onat ), X ) }.
% 26.01/26.37 (70494) {G2,W5,D3,L1,V0,M1} Q(70472) { c_Orderings_Oord__class_Oless(
% 26.01/26.37 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), v_k____ ) }.
% 26.01/26.37 (70823) {G3,W5,D3,L1,V0,M1} R(212,70494);d(493) {
% 26.01/26.37 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 26.01/26.37 ( tc_Nat_Onat ), v_k____ ) }.
% 26.01/26.37 (70941) {G4,W8,D5,L1,V0,M1} R(70823,191);d(509) { c_Nat_OSuc(
% 26.01/26.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.01/26.37 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ==> v_k____ }.
% 26.01/26.37 (81507) {G5,W0,D0,L0,V0,M0} S(5299);d(70941);r(20339) { }.
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 % SZS output end Refutation
% 26.01/26.37 found a proof!
% 26.01/26.37
% 26.01/26.37
% 26.01/26.37 Unprocessed initial clauses:
% 26.01/26.37
% 26.01/26.37 (81509) {G0,W14,D4,L2,V2,M2} { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1
% 26.01/26.37 ( X, Y ) ), Y = X }.
% 26.01/26.37 (81510) {G0,W4,D3,L1,V0,M1} { ! v_a____ = c_Groups_Ozero__class_Ozero(
% 26.01/26.37 tc_Complex_Ocomplex ) }.
% 26.01/26.37 (81511) {G0,W4,D3,L1,V0,M1} { ! v_k____ = c_Groups_Ozero__class_Ozero(
% 26.01/26.37 tc_Nat_Onat ) }.
% 26.01/26.37 (81512) {G0,W18,D5,L4,V2,M4} { ! class_Power_Opower( X ), !
% 26.01/26.37 class_Rings_Osemiring__0( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.37 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 26.01/26.37 c_Groups_Ozero__class_Ozero( X ) ), Y ) = c_Groups_Oone__class_Oone( X )
% 26.01/26.37 }.
% 26.01/26.37 (81513) {G0,W18,D5,L4,V2,M4} { ! class_Power_Opower( X ), !
% 26.01/26.37 class_Rings_Osemiring__0( X ), Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.37 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 26.01/26.37 c_Groups_Ozero__class_Ozero( X ) ), Y ) = c_Groups_Ozero__class_Ozero( X
% 26.01/26.37 ) }.
% 26.01/26.37 (81514) {G0,W18,D6,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.37 c_Groups_Oplus__class_Oplus( X, Y, Y ) = hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X,
% 26.01/26.37 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ), Y )
% 26.01/26.37 }.
% 26.01/26.37 (81515) {G0,W22,D6,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.37 c_Groups_Oplus__class_Oplus( X, Z, hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 26.01/26.37 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 26.01/26.37 (81516) {G0,W22,D6,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.37 ( X ), Z ), Y ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 26.01/26.37 c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Oone__class_Oone( X ) ) ), Y
% 26.01/26.37 ) }.
% 26.01/26.37 (81517) {G0,W23,D6,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.37 ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 26.01/26.37 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X )
% 26.01/26.37 }.
% 26.01/26.37 (81518) {G0,W23,D6,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.37 ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 26.01/26.37 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 26.01/26.37 }.
% 26.01/26.37 (81519) {G0,W27,D6,L4,V3,M4} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.37 ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 26.01/26.37 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 26.01/26.37 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 26.01/26.37 c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.37 (81520) {G0,W31,D6,L5,V6,M5} { !
% 26.01/26.37 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 26.01/26.37 ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 26.01/26.37 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 26.01/26.37 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 26.01/26.37 (81521) {G0,W27,D8,L1,V0,M1} { c_Groups_Oplus__class_Oplus(
% 26.01/26.37 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.01/26.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), skol2 )
% 26.01/26.37 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 26.01/26.37 v_a____ ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex
% 26.01/26.37 ), skol2 ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.01/26.37 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ) ) =
% 26.01/26.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 26.01/26.37 (81522) {G0,W12,D5,L2,V2,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 26.01/26.37 hAPP( c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) )
% 26.01/26.37 , Y ) = c_Groups_Oone__class_Oone( X ) }.
% 26.01/26.37 (81523) {G0,W25,D7,L2,V3,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 26.01/26.37 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 26.01/26.37 (81524) {G0,W30,D7,L2,V4,M2} { ! class_Groups_Ocomm__monoid__mult( X ),
% 26.01/26.37 hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 26.01/26.37 (81525) {G0,W30,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.37 ( hAPP( c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 26.01/26.37 (81526) {G0,W21,D5,L6,V3,M6} { ! class_Power_Opower( X ), !
% 26.01/26.37 class_Rings_Omult__zero( X ), ! class_Rings_Ono__zero__divisors( X ), !
% 26.01/26.37 class_Rings_Ozero__neq__one( X ), ! hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 26.01/26.37 ( X ), Z = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.37 (81527) {G0,W21,D5,L6,V3,M6} { ! class_Power_Opower( X ), !
% 26.01/26.37 class_Rings_Omult__zero( X ), ! class_Rings_Ono__zero__divisors( X ), !
% 26.01/26.37 class_Rings_Ozero__neq__one( X ), ! hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 26.01/26.37 ( X ), ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.37 (81528) {G0,W25,D5,L7,V3,M7} { ! class_Power_Opower( X ), !
% 26.01/26.37 class_Rings_Omult__zero( X ), ! class_Rings_Ono__zero__divisors( X ), !
% 26.01/26.37 class_Rings_Ozero__neq__one( X ), ! Z = c_Groups_Ozero__class_Ozero( X )
% 26.01/26.37 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 26.01/26.37 ( X ) }.
% 26.01/26.37 (81529) {G0,W13,D5,L2,V2,M2} { ! Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.37 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X
% 26.01/26.37 ), Y ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 26.01/26.37 (81530) {G0,W26,D6,L2,V2,M2} { Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.37 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X
% 26.01/26.37 ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 26.01/26.37 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 26.01/26.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 26.01/26.37 ( tc_Nat_Onat ) ) ) ) }.
% 26.01/26.37 (81531) {G0,W13,D5,L2,V2,M2} { ! Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.37 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.37 Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.37 (81532) {G0,W24,D7,L2,V2,M2} { Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.37 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.37 Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 26.01/26.37 ( tc_Nat_Onat ) ) ), X ) ) }.
% 26.01/26.37 (81533) {G0,W25,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.37 ( hAPP( c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 26.01/26.37 (81534) {G0,W25,D7,L2,V4,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 26.01/26.37 hAPP( c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 26.01/26.37 (81535) {G0,W11,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.37 ( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone
% 26.01/26.37 ( tc_Nat_Onat ) ) = Y }.
% 26.01/26.37 (81536) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 26.01/26.37 hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 26.01/26.37 tc_Nat_Onat ) ) = Y }.
% 26.01/26.37 (81537) {G0,W28,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.37 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 26.01/26.37 tc_Nat_Onat, Z, Y ) ) }.
% 26.01/26.37 (81538) {G0,W28,D7,L2,V4,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 26.01/26.37 hAPP( c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus
% 26.01/26.37 ( tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 26.01/26.37 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 26.01/26.37 (81539) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.37 ( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 26.01/26.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone
% 26.01/26.37 ( X ) }.
% 26.01/26.37 (81540) {G0,W12,D5,L2,V2,M2} { ! class_Power_Opower( X ), hAPP( hAPP(
% 26.01/26.37 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 26.01/26.37 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 26.01/26.37 (81541) {G0,W35,D7,L2,V5,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.37 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 26.01/26.37 (81542) {G0,W35,D8,L2,V5,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.37 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 26.01/26.37 (81543) {G0,W35,D7,L2,V5,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.37 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 26.01/26.37 (81544) {G0,W25,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.37 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 26.01/26.37 (81545) {G0,W25,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.37 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 26.01/26.37 (81546) {G0,W25,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.37 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 26.01/26.37 (81547) {G0,W25,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.37 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 26.01/26.37 (81548) {G0,W15,D5,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.37 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 26.01/26.37 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 26.01/26.37 (81549) {G0,W23,D4,L2,V5,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.37 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, U, T ),
% 26.01/26.37 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 26.01/26.37 , c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus( X
% 26.01/26.37 , T, Y ) ) }.
% 26.01/26.37 (81550) {G0,W17,D4,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.37 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y
% 26.01/26.37 ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, T, Y
% 26.01/26.37 ), Z ) }.
% 26.01/26.37 (81551) {G0,W17,D4,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.37 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y
% 26.01/26.37 ) = c_Groups_Oplus__class_Oplus( X, T, c_Groups_Oplus__class_Oplus( X, Z
% 26.01/26.37 , Y ) ) }.
% 26.01/26.37 (81552) {G0,W17,D4,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.37 c_Groups_Oplus__class_Oplus( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y )
% 26.01/26.37 ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 26.01/26.37 ), Y ) }.
% 26.01/26.37 (81553) {G0,W17,D4,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.37 c_Groups_Oplus__class_Oplus( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y )
% 26.01/26.37 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Oplus__class_Oplus( X, T
% 26.01/26.37 , Y ) ) }.
% 26.01/26.37 (81554) {G0,W11,D3,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.37 c_Groups_Oplus__class_Oplus( X, Z, Y ) = c_Groups_Oplus__class_Oplus( X,
% 26.01/26.37 Y, Z ) }.
% 26.01/26.37 (81555) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.37 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 26.01/26.37 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.37 (81556) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.37 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero(
% 26.01/26.37 X ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.37 (81557) {G0,W12,D3,L3,V3,M3} { !
% 26.01/26.37 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 26.01/26.37 ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 26.01/26.37 c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.37 (81558) {G0,W12,D3,L3,V3,M3} { !
% 26.01/26.37 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 26.01/26.37 ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 26.01/26.37 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 26.01/26.37 (81559) {G0,W9,D4,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.37 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Ozero__class_Ozero( X ) ) = Y
% 26.01/26.37 }.
% 26.01/26.37 (81560) {G0,W9,D4,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Ozero__class_Ozero( X ), Y ) = Y
% 26.01/26.38 }.
% 26.01/26.38 (81561) {G0,W37,D6,L4,V5,M4} { !
% 26.01/26.38 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 26.01/26.38 ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 26.01/26.38 ), U = Z, T = Y }.
% 26.01/26.38 (81562) {G0,W34,D6,L3,V5,M3} { !
% 26.01/26.38 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 26.01/26.38 ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 26.01/26.38 ) }.
% 26.01/26.38 (81563) {G0,W34,D6,L3,V5,M3} { !
% 26.01/26.38 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 26.01/26.38 ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 26.01/26.38 ) }.
% 26.01/26.38 (81564) {G0,W26,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z )
% 26.01/26.38 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, T, Y ) ), Z ) }.
% 26.01/26.38 (81565) {G0,W26,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus(
% 26.01/26.38 X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 26.01/26.38 (81566) {G0,W37,D6,L4,V5,M4} { !
% 26.01/26.38 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 26.01/26.38 ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 26.01/26.38 ) }.
% 26.01/26.38 (81567) {G0,W34,D6,L3,V5,M3} { !
% 26.01/26.38 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 26.01/26.38 ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 26.01/26.38 ), ! U = T }.
% 26.01/26.38 (81568) {G0,W34,D6,L3,V5,M3} { !
% 26.01/26.38 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 26.01/26.38 ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 26.01/26.38 ), ! Z = Y }.
% 26.01/26.38 (81569) {G0,W26,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 26.01/26.38 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 26.01/26.38 (81570) {G0,W11,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 26.01/26.38 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 26.01/26.38 (81571) {G0,W11,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X
% 26.01/26.38 ) ), Y ) = Y }.
% 26.01/26.38 (81572) {G0,W15,D5,L3,V3,M3} { ! class_Rings_Oring__1__no__zero__divisors
% 26.01/26.38 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 26.01/26.38 ( X ) }.
% 26.01/26.38 (81573) {G0,W15,D5,L3,V3,M3} { ! class_Power_Opower( X ), ! Z =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Oone__class_Oone(
% 26.01/26.38 X ) }.
% 26.01/26.38 (81574) {G0,W28,D6,L3,V3,M3} { ! class_Power_Opower( X ), Z =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 26.01/26.38 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 26.01/26.38 (81575) {G0,W27,D6,L2,V2,M2} { ! class_Rings_Oring__1( X ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone(
% 26.01/26.38 X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) )
% 26.01/26.38 }.
% 26.01/26.38 (81576) {G0,W35,D6,L3,V6,M3} { ! class_Rings_Oring( X ), !
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), W ), U ), T ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ) = Y }.
% 26.01/26.38 (81577) {G0,W35,D6,L3,V6,M3} { ! class_Rings_Oring( X ), !
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ) = Y,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), W ), U ), T ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) }.
% 26.01/26.38 (81578) {G0,W35,D6,L3,V6,M3} { ! class_Rings_Oring( X ), !
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), W ), U ), T ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ), T =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) }.
% 26.01/26.38 (81579) {G0,W35,D6,L3,V6,M3} { ! class_Rings_Oring( X ), ! T =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), W ), U ), T ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) }.
% 26.01/26.38 (81580) {G0,W51,D7,L2,V5,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.38 X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 26.01/26.38 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 26.01/26.38 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 26.01/26.38 (81581) {G0,W37,D6,L2,V5,M2} { ! class_Rings_Oring( X ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 26.01/26.38 Z ) ), Y ) ) }.
% 26.01/26.38 (81582) {G0,W11,D4,L2,V1,M2} { ! class_Power_Opower( X ),
% 26.01/26.38 c_Power_Opower__class_Opower( X ) = c_Power_Opower_Opower( X,
% 26.01/26.38 c_Groups_Oone__class_Oone( X ), c_Groups_Otimes__class_Otimes( X ) ) }.
% 26.01/26.38 (81583) {G0,W16,D5,L3,V2,M3} { ! Y = hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Ozero__class_Ozero
% 26.01/26.38 ( tc_Nat_Onat ) }.
% 26.01/26.38 (81584) {G0,W8,D4,L1,V1,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (81585) {G0,W7,D4,L1,V1,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 26.01/26.38 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 26.01/26.38 (81586) {G0,W7,D3,L1,V1,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 26.01/26.38 X, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (81587) {G0,W10,D4,L1,V2,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 26.01/26.38 , Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (81588) {G0,W9,D3,L1,V2,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 26.01/26.38 , X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 26.01/26.38 (81589) {G0,W13,D5,L1,V2,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), Y ), X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), X ), Y ) }.
% 26.01/26.38 (81590) {G0,W15,D4,L1,V3,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z
% 26.01/26.38 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus
% 26.01/26.38 ( tc_Nat_Onat, Z, X ) ) }.
% 26.01/26.38 (81591) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 26.01/26.38 (81592) {G0,W15,D4,L1,V3,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 26.01/26.38 ( tc_Nat_Onat, Y, X ) ) }.
% 26.01/26.38 (81593) {G0,W23,D7,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 Z ), Y ) ), X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat
% 26.01/26.38 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X
% 26.01/26.38 ) ) }.
% 26.01/26.38 (81594) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 26.01/26.38 (81595) {G0,W12,D3,L2,V3,M2} { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 26.01/26.38 , Z, Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 26.01/26.38 (81596) {G0,W12,D3,L2,V3,M2} { ! Y = X, c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, Z, Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X )
% 26.01/26.38 }.
% 26.01/26.38 (81597) {G0,W12,D3,L2,V3,M2} { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 26.01/26.38 , Z, Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 26.01/26.38 (81598) {G0,W12,D3,L2,V3,M2} { ! Z = X, c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, Z, Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y )
% 26.01/26.38 }.
% 26.01/26.38 (81599) {G0,W11,D5,L1,V4,M1} { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y
% 26.01/26.38 ), X ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 26.01/26.38 (81600) {G0,W10,D3,L2,V2,M2} { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 26.01/26.38 , Y, X ) = Y, X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (81601) {G0,W20,D5,L3,V3,M3} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), X ), Y ), Z = X, Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ) }.
% 26.01/26.38 (81602) {G0,W16,D5,L2,V3,M2} { ! Z = X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 26.01/26.38 (81603) {G0,W17,D5,L2,V3,M2} { ! Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 26.01/26.38 , Y ) }.
% 26.01/26.38 (81604) {G0,W20,D5,L3,V3,M3} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), Z ), X ), Y = X, Z = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ) }.
% 26.01/26.38 (81605) {G0,W16,D5,L2,V3,M2} { ! Y = X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 26.01/26.38 (81606) {G0,W17,D5,L2,V3,M2} { ! Z = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z )
% 26.01/26.38 , X ) }.
% 26.01/26.38 (81607) {G0,W17,D5,L3,V2,M3} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( tc_Nat_Onat ), Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y
% 26.01/26.38 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (81608) {G0,W13,D5,L2,V2,M2} { ! Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (81609) {G0,W13,D5,L2,V2,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (81610) {G0,W11,D3,L2,V2,M2} { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 26.01/26.38 , Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (81611) {G0,W11,D3,L2,V2,M2} { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 26.01/26.38 , Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (81612) {G0,W15,D3,L3,V2,M3} { ! Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (81613) {G0,W7,D4,L1,V1,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X
% 26.01/26.38 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 26.01/26.38 (81614) {G0,W10,D5,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), X ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (81615) {G0,W7,D4,L1,V1,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) = X }.
% 26.01/26.38 (81616) {G0,W10,D5,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (81617) {G0,W15,D4,L1,V3,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 26.01/26.38 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 26.01/26.38 (81618) {G0,W15,D4,L1,V3,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 26.01/26.38 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81619) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X )
% 26.01/26.38 = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 26.01/26.38 (81620) {G0,W15,D4,L1,V3,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 26.01/26.38 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 26.01/26.38 ( tc_Nat_Onat, Z, X ), Y ) }.
% 26.01/26.38 (81621) {G0,W15,D4,L1,V3,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 26.01/26.38 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 26.01/26.38 (81622) {G0,W9,D4,L1,V2,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), Y ) = X }.
% 26.01/26.38 (81623) {G0,W9,D4,L1,V2,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), X ) = Y }.
% 26.01/26.38 (81624) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) )
% 26.01/26.38 = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 26.01/26.38 (81625) {G0,W13,D5,L2,V2,M2} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( tc_Nat_Onat ), Y ), X ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 26.01/26.38 (81626) {G0,W13,D5,L2,V2,M2} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( tc_Nat_Onat ), Y ), X ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ), X =
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 26.01/26.38 (81627) {G0,W17,D5,L3,V2,M3} { ! Y = c_Groups_Oone__class_Oone(
% 26.01/26.38 tc_Nat_Onat ), ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP
% 26.01/26.38 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 26.01/26.38 (81628) {G0,W9,D5,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 26.01/26.38 (81629) {G0,W13,D5,L2,V2,M2} { ! c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 26.01/26.38 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 26.01/26.38 (81630) {G0,W13,D5,L2,V2,M2} { ! c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 26.01/26.38 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 26.01/26.38 (81631) {G0,W17,D5,L3,V2,M3} { ! Y = c_Groups_Oone__class_Oone(
% 26.01/26.38 tc_Nat_Onat ), ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) }.
% 26.01/26.38 (81632) {G0,W9,D5,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 26.01/26.38 (81633) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Omult__zero( X ), hAPP( hAPP
% 26.01/26.38 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) )
% 26.01/26.38 , Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.38 (81634) {G0,W12,D5,L2,V2,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.38 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), Y ) = c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ) }.
% 26.01/26.38 (81635) {G0,W12,D5,L2,V2,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.38 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), Y ) = c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ) }.
% 26.01/26.38 (81636) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Omult__zero( X ), hAPP( hAPP
% 26.01/26.38 ( c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.38 (81637) {G0,W12,D5,L2,V2,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.38 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.38 (81638) {G0,W12,D5,L2,V2,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.38 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.38 (81639) {G0,W19,D5,L4,V3,M4} { ! class_Rings_Oring__no__zero__divisors( X
% 26.01/26.38 ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 26.01/26.38 = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.38 (81640) {G0,W15,D5,L3,V3,M3} { ! class_Rings_Oring__no__zero__divisors( X
% 26.01/26.38 ), ! Z = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.38 (81641) {G0,W15,D5,L3,V3,M3} { ! class_Rings_Oring__no__zero__divisors( X
% 26.01/26.38 ), ! Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.38 (81642) {G0,W19,D5,L4,V3,M4} { ! class_Rings_Ono__zero__divisors( X ), Y =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.38 ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.38 (81643) {G0,W19,D5,L4,V3,M4} { ! class_Rings_Ono__zero__divisors( X ), !
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 26.01/26.38 = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.38 (81644) {G0,W7,D3,L2,V1,M2} { ! class_Rings_Ozero__neq__one( X ), !
% 26.01/26.38 c_Groups_Oone__class_Oone( X ) = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.38 (81645) {G0,W7,D3,L2,V1,M2} { ! class_Rings_Ozero__neq__one( X ), !
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oone__class_Oone( X ) }.
% 26.01/26.38 (81646) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.38 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 26.01/26.38 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 26.01/26.38 (81647) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.38 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 26.01/26.38 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 26.01/26.38 (81648) {G0,W26,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring( X ), hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 26.01/26.38 , T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 26.01/26.38 (81649) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.38 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, T, Z ) ), Y ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), T ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y )
% 26.01/26.38 ) }.
% 26.01/26.38 (81650) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.38 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, T, Z ) ), Y ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), T ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y )
% 26.01/26.38 ) }.
% 26.01/26.38 (81651) {G0,W32,D7,L2,V5,M2} { ! class_Rings_Osemiring( X ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ) ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), c_Groups_Oplus__class_Oplus( X, U, Z ) ), T ), Y ) }.
% 26.01/26.38 (81652) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.38 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 26.01/26.38 (81653) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.38 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 26.01/26.38 (81654) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.38 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 26.01/26.38 (81655) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.38 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 26.01/26.38 (81656) {G0,W17,D3,L3,V2,M3} { ! c_Groups_Ominus__class_Ominus(
% 26.01/26.38 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 26.01/26.38 (81657) {G0,W30,D7,L1,V4,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 26.01/26.38 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 26.01/26.38 (81658) {G0,W20,D5,L3,V3,M3} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), Z ), X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 26.01/26.38 Y = X }.
% 26.01/26.38 (81659) {G0,W17,D5,L2,V3,M2} { ! Z = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z )
% 26.01/26.38 , X ) }.
% 26.01/26.38 (81660) {G0,W16,D5,L2,V3,M2} { ! Y = X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 26.01/26.38 (81661) {G0,W11,D4,L2,V3,M2} { ! class_Groups_Ogroup__add( X ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, Z, Y )
% 26.01/26.38 , Y ) = Z }.
% 26.01/26.38 (81662) {G0,W11,D4,L2,V3,M2} { ! class_Groups_Ogroup__add( X ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, Z, Y )
% 26.01/26.38 , Y ) = Z }.
% 26.01/26.38 (81663) {G0,W23,D4,L2,V5,M2} { ! class_Groups_Oab__group__add( X ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 26.01/26.38 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 26.01/26.38 ( X, c_Groups_Ominus__class_Ominus( X, U, Z ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 26.01/26.38 (81664) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X )
% 26.01/26.38 ), Y ) = Y }.
% 26.01/26.38 (81665) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Ocomm__monoid__mult( X ),
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone
% 26.01/26.38 ( X ) ), Y ) = Y }.
% 26.01/26.38 (81666) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone
% 26.01/26.38 ( X ) ) = Y }.
% 26.01/26.38 (81667) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Ocomm__monoid__mult( X ),
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 26.01/26.38 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 26.01/26.38 (81668) {G0,W9,D4,L2,V2,M2} { ! class_Groups_Ogroup__add( X ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Ozero__class_Ozero( X ) ) =
% 26.01/26.38 Y }.
% 26.01/26.38 (81669) {G0,W10,D3,L3,V2,M3} { ! class_Groups_Ozero( X ), !
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) = Y, Y = c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ) }.
% 26.01/26.38 (81670) {G0,W10,D3,L3,V2,M3} { ! class_Groups_Ozero( X ), ! Y =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) = Y
% 26.01/26.38 }.
% 26.01/26.38 (81671) {G0,W25,D7,L2,V4,M2} { ! class_Groups_Oab__semigroup__mult( X ),
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 26.01/26.38 (81672) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__semigroup__add( X )
% 26.01/26.38 , ! c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus
% 26.01/26.38 ( X, Y, T ), Z = Y }.
% 26.01/26.38 (81673) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__ab__semigroup__add
% 26.01/26.38 ( X ), ! c_Groups_Oplus__class_Oplus( X, T, Z ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, T, Y ), Z = Y }.
% 26.01/26.38 (81674) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__semigroup__add( X )
% 26.01/26.38 , ! c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus
% 26.01/26.38 ( X, T, Y ), Z = Y }.
% 26.01/26.38 (81675) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__semigroup__add( X )
% 26.01/26.38 , ! c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus
% 26.01/26.38 ( X, Y, Z ), T = Y }.
% 26.01/26.38 (81676) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__semigroup__add( X )
% 26.01/26.38 , ! T = Y, c_Groups_Oplus__class_Oplus( X, T, Z ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 26.01/26.38 (81677) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__semigroup__add( X )
% 26.01/26.38 , ! c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus
% 26.01/26.38 ( X, T, Y ), Z = Y }.
% 26.01/26.38 (81678) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__semigroup__add( X )
% 26.01/26.38 , ! Z = Y, c_Groups_Oplus__class_Oplus( X, T, Z ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 26.01/26.38 (81679) {G0,W17,D4,L2,V4,M2} { ! class_Groups_Oab__semigroup__add( X ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y
% 26.01/26.38 ) = c_Groups_Oplus__class_Oplus( X, T, c_Groups_Oplus__class_Oplus( X, Z
% 26.01/26.38 , Y ) ) }.
% 26.01/26.38 (81680) {G0,W10,D3,L3,V2,M3} { ! class_Groups_Oone( X ), !
% 26.01/26.38 c_Groups_Oone__class_Oone( X ) = Y, Y = c_Groups_Oone__class_Oone( X )
% 26.01/26.38 }.
% 26.01/26.38 (81681) {G0,W10,D3,L3,V2,M3} { ! class_Groups_Oone( X ), ! Y =
% 26.01/26.38 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) = Y }.
% 26.01/26.38 (81682) {G0,W17,D3,L4,V5,M4} { ! class_Groups_Oab__group__add( X ), !
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 26.01/26.38 ( X, Z, Y ), ! U = T, Z = Y }.
% 26.01/26.38 (81683) {G0,W17,D3,L4,V5,M4} { ! class_Groups_Oab__group__add( X ), !
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 26.01/26.38 ( X, Z, Y ), ! Z = Y, U = T }.
% 26.01/26.38 (81684) {G0,W9,D4,L2,V2,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Ozero__class_Ozero( X ) ) = Y
% 26.01/26.38 }.
% 26.01/26.38 (81685) {G0,W9,D4,L2,V2,M2} { ! class_Groups_Omonoid__add( X ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Ozero__class_Ozero( X ) ) = Y
% 26.01/26.38 }.
% 26.01/26.38 (81686) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.38 ( X ), ! c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus(
% 26.01/26.38 X, Y, Y ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.38 (81687) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.38 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 26.01/26.38 }.
% 26.01/26.38 (81688) {G0,W9,D4,L2,V2,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Ozero__class_Ozero( X ), Y ) = Y
% 26.01/26.38 }.
% 26.01/26.38 (81689) {G0,W9,D4,L2,V2,M2} { ! class_Groups_Omonoid__add( X ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Ozero__class_Ozero( X ), Y ) = Y
% 26.01/26.38 }.
% 26.01/26.38 (81690) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), !
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ), Z = Y }.
% 26.01/26.38 (81691) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), ! Z = Y,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ) }.
% 26.01/26.38 (81692) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Oab__group__add( X ), ! Z =
% 26.01/26.38 Y, c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero
% 26.01/26.38 ( X ) }.
% 26.01/26.38 (81693) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Oab__group__add( X ), !
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ), Z = Y }.
% 26.01/26.38 (81694) {G0,W9,D3,L2,V2,M2} { ! class_Groups_Ogroup__add( X ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ) }.
% 26.01/26.38 (81695) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.38 ( X ), ! c_Groups_Oplus__class_Oplus( X, Y, Y ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 }.
% 26.01/26.38 (81696) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.38 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 }.
% 26.01/26.38 (81697) {G0,W9,D4,L1,V0,M1} { !
% 26.01/26.38 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 26.01/26.38 v_pa____ ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 26.01/26.38 (81698) {G0,W29,D7,L3,V3,M3} { ! class_Groups_Omonoid__mult( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP
% 26.01/26.38 ( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 26.01/26.38 ( tc_Nat_Onat ) ) ) ), Z ) = hAPP( hAPP( c_Power_Opower__class_Opower( X
% 26.01/26.38 ), Z ), Y ) }.
% 26.01/26.38 (81699) {G0,W35,D7,L2,V3,M2} { ! class_Rings_Ocomm__ring__1( X ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 26.01/26.38 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 26.01/26.38 (81700) {G0,W10,D3,L2,V2,M2} { ! Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 26.01/26.38 (81701) {G0,W18,D6,L2,V2,M2} { Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 26.01/26.38 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 26.01/26.38 ( tc_Nat_Onat ) ), X ) ) }.
% 26.01/26.38 (81702) {G0,W20,D7,L1,V0,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 26.01/26.38 v_k____, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 26.01/26.38 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 26.01/26.38 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 26.01/26.38 tc_Complex_Ocomplex ), c_Polynomial_Omonom( tc_Complex_Ocomplex, v_a____
% 26.01/26.38 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ) }.
% 26.01/26.38 (81703) {G0,W44,D6,L7,V6,M7} { ! class_Rings_Olinordered__semiring__1( X )
% 26.01/26.38 , ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 26.01/26.38 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 26.01/26.38 ), Y ) }.
% 26.01/26.38 (81704) {G0,W31,D6,L4,V3,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 26.01/26.38 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 26.01/26.38 (81705) {G0,W14,D4,L2,V2,M2} { ! Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), c_Fact_Ofact__class_Ofact( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 26.01/26.38 c_Fact_Ofact__class_Ofact( tc_Nat_Onat, X ) }.
% 26.01/26.38 (81706) {G0,W29,D7,L2,V2,M2} { Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), c_Fact_Ofact__class_Ofact( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 26.01/26.38 ( tc_Nat_Onat, Y, X ) ), c_Fact_Ofact__class_Ofact( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 26.01/26.38 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) ) }.
% 26.01/26.38 (81707) {G0,W5,D3,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 26.01/26.38 (81708) {G0,W10,D4,L1,V0,M1} { c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 26.01/26.38 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 26.01/26.38 v_pa____ ) ) }.
% 26.01/26.38 (81709) {G0,W5,D3,L1,V1,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.38 (81710) {G0,W5,D3,L1,V1,M1} { c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 X, c_Nat_OSuc( X ) ) }.
% 26.01/26.38 (81711) {G0,W10,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Nat_OSuc( Y ), c_Nat_OSuc( X ) ) }.
% 26.01/26.38 (81712) {G0,W6,D3,L1,V1,M1} { c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 26.01/26.38 (81713) {G0,W20,D3,L4,V5,M4} { !
% 26.01/26.38 class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 26.01/26.38 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 26.01/26.38 (81714) {G0,W20,D3,L4,V5,M4} { !
% 26.01/26.38 class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 26.01/26.38 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 26.01/26.38 , Y, T ) ) }.
% 26.01/26.38 (81715) {G0,W12,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), alpha1( X, Y ) }.
% 26.01/26.38 (81716) {G0,W9,D3,L2,V2,M2} { ! Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc
% 26.01/26.38 ( X ) ) }.
% 26.01/26.38 (81717) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 26.01/26.38 (81718) {G0,W9,D4,L2,V3,M2} { ! alpha1( X, Y ), Y = c_Nat_OSuc( skol3( Z,
% 26.01/26.38 Y ) ) }.
% 26.01/26.38 (81719) {G0,W9,D3,L2,V2,M2} { ! alpha1( X, Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol3( X, Y ), X ) }.
% 26.01/26.38 (81720) {G0,W11,D3,L3,V3,M3} { ! Y = c_Nat_OSuc( Z ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ), alpha1( X, Y ) }.
% 26.01/26.38 (81721) {G0,W10,D4,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 26.01/26.38 ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (81722) {G0,W10,D4,L2,V1,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc
% 26.01/26.38 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 26.01/26.38 (81723) {G0,W10,D4,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), X =
% 26.01/26.38 c_Nat_OSuc( skol4( X ) ) }.
% 26.01/26.38 (81724) {G0,W9,D3,L2,V2,M2} { ! X = c_Nat_OSuc( Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), X ) }.
% 26.01/26.38 (81725) {G0,W13,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, Y, skol5( X, Y ) ) ) }.
% 26.01/26.38 (81726) {G0,W11,D4,L2,V3,M2} { ! X = c_Nat_OSuc(
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81727) {G0,W8,D4,L1,V2,M1} { c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 Y, c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 26.01/26.38 (81728) {G0,W8,D4,L1,V2,M1} { c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 Y, c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 26.01/26.38 (81729) {G0,W20,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 c_Nat_OSuc( Z ) ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) ), c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81730) {G0,W20,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y
% 26.01/26.38 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc
% 26.01/26.38 ( Z ) ), X ) ) }.
% 26.01/26.38 (81731) {G0,W20,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 c_Nat_OSuc( Z ) ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81732) {G0,W20,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ),
% 26.01/26.38 Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc
% 26.01/26.38 ( Z ) ), X ) ) }.
% 26.01/26.38 (81733) {G0,W8,D3,L1,V2,M1} { c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 26.01/26.38 (81734) {G0,W15,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 26.01/26.38 c_Nat_OSuc( X ), Y ) = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 26.01/26.38 tc_Nat_Onat, X, Y ) ) }.
% 26.01/26.38 (81735) {G0,W22,D3,L4,V3,M4} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 26.01/26.38 , Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 26.01/26.38 (81736) {G0,W22,D3,L4,V3,M4} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 26.01/26.38 , Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 26.01/26.38 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 26.01/26.38 ) }.
% 26.01/26.38 (81737) {G0,W18,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 26.01/26.38 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 26.01/26.38 (81738) {G0,W6,D3,L1,V1,M1} { ! c_Fact_Ofact__class_Ofact( tc_Nat_Onat, X
% 26.01/26.38 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (81739) {G0,W7,D3,L1,V1,M1} { c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Fact_Ofact__class_Ofact(
% 26.01/26.38 tc_Nat_Onat, X ) ) }.
% 26.01/26.38 (81740) {G0,W7,D3,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 26.01/26.38 c_Fact_Ofact__class_Ofact( tc_Nat_Onat, X ) ) }.
% 26.01/26.38 (81741) {G0,W8,D4,L1,V0,M1} { c_Fact_Ofact__class_Ofact( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.38 (81742) {G0,W8,D4,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 26.01/26.38 c_Fact_Ofact__class_Ofact( tc_Nat_Onat, X ) ) }.
% 26.01/26.38 (81743) {G0,W9,D5,L1,V0,M1} { c_Fact_Ofact__class_Ofact( tc_Nat_Onat,
% 26.01/26.38 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.38 (81744) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Fact_Ofact__class_Ofact(
% 26.01/26.38 tc_Nat_Onat, X ), c_Fact_Ofact__class_Ofact( tc_Nat_Onat, Y ) ) }.
% 26.01/26.38 (81745) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.01/26.38 c_Fact_Ofact__class_Ofact( tc_Nat_Onat, Y ), c_Fact_Ofact__class_Ofact(
% 26.01/26.38 tc_Nat_Onat, X ) ) }.
% 26.01/26.38 (81746) {G0,W4,D2,L1,V1,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , X, X ) }.
% 26.01/26.38 (81747) {G0,W4,D3,L1,V1,M1} { ! X = c_Nat_OSuc( X ) }.
% 26.01/26.38 (81748) {G0,W4,D3,L1,V1,M1} { ! c_Nat_OSuc( X ) = X }.
% 26.01/26.38 (81749) {G0,W5,D3,L1,V1,M1} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Nat_OSuc( X ), X ) }.
% 26.01/26.38 (81750) {G0,W9,D3,L2,V2,M2} { c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) )
% 26.01/26.38 }.
% 26.01/26.38 (81751) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , X, c_Nat_OSuc( Y ) ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 26.01/26.38 X ) }.
% 26.01/26.38 (81752) {G0,W9,D3,L2,V2,M2} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.01/26.38 c_Nat_OSuc( X ), Y ) }.
% 26.01/26.38 (81753) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Nat_OSuc( X ), Y ), ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81754) {G0,W11,D2,L3,V2,M3} { Y = X, c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y )
% 26.01/26.38 }.
% 26.01/26.38 (81755) {G0,W7,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , Y, X ), ! Y = X }.
% 26.01/26.38 (81756) {G0,W7,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , X, Y ), ! Y = X }.
% 26.01/26.38 (81757) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y )
% 26.01/26.38 , X ) }.
% 26.01/26.38 (81758) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Nat_OSuc( Y ), X ), c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81759) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81760) {G0,W7,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , Y, X ), ! Y = X }.
% 26.01/26.38 (81761) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 26.01/26.38 , X ) }.
% 26.01/26.38 (81762) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 26.01/26.38 Y = X }.
% 26.01/26.38 (81763) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81764) {G0,W7,D2,L2,V2,M2} { ! Y = X, c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81765) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , Y, c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 26.01/26.38 , X ) }.
% 26.01/26.38 (81766) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 26.01/26.38 c_Nat_OSuc( X ) ) }.
% 26.01/26.38 (81767) {G0,W12,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), Y = X }.
% 26.01/26.38 (81768) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X )
% 26.01/26.38 ) }.
% 26.01/26.38 (81769) {G0,W8,D3,L2,V2,M2} { ! Y = X, c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 26.01/26.38 (81770) {G0,W13,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X ) }.
% 26.01/26.38 (81771) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 26.01/26.38 c_Nat_OSuc( X ) ) }.
% 26.01/26.38 (81772) {G0,W9,D3,L2,V2,M2} { ! Y = c_Nat_OSuc( X ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 26.01/26.38 (81773) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Nat_OSuc( Y ), X ), c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81774) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y )
% 26.01/26.38 , X ) }.
% 26.01/26.38 (81775) {G0,W8,D3,L2,V2,M2} { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X
% 26.01/26.38 }.
% 26.01/26.38 (81776) {G0,W8,D3,L2,V2,M2} { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X )
% 26.01/26.38 }.
% 26.01/26.38 (81777) {G0,W10,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc( X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81778) {G0,W10,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Nat_OSuc( Y ), c_Nat_OSuc( X ) ) }.
% 26.01/26.38 (81779) {G0,W10,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc( X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81780) {G0,W10,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.01/26.38 c_Nat_OSuc( Y ), c_Nat_OSuc( X ) ) }.
% 26.01/26.38 (81781) {G0,W12,D3,L3,V2,M3} { c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X
% 26.01/26.38 ) ), Y = X }.
% 26.01/26.38 (81782) {G0,W12,D3,L3,V2,M3} { c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , Y, X ), ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 26.01/26.38 c_Nat_OSuc( X ) ) }.
% 26.01/26.38 (81783) {G0,W12,D3,L3,V2,M3} { c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X
% 26.01/26.38 ) ), X = Y }.
% 26.01/26.38 (81784) {G0,W11,D2,L3,V2,M3} { Y = X, c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y )
% 26.01/26.38 }.
% 26.01/26.38 (81785) {G0,W13,D2,L4,V3,M4} { ! class_Rings_Olinordered__idom( X ), Z = Y
% 26.01/26.38 , c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless
% 26.01/26.38 ( X, Y, Z ) }.
% 26.01/26.38 (81786) {G0,W4,D2,L1,V1,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , X, X ) }.
% 26.01/26.38 (81787) {G0,W7,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , Y, X ), ! X = Y }.
% 26.01/26.38 (81788) {G0,W7,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , Y, X ), ! Y = X }.
% 26.01/26.38 (81789) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81790) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X )
% 26.01/26.38 ) }.
% 26.01/26.38 (81791) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 26.01/26.38 c_Nat_OSuc( X ) ) }.
% 26.01/26.38 (81792) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 26.01/26.38 c_Nat_OSuc( X ) ) }.
% 26.01/26.38 (81793) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y )
% 26.01/26.38 , X ) }.
% 26.01/26.38 (81794) {G0,W12,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 26.01/26.38 c_Nat_OSuc( Y ) ), X = Y }.
% 26.01/26.38 (81795) {G0,W12,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! X = Y, c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , X, c_Nat_OSuc( Y ) ) }.
% 26.01/26.38 (81796) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 26.01/26.38 , X ) }.
% 26.01/26.38 (81797) {G0,W13,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X, c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 26.01/26.38 (81798) {G0,W13,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z )
% 26.01/26.38 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 26.01/26.38 (81799) {G0,W12,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), Y = X }.
% 26.01/26.38 (81800) {G0,W13,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X ) }.
% 26.01/26.38 (81801) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , c_Nat_OSuc( Y ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 26.01/26.38 ) }.
% 26.01/26.38 (81802) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Nat_OSuc( Y ), X ), c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81803) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Nat_OSuc( Y ), X ), c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81804) {G0,W8,D3,L2,V2,M2} { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X
% 26.01/26.38 }.
% 26.01/26.38 (81805) {G0,W10,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc( X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81806) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81807) {G0,W7,D2,L2,V2,M2} { ! Y = X, c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81808) {G0,W14,D4,L3,V3,M3} { alpha23( X, Y, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ), hBOOL( hAPP( hAPP( X
% 26.01/26.38 , Y ), Z ) ) }.
% 26.01/26.38 (81809) {G0,W16,D4,L3,V3,M3} { alpha23( X, Y, Z ), ! hBOOL( hAPP( hAPP( X
% 26.01/26.38 , Y ), Z ) ), hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 26.01/26.38 (81810) {G0,W11,D2,L3,V3,M3} { ! alpha23( X, Y, Z ), alpha24( X, Y, Z ), Z
% 26.01/26.38 = Y }.
% 26.01/26.38 (81811) {G0,W14,D4,L3,V3,M3} { ! alpha23( X, Y, Z ), alpha24( X, Y, Z ), !
% 26.01/26.38 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 26.01/26.38 (81812) {G0,W8,D2,L2,V3,M2} { ! alpha24( X, Y, Z ), alpha23( X, Y, Z ) }.
% 26.01/26.38 (81813) {G0,W13,D4,L3,V3,M3} { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ),
% 26.01/26.38 alpha23( X, Y, Z ) }.
% 26.01/26.38 (81814) {G0,W8,D2,L2,V3,M2} { ! alpha24( X, Y, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 26.01/26.38 (81815) {G0,W10,D4,L2,V3,M2} { ! alpha24( X, Y, Z ), ! hBOOL( hAPP( hAPP(
% 26.01/26.38 X, Y ), Z ) ) }.
% 26.01/26.38 (81816) {G0,W14,D4,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha24( X, Y, Z )
% 26.01/26.38 }.
% 26.01/26.38 (81817) {G0,W14,D5,L1,V1,M1} { c_Fact_Ofact__class_Ofact( tc_Nat_Onat,
% 26.01/26.38 c_Nat_OSuc( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), c_Nat_OSuc( X ) ), c_Fact_Ofact__class_Ofact( tc_Nat_Onat
% 26.01/26.38 , X ) ) }.
% 26.01/26.38 (81818) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 26.01/26.38 (81819) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 26.01/26.38 (81820) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 26.01/26.38 (81821) {G0,W7,D4,L1,V0,M1} { c_Fact_Ofact__class_Ofact( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone(
% 26.01/26.38 tc_Nat_Onat ) }.
% 26.01/26.38 (81822) {G0,W30,D5,L5,V4,M5} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 26.01/26.38 (81823) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 26.01/26.38 (81824) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 26.01/26.38 (81825) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ) ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 26.01/26.38 (81826) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 26.01/26.38 (81827) {G0,W34,D5,L6,V5,M6} { ! class_Rings_Olinordered__semiring__strict
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 26.01/26.38 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 26.01/26.38 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 26.01/26.38 (81828) {G0,W34,D5,L6,V5,M6} { ! class_Rings_Olinordered__semiring__strict
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, U, T ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 X ), U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 26.01/26.38 (81829) {G0,W34,D5,L6,V5,M6} { ! class_Rings_Olinordered__semiring__strict
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 26.01/26.38 (81830) {G0,W34,D5,L6,V5,M6} { ! class_Rings_Olinordered__semiring__strict
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 26.01/26.38 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 26.01/26.38 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 26.01/26.38 (81831) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 26.01/26.38 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 26.01/26.38 (81832) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring__strict
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 26.01/26.38 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 26.01/26.38 (81833) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 26.01/26.38 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 26.01/26.38 (81834) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring__strict
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 26.01/26.38 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 26.01/26.38 (81835) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring__strict
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 26.01/26.38 (81836) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring__strict
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 26.01/26.38 (81837) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ), Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 26.01/26.38 ) }.
% 26.01/26.38 (81838) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless( X
% 26.01/26.38 , c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X
% 26.01/26.38 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 26.01/26.38 ) ) }.
% 26.01/26.38 (81839) {G0,W18,D3,L4,V4,M4} { ! class_Groups_Oordered__comm__monoid__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ), Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 26.01/26.38 ) ) }.
% 26.01/26.38 (81840) {G0,W18,D3,L4,V4,M4} { ! class_Groups_Oordered__comm__monoid__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless( X
% 26.01/26.38 , T, Z ), c_Orderings_Oord__class_Oless( X, T,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 26.01/26.38 (81841) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero
% 26.01/26.38 ( X ) ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 ) }.
% 26.01/26.38 (81842) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X, Z
% 26.01/26.38 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 ) }.
% 26.01/26.38 (81843) {G0,W27,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 26.01/26.38 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 26.01/26.38 (81844) {G0,W30,D5,L5,V4,M5} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) =
% 26.01/26.38 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 X ), Y ), Z = Y }.
% 26.01/26.38 (81845) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 26.01/26.38 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 26.01/26.38 (81846) {G0,W18,D5,L3,V3,M3} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 26.01/26.38 hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 26.01/26.38 (81847) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 26.01/26.38 (81848) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 26.01/26.38 (81849) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 26.01/26.38 (81850) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), T ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 26.01/26.38 (81851) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 26.01/26.38 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 26.01/26.38 (81852) {G0,W21,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 26.01/26.38 (81853) {G0,W21,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 26.01/26.38 (81854) {G0,W23,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 26.01/26.38 (81855) {G0,W17,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 26.01/26.38 (81856) {G0,W17,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 26.01/26.38 (81857) {G0,W23,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 26.01/26.38 (81858) {G0,W13,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 26.01/26.38 ( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 26.01/26.38 (81859) {G0,W14,D6,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), c_Nat_OSuc
% 26.01/26.38 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = X }.
% 26.01/26.38 (81860) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 26.01/26.38 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X
% 26.01/26.38 ) ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81861) {G0,W19,D5,L2,V3,M2} { c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 26.01/26.38 (81862) {G0,W18,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 26.01/26.38 (81863) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 26.01/26.38 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y
% 26.01/26.38 ) ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 26.01/26.38 (81864) {G0,W19,D5,L2,V3,M2} { c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 26.01/26.38 (81865) {G0,W18,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Z, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 26.01/26.38 (81866) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 26.01/26.38 (81867) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 26.01/26.38 (81868) {G0,W21,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 26.01/26.38 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 26.01/26.38 (81869) {G0,W21,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 26.01/26.38 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 26.01/26.38 (81870) {G0,W17,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X
% 26.01/26.38 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 26.01/26.38 (81871) {G0,W16,D3,L3,V4,M3} { !
% 26.01/26.38 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 26.01/26.38 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 26.01/26.38 ( X, T, Y ) }.
% 26.01/26.38 (81872) {G0,W16,D3,L3,V4,M3} { !
% 26.01/26.38 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 26.01/26.38 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 26.01/26.38 , Y, Z ) ) }.
% 26.01/26.38 (81873) {G0,W16,D3,L3,V4,M3} { !
% 26.01/26.38 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 26.01/26.38 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 26.01/26.38 ( X, Z, Y ) }.
% 26.01/26.38 (81874) {G0,W16,D3,L3,V4,M3} { !
% 26.01/26.38 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 26.01/26.38 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 26.01/26.38 , T, Y ) ) }.
% 26.01/26.38 (81875) {G0,W16,D3,L3,V4,M3} { !
% 26.01/26.38 class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 26.01/26.38 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 26.01/26.38 , Y, T ) ) }.
% 26.01/26.38 (81876) {G0,W16,D3,L3,V4,M3} { !
% 26.01/26.38 class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 26.01/26.38 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 26.01/26.38 , T, Y ) ) }.
% 26.01/26.38 (81877) {G0,W20,D3,L4,V5,M4} { !
% 26.01/26.38 class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 26.01/26.38 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 26.01/26.38 , T ) ) }.
% 26.01/26.38 (81878) {G0,W16,D3,L3,V4,M3} { !
% 26.01/26.38 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 26.01/26.38 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 26.01/26.38 ( X, Z, Y ) }.
% 26.01/26.38 (81879) {G0,W16,D3,L3,V4,M3} { !
% 26.01/26.38 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 26.01/26.38 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 26.01/26.38 ( X, Z, Y ) }.
% 26.01/26.38 (81880) {G0,W19,D3,L4,V5,M4} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.38 ), ! c_Groups_Ominus__class_Ominus( X, U, T ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 26.01/26.38 ( X, U, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 26.01/26.38 (81881) {G0,W19,D3,L4,V5,M4} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.38 ), ! c_Groups_Ominus__class_Ominus( X, U, T ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 26.01/26.38 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, U, T ) }.
% 26.01/26.38 (81882) {G0,W16,D3,L3,V4,M3} { !
% 26.01/26.38 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 26.01/26.38 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 26.01/26.38 (81883) {G0,W16,D3,L3,V4,M3} { !
% 26.01/26.38 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 26.01/26.38 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 26.01/26.38 (81884) {G0,W16,D3,L3,V4,M3} { !
% 26.01/26.38 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 26.01/26.38 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 26.01/26.38 (81885) {G0,W16,D3,L3,V4,M3} { !
% 26.01/26.38 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 26.01/26.38 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 26.01/26.38 (81886) {G0,W16,D3,L3,V4,M3} { ! class_Groups_Oordered__ab__semigroup__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 26.01/26.38 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 26.01/26.38 (81887) {G0,W16,D3,L3,V4,M3} { ! class_Groups_Oordered__ab__semigroup__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 26.01/26.38 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 26.01/26.38 (81888) {G0,W20,D3,L4,V5,M4} { ! class_Groups_Oordered__ab__semigroup__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 26.01/26.38 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 26.01/26.38 (81889) {G0,W16,D3,L3,V4,M3} { !
% 26.01/26.38 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 26.01/26.38 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 26.01/26.38 (81890) {G0,W16,D3,L3,V4,M3} { !
% 26.01/26.38 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 26.01/26.38 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 26.01/26.38 (81891) {G0,W5,D3,L1,V1,M1} { ! c_Nat_OSuc( X ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (81892) {G0,W5,D3,L1,V1,M1} { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 26.01/26.38 = c_Nat_OSuc( X ) }.
% 26.01/26.38 (81893) {G0,W5,D3,L1,V1,M1} { ! c_Nat_OSuc( X ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (81894) {G0,W5,D3,L1,V1,M1} { ! c_Nat_OSuc( X ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (81895) {G0,W5,D3,L1,V1,M1} { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 26.01/26.38 = c_Nat_OSuc( X ) }.
% 26.01/26.38 (81896) {G0,W5,D3,L1,V1,M1} { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 26.01/26.38 = c_Nat_OSuc( X ) }.
% 26.01/26.38 (81897) {G0,W19,D3,L4,V5,M4} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.38 ), ! c_Groups_Ominus__class_Ominus( X, U, T ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 26.01/26.38 (81898) {G0,W19,D3,L4,V5,M4} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.38 ), ! c_Groups_Ominus__class_Ominus( X, U, T ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 26.01/26.38 (81899) {G0,W11,D4,L1,V2,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 26.01/26.38 , c_Nat_OSuc( X ) ) = c_Nat_OSuc( c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, Y, X ) ) }.
% 26.01/26.38 (81900) {G0,W11,D4,L1,V2,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 26.01/26.38 c_Nat_OSuc( Y ), X ) = c_Nat_OSuc( c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, Y, X ) ) }.
% 26.01/26.38 (81901) {G0,W11,D4,L1,V2,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 26.01/26.38 c_Nat_OSuc( Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 26.01/26.38 c_Nat_OSuc( X ) ) }.
% 26.01/26.38 (81902) {G0,W9,D3,L2,V1,M2} { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 26.01/26.38 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 26.01/26.38 (81903) {G0,W8,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , Y, X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (81904) {G0,W5,D3,L1,V1,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.38 (81905) {G0,W9,D3,L2,V1,M2} { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 26.01/26.38 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 26.01/26.38 (81906) {G0,W9,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! X =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (81907) {G0,W5,D3,L1,V1,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.38 (81908) {G0,W9,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (81909) {G0,W9,D3,L2,V1,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.38 (81910) {G0,W5,D3,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 26.01/26.38 (81911) {G0,W18,D5,L2,V3,M2} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ), Y =
% 26.01/26.38 X }.
% 26.01/26.38 (81912) {G0,W18,D5,L2,V3,M2} { ! Y = X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ) =
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 26.01/26.38 ), X ) }.
% 26.01/26.38 (81913) {G0,W17,D5,L1,V3,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 26.01/26.38 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ),
% 26.01/26.38 c_Nat_OSuc( X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 26.01/26.38 (81914) {G0,W11,D4,L1,V2,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 26.01/26.38 , c_Nat_OSuc( Y ), c_Nat_OSuc( X ) ) = c_Groups_Ominus__class_Ominus(
% 26.01/26.38 tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81915) {G0,W7,D3,L1,V2,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), Y ) }.
% 26.01/26.38 (81916) {G0,W7,D3,L1,V2,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), X ) }.
% 26.01/26.38 (81917) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81918) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 26.01/26.38 (81919) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 26.01/26.38 (81920) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 26.01/26.38 (81921) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 26.01/26.38 (81922) {G0,W18,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z )
% 26.01/26.38 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 26.01/26.38 ( tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) )
% 26.01/26.38 }.
% 26.01/26.38 (81923) {G0,W17,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 26.01/26.38 (81924) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81925) {G0,W7,D3,L1,V2,M1} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 26.01/26.38 (81926) {G0,W7,D3,L1,V2,M1} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 26.01/26.38 (81927) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 26.01/26.38 skol6( X, Y ) ) }.
% 26.01/26.38 (81928) {G0,W10,D3,L2,V3,M2} { ! X = c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 26.01/26.38 ) }.
% 26.01/26.38 (81929) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81930) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 26.01/26.38 (81931) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 26.01/26.38 (81932) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 26.01/26.38 (81933) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 26.01/26.38 (81934) {G0,W18,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T
% 26.01/26.38 , Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 26.01/26.38 (81935) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81936) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81937) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 26.01/26.38 (81938) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (81939) {G0,W9,D5,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 26.01/26.38 , X ), X ) ) }.
% 26.01/26.38 (81940) {G0,W14,D6,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 26.01/26.38 , X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X )
% 26.01/26.38 ) ) }.
% 26.01/26.38 (81941) {G0,W18,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 26.01/26.38 (81942) {G0,W18,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 26.01/26.38 (81943) {G0,W22,D5,L3,V4,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T
% 26.01/26.38 , Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 26.01/26.38 (81944) {G0,W18,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z )
% 26.01/26.38 , c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 26.01/26.38 (81945) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ), X ) }.
% 26.01/26.38 (81946) {G0,W22,D3,L4,V3,M4} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 26.01/26.38 , Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 26.01/26.38 (81947) {G0,W22,D3,L4,V3,M4} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 26.01/26.38 , Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 26.01/26.38 (81948) {G0,W23,D4,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 26.01/26.38 , Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 26.01/26.38 (81949) {G0,W20,D3,L4,V3,M4} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 26.01/26.38 , Z ), ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 26.01/26.38 (81950) {G0,W20,D3,L4,V3,M4} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 26.01/26.38 , Z ), ! X = Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 26.01/26.38 (81951) {G0,W13,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 26.01/26.38 (81952) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 26.01/26.38 (81953) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 26.01/26.38 (81954) {G0,W7,D3,L1,V2,M1} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 26.01/26.38 (81955) {G0,W15,D3,L3,V2,M3} { ! class_Rings_Olinordered__idom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 26.01/26.38 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 26.01/26.38 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.38 (81956) {G0,W15,D3,L3,V2,M3} { ! class_Rings_Olinordered__idom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 26.01/26.38 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.38 (81957) {G0,W23,D5,L4,V3,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 26.01/26.38 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 26.01/26.38 c_Groups_Oone__class_Oone( X ) ) }.
% 26.01/26.38 (81958) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 26.01/26.38 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 26.01/26.38 (81959) {G0,W30,D5,L5,V4,M5} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 26.01/26.38 ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Oone__class_Oone( X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 26.01/26.38 (81960) {G0,W30,D5,L5,V4,M5} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 26.01/26.38 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 26.01/26.38 (81961) {G0,W33,D5,L6,V4,M6} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 26.01/26.38 (81962) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( X,
% 26.01/26.38 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 26.01/26.38 ( X ), Y ), Z ) ) }.
% 26.01/26.38 (81963) {G0,W31,D7,L3,V4,M3} { ! class_Groups_Omonoid__mult( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 26.01/26.38 tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 26.01/26.38 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 26.01/26.38 (81964) {G0,W13,D5,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), c_Nat_OSuc
% 26.01/26.38 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 26.01/26.38 (81965) {G0,W13,D5,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), X =
% 26.01/26.38 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 26.01/26.38 (81966) {G0,W39,D6,L3,V5,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 26.01/26.38 (81967) {G0,W39,D6,L3,V5,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 26.01/26.38 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 26.01/26.38 (81968) {G0,W39,D6,L3,V5,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 26.01/26.38 (81969) {G0,W39,D6,L3,V5,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 26.01/26.38 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 26.01/26.38 (81970) {G0,W21,D6,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 26.01/26.38 c_Fact_Ofact__class_Ofact( tc_Nat_Onat, X ) = hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 26.01/26.38 c_Fact_Ofact__class_Ofact( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 26.01/26.38 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 26.01/26.38 (81971) {G0,W22,D6,L1,V5,M1} { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z
% 26.01/26.38 ), Y ), c_Nat_OSuc( X ) ) = hAPP( hAPP( Z, Y ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower_Opower( U, T, Z ), Y ), X ) ) }.
% 26.01/26.38 (81972) {G0,W44,D6,L7,V6,M7} { !
% 26.01/26.38 class_Rings_Olinordered__semiring__1__strict( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 26.01/26.38 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), U ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 26.01/26.38 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 26.01/26.38 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 26.01/26.38 (81973) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Olinordered__ring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Ozero__class_Ozero
% 26.01/26.38 ( X ) ) }.
% 26.01/26.38 (81974) {G0,W26,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha2( X, Y, Z, T ),
% 26.01/26.38 alpha14( X, Y, Z, T ) }.
% 26.01/26.38 (81975) {G0,W21,D5,L3,V4,M3} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP
% 26.01/26.38 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 26.01/26.38 (81976) {G0,W21,D5,L3,V4,M3} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! alpha14( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP
% 26.01/26.38 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 26.01/26.38 (81977) {G0,W10,D3,L2,V4,M2} { ! alpha14( X, Y, Z, T ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 26.01/26.38 }.
% 26.01/26.38 (81978) {G0,W9,D2,L2,V4,M2} { ! alpha14( X, Y, Z, T ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 26.01/26.38 (81979) {G0,W14,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless( X, Z,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X, Y
% 26.01/26.38 , T ), alpha14( X, Y, Z, T ) }.
% 26.01/26.38 (81980) {G0,W10,D3,L2,V4,M2} { ! alpha2( X, Y, Z, T ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 26.01/26.38 }.
% 26.01/26.38 (81981) {G0,W9,D2,L2,V4,M2} { ! alpha2( X, Y, Z, T ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 26.01/26.38 (81982) {G0,W14,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless( X
% 26.01/26.38 , T, Y ), alpha2( X, Y, Z, T ) }.
% 26.01/26.38 (81983) {G0,W26,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha3( X, Y, Z, T ),
% 26.01/26.38 alpha15( X, Y, Z, T ) }.
% 26.01/26.38 (81984) {G0,W21,D5,L3,V4,M3} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP
% 26.01/26.38 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 26.01/26.38 (81985) {G0,W21,D5,L3,V4,M3} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! alpha15( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP
% 26.01/26.38 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 26.01/26.38 (81986) {G0,W10,D3,L2,V4,M2} { ! alpha15( X, Y, Z, T ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 26.01/26.38 }.
% 26.01/26.38 (81987) {G0,W9,D2,L2,V4,M2} { ! alpha15( X, Y, Z, T ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 26.01/26.38 (81988) {G0,W14,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless( X, T,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X, Y
% 26.01/26.38 , Z ), alpha15( X, Y, Z, T ) }.
% 26.01/26.38 (81989) {G0,W10,D3,L2,V4,M2} { ! alpha3( X, Y, Z, T ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 26.01/26.38 }.
% 26.01/26.38 (81990) {G0,W9,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 26.01/26.38 (81991) {G0,W14,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 26.01/26.38 , Z, Y ), alpha3( X, Y, Z, T ) }.
% 26.01/26.38 (81992) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 , Y ), ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 26.01/26.38 (81993) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 26.01/26.38 (81994) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semiring__strict
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ), Y ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 26.01/26.38 ( X ), Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 26.01/26.38 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 26.01/26.38 (81995) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semiring__strict
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ), Y ), ! c_Orderings_Oord__class_Oless( X, Z,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.38 (81996) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semiring__strict
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ), Y ), ! c_Orderings_Oord__class_Oless( X, Z,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.38 (81997) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semiring__strict
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 26.01/26.38 }.
% 26.01/26.38 (81998) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semiring__strict
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 26.01/26.38 }.
% 26.01/26.38 (81999) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ) ), ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 26.01/26.38 (82000) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ) ), ! c_Orderings_Oord__class_Oless( X, Z, T ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 26.01/26.38 (82001) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semiring__strict
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero
% 26.01/26.38 ( X ) ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 26.01/26.38 ( X ), Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 26.01/26.38 ( X ) ) }.
% 26.01/26.38 (82002) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ) ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero
% 26.01/26.38 ( X ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 26.01/26.38 (82003) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring__strict
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 26.01/26.38 (82004) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring__strict
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 26.01/26.38 (82005) {G0,W25,D5,L4,V4,M4} { !
% 26.01/26.38 class_Rings_Olinordered__comm__semiring__strict( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 26.01/26.38 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 26.01/26.38 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 26.01/26.38 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 26.01/26.38 (82006) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 26.01/26.38 (82007) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 26.01/26.38 (82008) {G0,W18,D3,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 26.01/26.38 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 26.01/26.38 ( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 26.01/26.38 (82009) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 26.01/26.38 }.
% 26.01/26.38 (82010) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 26.01/26.38 (82011) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X
% 26.01/26.38 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 26.01/26.38 }.
% 26.01/26.38 (82012) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero
% 26.01/26.38 ( X ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X
% 26.01/26.38 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.38 (82013) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ), Y ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 26.01/26.38 ( X ), Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 26.01/26.38 ( X ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 26.01/26.38 (82014) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero
% 26.01/26.38 ( X ) ), ! c_Orderings_Oord__class_Oless( X, Z,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 ) }.
% 26.01/26.38 (82015) {G0,W8,D3,L2,V1,M2} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.38 (82016) {G0,W8,D3,L2,V1,M2} { ! class_Rings_Olinordered__semidom( X ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.38 c_Groups_Oone__class_Oone( X ) ) }.
% 26.01/26.38 (82017) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 26.01/26.38 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.38 (82018) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X
% 26.01/26.38 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 26.01/26.38 (82019) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Olinordered__ring( X ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 26.01/26.38 (82020) {G0,W20,D5,L4,V3,M4} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha4(
% 26.01/26.38 X, Y, Z ), alpha16( X, Y, Z ) }.
% 26.01/26.38 (82021) {G0,W16,D5,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 26.01/26.38 (82022) {G0,W16,D5,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 26.01/26.38 (82023) {G0,W9,D3,L2,V3,M2} { ! alpha16( X, Y, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 ) }.
% 26.01/26.38 (82024) {G0,W9,D3,L2,V3,M2} { ! alpha16( X, Y, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 ) }.
% 26.01/26.38 (82025) {G0,W14,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 X, Y, c_Groups_Ozero__class_Ozero( X ) ), alpha16( X, Y, Z ) }.
% 26.01/26.38 (82026) {G0,W9,D3,L2,V3,M2} { ! alpha4( X, Y, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 26.01/26.38 ) }.
% 26.01/26.38 (82027) {G0,W9,D3,L2,V3,M2} { ! alpha4( X, Y, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 26.01/26.38 ) }.
% 26.01/26.38 (82028) {G0,W14,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 26.01/26.38 ), alpha4( X, Y, Z ) }.
% 26.01/26.38 (82029) {G0,W20,D5,L4,V3,M4} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 26.01/26.38 ( X ) ), alpha5( X, Y, Z ), alpha17( X, Y, Z ) }.
% 26.01/26.38 (82030) {G0,W16,D5,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP
% 26.01/26.38 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.38 (82031) {G0,W16,D5,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.38 (82032) {G0,W9,D3,L2,V3,M2} { ! alpha17( X, Y, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 ) }.
% 26.01/26.38 (82033) {G0,W9,D3,L2,V3,M2} { ! alpha17( X, Y, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 26.01/26.38 ) }.
% 26.01/26.38 (82034) {G0,W14,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 X, c_Groups_Ozero__class_Ozero( X ), Y ), alpha17( X, Y, Z ) }.
% 26.01/26.38 (82035) {G0,W9,D3,L2,V3,M2} { ! alpha5( X, Y, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 26.01/26.38 ) }.
% 26.01/26.38 (82036) {G0,W9,D3,L2,V3,M2} { ! alpha5( X, Y, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 ) }.
% 26.01/26.38 (82037) {G0,W14,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 ), alpha5( X, Y, Z ) }.
% 26.01/26.38 (82038) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__cancel__semiring( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 X ), Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 26.01/26.38 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 26.01/26.38 (82039) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__cancel__semiring( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 X ), Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 26.01/26.38 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.38 (82040) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__cancel__semiring( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 X ), Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 26.01/26.38 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.38 (82041) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__cancel__semiring( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 26.01/26.38 ( X ) ) }.
% 26.01/26.38 (82042) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__ring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 26.01/26.38 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 26.01/26.38 (82043) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Oordered__semiring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 26.01/26.38 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 26.01/26.38 (82044) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Oordered__semiring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 26.01/26.38 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 26.01/26.38 (82045) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Oordered__comm__semiring( X )
% 26.01/26.38 , ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 26.01/26.38 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 26.01/26.38 (82046) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Oordered__ring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 26.01/26.38 (82047) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Oordered__ring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 26.01/26.38 (82048) {G0,W34,D5,L6,V5,M6} { ! class_Rings_Oordered__semiring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 26.01/26.38 (82049) {G0,W34,D5,L6,V5,M6} { ! class_Rings_Oordered__semiring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 26.01/26.38 (82050) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__ring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 X ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 26.01/26.38 (82051) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__ring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 26.01/26.38 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 26.01/26.38 (82052) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__cancel__semiring( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 X ), Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 26.01/26.38 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.38 (82053) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__cancel__semiring( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 26.01/26.38 ( X ) ) }.
% 26.01/26.38 (82054) {G0,W15,D5,L3,V2,M3} { ! class_Power_Opower( X ), !
% 26.01/26.38 class_Rings_Osemiring__0( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 26.01/26.38 X ), c_Groups_Ozero__class_Ozero( X ) ), c_Nat_OSuc( Y ) ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.38 (82055) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 26.01/26.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ), Y ) }.
% 26.01/26.38 (82056) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 26.01/26.38 ( X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y
% 26.01/26.38 , Y ) ) }.
% 26.01/26.38 (82057) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 26.01/26.38 ( X ) ) }.
% 26.01/26.38 (82058) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 26.01/26.38 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ) ) }.
% 26.01/26.38 (82059) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 26.01/26.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 26.01/26.38 (82060) {G0,W23,D3,L5,V3,M5} { ! class_Groups_Oordered__comm__monoid__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 26.01/26.38 ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 }.
% 26.01/26.38 (82061) {G0,W23,D3,L5,V3,M5} { ! class_Groups_Oordered__comm__monoid__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 26.01/26.38 ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 }.
% 26.01/26.38 (82062) {G0,W27,D3,L6,V3,M6} { ! class_Groups_Oordered__comm__monoid__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 26.01/26.38 ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 26.01/26.38 = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.38 (82063) {G0,W18,D3,L4,V4,M4} { ! class_Groups_Oordered__comm__monoid__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 26.01/26.38 Y, Z ) ) }.
% 26.01/26.38 (82064) {G0,W18,D3,L4,V4,M4} { ! class_Groups_Oordered__comm__monoid__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 26.01/26.38 Z, Y ) ) }.
% 26.01/26.38 (82065) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 26.01/26.38 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 26.01/26.38 Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.38 (82066) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 26.01/26.38 (82067) {G0,W17,D5,L3,V3,M3} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 26.01/26.38 ( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 26.01/26.38 (82068) {G0,W8,D3,L2,V1,M2} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.38 (82069) {G0,W8,D3,L2,V1,M2} { ! class_Rings_Olinordered__semidom( X ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.38 c_Groups_Oone__class_Oone( X ) ) }.
% 26.01/26.38 (82070) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 26.01/26.38 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.38 (82071) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus
% 26.01/26.38 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 26.01/26.38 (82072) {G0,W10,D4,L2,V2,M2} { ! class_Rings_Olinordered__semidom( X ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oplus__class_Oplus( X, Y,
% 26.01/26.38 c_Groups_Oone__class_Oone( X ) ) ) }.
% 26.01/26.38 (82073) {G0,W21,D6,L2,V3,M2} { ! class_Power_Opower( X ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 26.01/26.38 (82074) {G0,W21,D6,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.38 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 26.01/26.38 (82075) {G0,W21,D7,L2,V3,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 26.01/26.38 hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 26.01/26.38 (82076) {G0,W21,D6,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 26.01/26.38 (82077) {G0,W21,D7,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 26.01/26.38 (82078) {G0,W17,D5,L3,V3,M3} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 26.01/26.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 26.01/26.38 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 26.01/26.38 (82079) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 26.01/26.38 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 26.01/26.38 (82080) {G0,W23,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 26.01/26.38 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 26.01/26.38 (82081) {G0,W23,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 26.01/26.38 T = Z, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP(
% 26.01/26.38 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 26.01/26.38 (82082) {G0,W14,D4,L3,V2,M3} { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 26.01/26.38 , Y, X ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 26.01/26.38 alpha6( X, Y ), alpha18( X, Y ) }.
% 26.01/26.38 (82083) {G0,W11,D4,L2,V2,M2} { ! alpha6( X, Y ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.38 (82084) {G0,W11,D4,L2,V2,M2} { ! alpha18( X, Y ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.38 (82085) {G0,W7,D3,L2,V2,M2} { ! alpha18( X, Y ), Y =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (82086) {G0,W8,D4,L2,V2,M2} { ! alpha18( X, Y ), X = c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.38 (82087) {G0,W12,D4,L3,V2,M3} { ! Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 26.01/26.38 ) ), alpha18( X, Y ) }.
% 26.01/26.38 (82088) {G0,W8,D4,L2,V2,M2} { ! alpha6( X, Y ), Y = c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.38 (82089) {G0,W7,D3,L2,V2,M2} { ! alpha6( X, Y ), X =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (82090) {G0,W12,D4,L3,V2,M3} { ! Y = c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha6( X, Y ) }.
% 26.01/26.38 (82091) {G0,W14,D4,L3,V2,M3} { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ),
% 26.01/26.38 alpha7( X, Y ), alpha19( X, Y ) }.
% 26.01/26.38 (82092) {G0,W11,D4,L2,V2,M2} { ! alpha7( X, Y ), c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (82093) {G0,W11,D4,L2,V2,M2} { ! alpha19( X, Y ), c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (82094) {G0,W7,D3,L2,V2,M2} { ! alpha19( X, Y ), Y =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (82095) {G0,W8,D4,L2,V2,M2} { ! alpha19( X, Y ), X = c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.38 (82096) {G0,W12,D4,L3,V2,M3} { ! Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 26.01/26.38 ) ), alpha19( X, Y ) }.
% 26.01/26.38 (82097) {G0,W8,D4,L2,V2,M2} { ! alpha7( X, Y ), Y = c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.38 (82098) {G0,W7,D3,L2,V2,M2} { ! alpha7( X, Y ), X =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (82099) {G0,W12,D4,L3,V2,M3} { ! Y = c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha7( X, Y ) }.
% 26.01/26.38 (82100) {G0,W17,D5,L3,V3,M3} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 26.01/26.38 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 26.01/26.38 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 26.01/26.38 (82101) {G0,W15,D5,L2,V2,M2} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ) ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 26.01/26.38 ) ) }.
% 26.01/26.38 (82102) {G0,W15,D5,L2,V2,M2} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ) ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 26.01/26.38 ) ) }.
% 26.01/26.38 (82103) {G0,W20,D5,L3,V2,M3} { ! Y = c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X = c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.38 (82104) {G0,W6,D4,L1,V0,M1} { c_Groups_Oone__class_Oone( tc_Nat_Onat ) =
% 26.01/26.38 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.38 (82105) {G0,W17,D6,L1,V2,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), Y ), c_Nat_OSuc( X ) ) = c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 26.01/26.38 , Y ), X ) ) }.
% 26.01/26.38 (82106) {G0,W17,D6,L1,V2,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), c_Nat_OSuc( Y ) ), X ) = c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 26.01/26.38 , Y ), X ) ) }.
% 26.01/26.38 (82107) {G0,W8,D4,L1,V1,M1} { c_Nat_OSuc( X ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 26.01/26.38 tc_Nat_Onat ) ) }.
% 26.01/26.38 (82108) {G0,W8,D4,L1,V1,M1} { c_Nat_OSuc( X ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 26.01/26.38 tc_Nat_Onat ), X ) }.
% 26.01/26.38 (82109) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 26.01/26.38 (82110) {G0,W13,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 26.01/26.38 (82111) {G0,W13,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 26.01/26.38 (82112) {G0,W20,D6,L1,V1,M1} { c_Fact_Ofact__class_Ofact( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 26.01/26.38 tc_Nat_Onat ) ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), c_Fact_Ofact__class_Ofact(
% 26.01/26.38 tc_Nat_Onat, X ) ) }.
% 26.01/26.38 (82113) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 26.01/26.38 (82114) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 26.01/26.38 (82115) {G0,W19,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 26.01/26.38 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y
% 26.01/26.38 ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 26.01/26.38 (82116) {G0,W18,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 26.01/26.38 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y
% 26.01/26.38 ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 26.01/26.38 (82117) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 26.01/26.38 (82118) {G0,W19,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 26.01/26.38 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X
% 26.01/26.38 ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ) }.
% 26.01/26.38 (82119) {G0,W18,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 26.01/26.38 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X
% 26.01/26.38 ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (82120) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 26.01/26.38 (82121) {G0,W15,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), Y ) }.
% 26.01/26.38 (82122) {G0,W15,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), X ) }.
% 26.01/26.38 (82123) {G0,W20,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 26.01/26.38 (82124) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 26.01/26.38 (82125) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 26.01/26.38 (82126) {G0,W21,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP
% 26.01/26.38 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = Y }.
% 26.01/26.38 (82127) {G0,W21,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! Z = Y,
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) = hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 26.01/26.38 (82128) {G0,W8,D4,L1,V1,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 26.01/26.38 c_Nat_OSuc( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 26.01/26.38 (82129) {G0,W14,D5,L1,V2,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 26.01/26.38 , Y, c_Nat_OSuc( X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 26.01/26.38 ( tc_Nat_Onat ) ), X ) }.
% 26.01/26.38 (82130) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 26.01/26.38 (82131) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 26.01/26.38 (82132) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus
% 26.01/26.38 ( tc_Nat_Onat, Y, X ) ) }.
% 26.01/26.38 (82133) {G0,W11,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (82134) {G0,W11,D3,L2,V2,M2} { ! c_Groups_Ominus__class_Ominus(
% 26.01/26.38 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (82135) {G0,W11,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (82136) {G0,W13,D4,L2,V2,M2} { c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.38 , Y, X ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 26.01/26.38 (82137) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, Z, X ), Y ) }.
% 26.01/26.38 (82138) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 26.01/26.38 (82139) {G0,W19,D4,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 26.01/26.38 tc_Nat_Onat, X, Y ), Z ) }.
% 26.01/26.38 (82140) {G0,W19,D4,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, X, Z ), Y ) }.
% 26.01/26.38 (82141) {G0,W19,D4,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 26.01/26.38 (82142) {G0,W16,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y )
% 26.01/26.38 = Z, X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 26.01/26.38 (82143) {G0,W16,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y
% 26.01/26.38 ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 26.01/26.38 (82144) {G0,W13,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Y ) = X }.
% 26.01/26.38 (82145) {G0,W18,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 26.01/26.38 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 26.01/26.38 (82146) {G0,W18,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 26.01/26.38 (82147) {G0,W19,D4,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, Z, X ), Y ) }.
% 26.01/26.38 (82148) {G0,W13,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 26.01/26.38 (82149) {G0,W14,D4,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, X, Z ), Y ) ) }.
% 26.01/26.38 (82150) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 26.01/26.38 (82151) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 26.01/26.38 (82152) {G0,W19,D4,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, Z, Y ), X ) }.
% 26.01/26.38 (82153) {G0,W19,D5,L3,V2,M3} { ! hAPP( hAPP( c_Power_Opower__class_Opower
% 26.01/26.38 ( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 26.01/26.38 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.38 (82154) {G0,W14,D5,L2,V2,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 26.01/26.38 ), X ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.38 (82155) {G0,W15,D5,L2,V2,M2} { ! Y = c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.38 (82156) {G0,W12,D6,L1,V1,M1} { hAPP( hAPP( c_Power_Opower__class_Opower(
% 26.01/26.38 tc_Nat_Onat ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) )
% 26.01/26.38 , X ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.38 (82157) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 26.01/26.38 (82158) {G0,W19,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (82159) {G0,W15,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 26.01/26.38 ), X ) ) }.
% 26.01/26.38 (82160) {G0,W14,D5,L2,V2,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 26.01/26.38 (82161) {G0,W13,D4,L3,V2,M3} { ! class_Groups_Ozero( X ), !
% 26.01/26.38 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.38 (82162) {G0,W13,D4,L3,V2,M3} { ! class_Groups_Ozero( X ), ! Y =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 26.01/26.38 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.38 (82163) {G0,W10,D3,L2,V1,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), c_Fact_Ofact__class_Ofact( tc_Nat_Onat, X ) =
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 26.01/26.38 (82164) {G0,W20,D6,L2,V1,M2} { X = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), c_Fact_Ofact__class_Ofact( tc_Nat_Onat, X ) = hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 26.01/26.38 c_Fact_Ofact__class_Ofact( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 26.01/26.38 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 26.01/26.38 (82165) {G0,W20,D6,L2,V3,M2} { ! class_Rings_Olinordered__ring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.38 (82166) {G0,W28,D6,L4,V3,M4} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ), ! Z =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 }.
% 26.01/26.38 (82167) {G0,W24,D6,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), Z = c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 26.01/26.38 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 26.01/26.38 (82168) {G0,W24,D6,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), Y = c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 26.01/26.38 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 26.01/26.38 (82169) {G0,W12,D4,L2,V1,M2} { ! class_Rings_Olinordered__semidom( X ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 26.01/26.38 c_Groups_Oone__class_Oone( X ) ) ) }.
% 26.01/26.38 (82170) {G0,W20,D6,L2,V3,M2} { ! class_Rings_Olinordered__ring( X ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 26.01/26.38 ) ) }.
% 26.01/26.38 (82171) {G0,W24,D6,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus(
% 26.01/26.38 X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 }.
% 26.01/26.38 (82172) {G0,W24,D6,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus(
% 26.01/26.38 X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 26.01/26.38 }.
% 26.01/26.38 (82173) {G0,W28,D6,L4,V3,M4} { ! class_Rings_Olinordered__ring__strict( X
% 26.01/26.38 ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 26.01/26.38 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.38 (82174) {G0,W37,D6,L3,V6,M3} { ! class_Rings_Oordered__ring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless( X, T,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 26.01/26.38 (82175) {G0,W37,D6,L3,V6,M3} { ! class_Rings_Oordered__ring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 26.01/26.38 ( X, Z, W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 26.01/26.38 (82176) {G0,W37,D6,L3,V6,M3} { ! class_Rings_Oordered__ring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 26.01/26.38 (82177) {G0,W37,D6,L3,V6,M3} { ! class_Rings_Oordered__ring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 26.01/26.38 X, W, Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless( X,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 26.01/26.38 (82178) {G0,W26,D5,L5,V3,M5} { ! class_Rings_Olinordered__idom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 X ), Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 26.01/26.38 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 26.01/26.38 (82179) {G0,W26,D5,L5,V3,M5} { ! class_Rings_Olinordered__idom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 26.01/26.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 X ), Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 26.01/26.38 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 26.01/26.38 (82180) {G0,W22,D6,L3,V3,M3} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 26.01/26.38 (82181) {G0,W26,D6,L3,V3,M3} { ! class_Rings_Olinordered__semidom( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 26.01/26.38 (82182) {G0,W37,D6,L3,V6,M3} { ! class_Rings_Oordered__ring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 26.01/26.38 (82183) {G0,W37,D6,L3,V6,M3} { ! class_Rings_Oordered__ring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), Z ), U ), Y ) ) }.
% 26.01/26.38 (82184) {G0,W37,D6,L3,V6,M3} { ! class_Rings_Oordered__ring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 26.01/26.38 (82185) {G0,W37,D6,L3,V6,M3} { ! class_Rings_Oordered__ring( X ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.38 ( X ), Z ), U ), Y ) ) }.
% 26.01/26.38 (82186) {G0,W11,D4,L2,V3,M2} { ! hBOOL( hAPP( Z,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), alpha8( X, Y, Z )
% 26.01/26.38 }.
% 26.01/26.38 (82187) {G0,W11,D4,L2,V3,M2} { ! hBOOL( hAPP( Z,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), alpha20( X, Y, Z
% 26.01/26.38 ) }.
% 26.01/26.38 (82188) {G0,W15,D4,L3,V3,M3} { ! alpha8( X, Y, Z ), ! alpha20( X, Y, Z ),
% 26.01/26.38 hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 26.01/26.38 }.
% 26.01/26.38 (82189) {G0,W14,D3,L3,V4,M3} { ! alpha20( X, Y, Z ), ! Y =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T ) )
% 26.01/26.38 }.
% 26.01/26.38 (82190) {G0,W11,D4,L2,V5,M2} { ! hBOOL( hAPP( Z, skol7( T, U, Z ) ) ),
% 26.01/26.38 alpha20( X, Y, Z ) }.
% 26.01/26.38 (82191) {G0,W13,D4,L2,V3,M2} { Y = c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, X, skol7( X, Y, Z ) ), alpha20( X, Y, Z ) }.
% 26.01/26.38 (82192) {G0,W13,D4,L3,V3,M3} { ! alpha8( X, Y, Z ), !
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 26.01/26.38 (82193) {G0,W8,D2,L2,V3,M2} { c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 Y, X ), alpha8( X, Y, Z ) }.
% 26.01/26.38 (82194) {G0,W9,D4,L2,V3,M2} { ! hBOOL( hAPP( Z,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha8( X, Y, Z ) }.
% 26.01/26.38 (82195) {G0,W11,D4,L2,V3,M2} { ! hBOOL( hAPP( Z,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), ! alpha9( X, Y, Z
% 26.01/26.38 ) }.
% 26.01/26.38 (82196) {G0,W11,D4,L2,V3,M2} { ! hBOOL( hAPP( Z,
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), ! alpha21( X, Y,
% 26.01/26.38 Z ) }.
% 26.01/26.38 (82197) {G0,W15,D4,L3,V3,M3} { alpha9( X, Y, Z ), alpha21( X, Y, Z ),
% 26.01/26.38 hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 26.01/26.38 }.
% 26.01/26.38 (82198) {G0,W11,D4,L2,V5,M2} { ! alpha21( X, Y, Z ), ! hBOOL( hAPP( Z,
% 26.01/26.38 skol8( T, U, Z ) ) ) }.
% 26.01/26.38 (82199) {G0,W13,D4,L2,V3,M2} { ! alpha21( X, Y, Z ), Y =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol8( X, Y, Z ) ) }.
% 26.01/26.38 (82200) {G0,W14,D3,L3,V4,M3} { ! Y = c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T ) ), alpha21( X, Y, Z ) }.
% 26.01/26.38 (82201) {G0,W8,D2,L2,V3,M2} { ! alpha9( X, Y, Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (82202) {G0,W9,D4,L2,V3,M2} { ! alpha9( X, Y, Z ), ! hBOOL( hAPP( Z,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 26.01/26.38 (82203) {G0,W13,D4,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ) ) ), alpha9( X, Y, Z ) }.
% 26.01/26.38 (82204) {G0,W39,D6,L3,V5,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 26.01/26.38 (82205) {G0,W39,D6,L3,V5,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 26.01/26.38 (82206) {G0,W40,D7,L2,V5,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 26.01/26.38 (82207) {G0,W37,D6,L3,V5,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 26.01/26.38 (82208) {G0,W37,D6,L3,V5,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 26.01/26.38 (82209) {G0,W39,D6,L3,V5,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 26.01/26.38 (82210) {G0,W39,D6,L3,V5,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T
% 26.01/26.38 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 26.01/26.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 26.01/26.38 (82211) {G0,W40,D7,L2,V5,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 26.01/26.38 (82212) {G0,W37,D6,L3,V5,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 26.01/26.38 (82213) {G0,W37,D6,L3,V5,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! T = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 26.01/26.38 (82214) {G0,W26,D7,L1,V3,M1} { hAPP( hAPP( c_Power_Opower__class_Opower(
% 26.01/26.38 tc_Int_Oint ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 26.01/26.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 26.01/26.38 (82215) {G0,W23,D7,L1,V3,M1} { hAPP( hAPP( c_Power_Opower__class_Opower(
% 26.01/26.38 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z
% 26.01/26.38 ), Y ) ), X ) = hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 26.01/26.38 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 26.01/26.38 ) }.
% 26.01/26.38 (82216) {G0,W16,D4,L2,V2,M2} { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 26.01/26.38 , Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 26.01/26.38 c_Fact_Ofact__class_Ofact( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, Y, X ) ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 26.01/26.38 (82217) {G0,W32,D6,L2,V2,M2} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 26.01/26.38 , X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 26.01/26.38 c_Fact_Ofact__class_Ofact( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Nat_Onat, Y, X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 26.01/26.38 c_Fact_Ofact__class_Ofact( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ),
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 26.01/26.38 (82218) {G0,W7,D3,L1,V0,M1} {
% 26.01/26.38 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 26.01/26.38 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 26.01/26.38 tc_Complex_Ocomplex, v_pa____ ) }.
% 26.01/26.38 (82219) {G0,W16,D4,L2,V3,M2} { ! class_Groups_Ozero( X ),
% 26.01/26.38 c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) = c_Polynomial_OpCons( X,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( X ), c_Polynomial_Omonom( X, Z, Y ) ) }.
% 26.01/26.38 (82220) {G0,W14,D5,L2,V2,M2} { ! class_Groups_Ozero( X ),
% 26.01/26.38 c_Polynomial_Omonom( X, Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 26.01/26.38 c_Polynomial_OpCons( X, Y, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Polynomial_Opoly( X ) ) ) }.
% 26.01/26.38 (82221) {G0,W28,D6,L2,V5,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 26.01/26.38 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 26.01/26.38 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 26.01/26.38 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 26.01/26.38 (82222) {G0,W19,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ), X =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 26.01/26.38 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 26.01/26.38 (82223) {G0,W14,D5,L2,V2,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 26.01/26.38 (82224) {G0,W15,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 26.01/26.38 ), X ) ) }.
% 26.01/26.38 (82225) {G0,W17,D7,L1,V0,M1} { !
% 26.01/26.38 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 26.01/26.38 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 26.01/26.38 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 26.01/26.38 tc_Complex_Ocomplex ), c_Polynomial_Omonom( tc_Complex_Ocomplex, v_a____
% 26.01/26.38 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ) ) }.
% 26.01/26.38 (82226) {G0,W16,D5,L3,V1,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Nat_Onat ) ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 26.01/26.38 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.38 (82227) {G0,W19,D8,L1,V0,M1} { hAPP( c_Polynomial_Opoly(
% 26.01/26.38 tc_Complex_Ocomplex, c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), c_Polynomial_Omonom(
% 26.01/26.38 tc_Complex_Ocomplex, v_a____, c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 26.01/26.38 , v_k____, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ), skol9 ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 26.01/26.38 (82228) {G0,W6,D3,L1,V0,M1} { !
% 26.01/26.38 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 26.01/26.38 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ) )
% 26.01/26.38 }.
% 26.01/26.38 (82229) {G0,W6,D3,L1,V0,M1} { !
% 26.01/26.38 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 26.01/26.38 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____
% 26.01/26.38 ) ) }.
% 26.01/26.38 (82230) {G0,W9,D4,L1,V0,M1} { ! hAPP( c_Polynomial_Opoly(
% 26.01/26.38 tc_Complex_Ocomplex, v_q____ ), c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Complex_Ocomplex ) ) = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Complex_Ocomplex ) }.
% 26.01/26.38 (82231) {G0,W6,D3,L1,V0,M1} { !
% 26.01/26.38 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 26.01/26.38 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ )
% 26.01/26.38 ) }.
% 26.01/26.38 (82232) {G0,W6,D3,L1,V0,M1} { !
% 26.01/26.38 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 26.01/26.38 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ )
% 26.01/26.38 ) }.
% 26.01/26.38 (82233) {G0,W8,D4,L1,V0,M1} { ! hAPP( c_Polynomial_Opoly(
% 26.01/26.38 tc_Complex_Ocomplex, v_pa____ ), v_c____ ) = c_Groups_Ozero__class_Ozero
% 26.01/26.38 ( tc_Complex_Ocomplex ) }.
% 26.01/26.38 (82234) {G0,W14,D4,L1,V1,M1} { hAPP( c_Polynomial_Opoly(
% 26.01/26.38 tc_Complex_Ocomplex, v_q____ ), X ) = hAPP( c_Polynomial_Opoly(
% 26.01/26.38 tc_Complex_Ocomplex, v_pa____ ), c_Groups_Oplus__class_Oplus(
% 26.01/26.38 tc_Complex_Ocomplex, v_c____, X ) ) }.
% 26.01/26.38 (82235) {G0,W4,D2,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, X, X ) }.
% 26.01/26.38 (82236) {G0,W8,D2,L2,V2,M2} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y
% 26.01/26.38 ) }.
% 26.01/26.38 (82237) {G0,W7,D2,L2,V2,M2} { ! Y = X, c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ) }.
% 26.01/26.38 (82238) {G0,W12,D2,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 26.01/26.38 , Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 26.01/26.38 (82239) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.38 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 26.01/26.38 , Y ), Y = X }.
% 26.01/26.38 (82240) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Int_Oint, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 26.01/26.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 26.01/26.38 (82241) {G0,W18,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Int_Oint ), X = c_Groups_Oone__class_Oone(
% 26.01/26.38 tc_Int_Oint ) }.
% 26.01/26.38 (82242) {G0,W18,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y = c_Groups_Oone__class_Oone(
% 26.01/26.38 tc_Int_Oint ) }.
% 26.01/26.38 (82243) {G0,W22,D5,L4,V2,M4} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.38 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! X =
% 26.01/26.38 c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y = c_Groups_Oone__class_Oone
% 26.01/26.38 ( tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 26.01/26.38 , X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 26.01/26.38 (82244) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Int_Oint ), c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X )
% 26.01/26.38 = c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 26.01/26.38 (82245) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 26.01/26.38 (82246) {G0,W23,D7,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 26.01/26.38 Z ), Y ) ), X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 26.01/26.38 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X
% 26.01/26.38 ) ) }.
% 26.01/26.38 (82247) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Int_Oint ), Z ), c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) )
% 26.01/26.38 = c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 26.01/26.38 (82248) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Int_Oint ), Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 26.01/26.38 (82249) {G0,W13,D5,L1,V2,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Int_Oint ), Y ), X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Int_Oint ), X ), Y ) }.
% 26.01/26.38 (82250) {G0,W9,D5,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Int_Oint ), X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 26.01/26.38 (82251) {G0,W9,D5,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 26.01/26.38 (82252) {G0,W28,D8,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 26.01/26.38 ( c_Polynomial_Opoly( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.38 tc_Polynomial_Opoly( X ) ), T ), Z ) ), Y ) = hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Opoly( X, T ), Y )
% 26.01/26.38 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 26.01/26.38 (82253) {G0,W24,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 26.01/26.38 ( c_Polynomial_Opoly( X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly
% 26.01/26.38 ( X ), T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP(
% 26.01/26.38 c_Polynomial_Opoly( X, T ), Y ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) )
% 26.01/26.38 }.
% 26.01/26.38 (82254) {G0,W12,D6,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.38 ( c_Polynomial_Opoly( X, c_Groups_Oone__class_Oone( tc_Polynomial_Opoly(
% 26.01/26.38 X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 26.01/26.38 (82255) {G0,W24,D6,L2,V4,M2} { ! class_Rings_Ocomm__ring( X ), hAPP(
% 26.01/26.38 c_Polynomial_Opoly( X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly
% 26.01/26.38 ( X ), T, Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP(
% 26.01/26.38 c_Polynomial_Opoly( X, T ), Y ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) )
% 26.01/26.38 }.
% 26.01/26.38 (82256) {G0,W24,D8,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.38 ( c_Polynomial_Opoly( X, hAPP( hAPP( c_Power_Opower__class_Opower(
% 26.01/26.38 tc_Polynomial_Opoly( X ) ), T ), Z ) ), Y ) = hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), hAPP( c_Polynomial_Opoly( X, T ), Y )
% 26.01/26.38 ), Z ) }.
% 26.01/26.38 (82257) {G0,W15,D6,L2,V2,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.38 (82258) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 26.01/26.38 (82259) {G0,W15,D6,L2,V2,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.38 (82260) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 26.01/26.38 (82261) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Oab__group__add( X ),
% 26.01/26.38 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y,
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 26.01/26.38 (82262) {G0,W31,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 26.01/26.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 26.01/26.38 ) ) }.
% 26.01/26.38 (82263) {G0,W14,D3,L4,V3,M4} { ! class_Int_Oring__char__0( X ), !
% 26.01/26.38 class_Rings_Oidom( X ), ! c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly
% 26.01/26.38 ( X, Y ), Z = Y }.
% 26.01/26.38 (82264) {G0,W14,D3,L4,V3,M4} { ! class_Int_Oring__char__0( X ), !
% 26.01/26.38 class_Rings_Oidom( X ), ! Z = Y, c_Polynomial_Opoly( X, Z ) =
% 26.01/26.38 c_Polynomial_Opoly( X, Y ) }.
% 26.01/26.38 (82265) {G0,W18,D5,L4,V2,M4} { ! class_Int_Oring__char__0( X ), !
% 26.01/26.38 class_Rings_Oidom( X ), ! c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly
% 26.01/26.38 ( X, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 26.01/26.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.38 (82266) {G0,W18,D5,L4,V2,M4} { ! class_Int_Oring__char__0( X ), !
% 26.01/26.38 class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.38 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly( X, Y ) =
% 26.01/26.38 c_Polynomial_Opoly( X, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 26.01/26.38 X ) ) ) }.
% 26.01/26.38 (82267) {G0,W12,D6,L2,V2,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 26.01/26.38 ( c_Polynomial_Opoly( X, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 26.01/26.38 ( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.38 (82268) {G0,W11,D3,L2,V5,M2} { !
% 26.01/26.38 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP( X
% 26.01/26.38 , T ) = hAPP( X, U ) }.
% 26.01/26.38 (82269) {G0,W13,D4,L2,V3,M2} { ! hAPP( X, skol10( X ) ) = hAPP( X, skol27
% 26.01/26.38 ( X ) ), c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X )
% 26.01/26.38 }.
% 26.01/26.38 (82270) {G0,W24,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 26.01/26.38 ( c_Polynomial_Opoly( X, c_Polynomial_OpCons( X, T, Z ) ), Y ) =
% 26.01/26.38 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 26.01/26.38 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( c_Polynomial_Opoly( X, Z )
% 26.01/26.38 , Y ) ) ) }.
% 26.01/26.38 (82271) {G0,W22,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 26.01/26.38 ( c_Polynomial_Opoly( X, c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP(
% 26.01/26.38 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 26.01/26.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 26.01/26.38 (82272) {G0,W14,D3,L3,V5,M3} { ! class_Groups_Ozero( X ), !
% 26.01/26.38 c_Polynomial_OpCons( X, U, T ) = c_Polynomial_OpCons( X, Z, Y ), U = Z
% 26.01/26.38 }.
% 26.01/26.39 (82273) {G0,W14,D3,L3,V5,M3} { ! class_Groups_Ozero( X ), !
% 26.01/26.39 c_Polynomial_OpCons( X, U, T ) = c_Polynomial_OpCons( X, Z, Y ), T = Y
% 26.01/26.39 }.
% 26.01/26.39 (82274) {G0,W17,D3,L4,V5,M4} { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y
% 26.01/26.39 , c_Polynomial_OpCons( X, U, T ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 26.01/26.39 (82275) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ozero( X ), !
% 26.01/26.39 c_Polynomial_Omonom( X, T, Z ) = c_Polynomial_Omonom( X, Y, Z ), T = Y
% 26.01/26.39 }.
% 26.01/26.39 (82276) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ozero( X ), ! T = Y,
% 26.01/26.39 c_Polynomial_Omonom( X, T, Z ) = c_Polynomial_Omonom( X, Y, Z ) }.
% 26.01/26.39 (82277) {G0,W33,D8,L2,V4,M2} { ! class_Rings_Ocomm__ring__1( X ), hAPP(
% 26.01/26.39 c_Polynomial_Opoly( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ), c_Polynomial_Omonom( X,
% 26.01/26.39 c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y ) = hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 26.01/26.39 X, Z ), Y ) ) }.
% 26.01/26.39 (82278) {G0,W13,D5,L2,V1,M2} { ! class_Groups_Ozero( X ),
% 26.01/26.39 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.39 (82279) {G0,W14,D4,L3,V3,M3} { ! class_Groups_Ozero( X ), !
% 26.01/26.39 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82280) {G0,W15,D4,L3,V3,M3} { ! class_Groups_Ozero( X ), !
% 26.01/26.39 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.39 (82281) {G0,W19,D4,L4,V3,M4} { ! class_Groups_Ozero( X ), ! Z =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X, Z, Y ) =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.39 (82282) {G0,W25,D5,L2,V5,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 26.01/26.39 c_Polynomial_OpCons( X, U, T ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 26.01/26.39 c_Polynomial_OpCons( X, c_Groups_Oplus__class_Oplus( X, U, Z ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 26.01/26.39 (82283) {G0,W13,D5,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) =
% 26.01/26.39 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 26.01/26.39 (82284) {G0,W25,D5,L2,V5,M2} { ! class_Groups_Oab__group__add( X ),
% 26.01/26.39 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 26.01/26.39 c_Polynomial_OpCons( X, U, T ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 26.01/26.39 c_Polynomial_OpCons( X, c_Groups_Ominus__class_Ominus( X, U, Z ),
% 26.01/26.39 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 26.01/26.39 (82285) {G0,W14,D4,L3,V3,M3} { ! class_Groups_Ozero( X ), !
% 26.01/26.39 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82286) {G0,W14,D4,L3,V3,M3} { ! class_Groups_Ozero( X ), ! Z =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), c_Polynomial_Omonom( X, Z, Y ) =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.39 (82287) {G0,W11,D4,L2,V2,M2} { ! class_Groups_Ozero( X ),
% 26.01/26.39 c_Polynomial_Omonom( X, c_Groups_Ozero__class_Ozero( X ), Y ) =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.39 (82288) {G0,W21,D4,L2,V4,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 26.01/26.39 c_Polynomial_Omonom( X, T, Z ), c_Polynomial_Omonom( X, Y, Z ) ) =
% 26.01/26.39 c_Polynomial_Omonom( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 26.01/26.39 (82289) {G0,W21,D4,L2,V4,M2} { ! class_Groups_Oab__group__add( X ),
% 26.01/26.39 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 26.01/26.39 c_Polynomial_Omonom( X, T, Z ), c_Polynomial_Omonom( X, Y, Z ) ) =
% 26.01/26.39 c_Polynomial_Omonom( X, c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 26.01/26.39 (82290) {G0,W12,D4,L1,V0,M1} { hAPP( c_Polynomial_Opoly(
% 26.01/26.39 tc_Complex_Ocomplex, v_pa____ ), v_c____ ) = hAPP( c_Polynomial_Opoly(
% 26.01/26.39 tc_Complex_Ocomplex, v_q____ ), c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Complex_Ocomplex ) ) }.
% 26.01/26.39 (82291) {G0,W23,D4,L3,V1,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 26.01/26.39 tc_Complex_Ocomplex, X ),
% 26.01/26.39 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 26.01/26.39 v_pa____ ) ), c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 26.01/26.39 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 26.01/26.39 tc_Complex_Ocomplex, X ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex
% 26.01/26.39 , X ), skol11( X ) ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex )
% 26.01/26.39 }.
% 26.01/26.39 (82292) {G0,W17,D5,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 26.01/26.39 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) }.
% 26.01/26.39 (82293) {G0,W52,D9,L1,V1,M1} { hAPP( c_Polynomial_Opoly(
% 26.01/26.39 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ), X )
% 26.01/26.39 = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 26.01/26.39 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 26.01/26.39 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 26.01/26.39 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 26.01/26.39 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ), hAPP(
% 26.01/26.39 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), v_k____ ) ),
% 26.01/26.39 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 26.01/26.39 tc_Complex_Ocomplex, v_a____, v_s____ ) ), X ) ) ) }.
% 26.01/26.39 (82294) {G0,W16,D5,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 26.01/26.39 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) }.
% 26.01/26.39 (82295) {G0,W38,D9,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 26.01/26.39 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 26.01/26.39 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 26.01/26.39 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 26.01/26.39 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 26.01/26.39 v_q____ ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ) }.
% 26.01/26.39 (82296) {G0,W38,D9,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 26.01/26.39 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 26.01/26.39 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 26.01/26.39 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 26.01/26.39 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 26.01/26.39 v_q____ ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 26.01/26.39 (82297) {G0,W33,D10,L1,V0,M1} { hAPP( c_Polynomial_Opoly(
% 26.01/26.39 tc_Complex_Ocomplex, v_q____ ), c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Complex_Ocomplex ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_Complex_Ocomplex ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 26.01/26.39 c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 26.01/26.39 (82298) {G0,W31,D10,L1,V1,M1} { hAPP( c_Polynomial_Opoly(
% 26.01/26.39 tc_Complex_Ocomplex, v_q____ ), X ) = hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 26.01/26.39 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 26.01/26.39 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 26.01/26.39 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 26.01/26.39 v_q____ ) ), X ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 26.01/26.39 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 26.01/26.39 (82299) {G0,W24,D7,L1,V0,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 26.01/26.39 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 26.01/26.39 v_s____ ), v_k____ ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 26.01/26.39 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 26.01/26.39 c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 26.01/26.39 (82300) {G0,W17,D7,L1,V0,M1} {
% 26.01/26.39 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 26.01/26.39 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 26.01/26.39 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 26.01/26.39 (82301) {G0,W19,D8,L1,V0,M1} { hAPP( c_Polynomial_Opoly(
% 26.01/26.39 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 26.01/26.39 (82302) {G0,W16,D7,L1,V0,M1} { !
% 26.01/26.39 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 26.01/26.39 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 26.01/26.39 c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) ) }.
% 26.01/26.39 (82303) {G0,W5,D3,L1,V0,M1} { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 26.01/26.39 = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 26.01/26.39 (82304) {G0,W6,D3,L1,V0,M1} { c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 26.01/26.39 tc_Int_Oint ) ) }.
% 26.01/26.39 (82305) {G0,W10,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Int_Oint ), X ) }.
% 26.01/26.39 (82306) {G0,W10,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 26.01/26.39 ( tc_Int_Oint ), X ) }.
% 26.01/26.39 (82307) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Int_Oint
% 26.01/26.39 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 26.01/26.39 (82308) {G0,W7,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Int_Oint
% 26.01/26.39 , Y, X ), ! Y = X }.
% 26.01/26.39 (82309) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, Y, X ), Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y
% 26.01/26.39 , X ) }.
% 26.01/26.39 (82310) {G0,W4,D2,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, X, X ) }.
% 26.01/26.39 (82311) {G0,W8,D2,L2,V2,M2} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, Y, X ), c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, X, Y ) }.
% 26.01/26.39 (82312) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, Y, X ), c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, Y, X ) }.
% 26.01/26.39 (82313) {G0,W7,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 26.01/26.39 (82314) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, Y, X ), Y = X, c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, Y, X ) }.
% 26.01/26.39 (82315) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, Y, X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 26.01/26.39 , Y, X ), Y = X }.
% 26.01/26.39 (82316) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, Y, X ), c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, Y, X ) }.
% 26.01/26.39 (82317) {G0,W7,D2,L2,V2,M2} { ! Y = X, c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, Y, X ) }.
% 26.01/26.39 (82318) {G0,W12,D2,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, Y, X ), ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, X, Z ), c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, Y, Z ) }.
% 26.01/26.39 (82319) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, Y, X ), ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, X, Y ), Y = X }.
% 26.01/26.39 (82320) {G0,W18,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Int_Oint, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T
% 26.01/26.39 , Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, T ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }.
% 26.01/26.39 (82321) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, Y, X ), c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 26.01/26.39 (82322) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 26.01/26.39 (82323) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 26.01/26.39 tc_Int_Oint ) ), X ) }.
% 26.01/26.39 (82324) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 26.01/26.39 (82325) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 26.01/26.39 (82326) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 26.01/26.39 (82327) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 26.01/26.39 (82328) {G0,W14,D4,L2,V1,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 26.01/26.39 (82329) {G0,W17,D5,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 26.01/26.39 tc_Int_Oint ), X ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 26.01/26.39 (82330) {G0,W17,D5,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Int_Oint, X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 26.01/26.39 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 26.01/26.39 (82331) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 26.01/26.39 (82332) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 26.01/26.39 tc_Int_Oint ) ), X ) }.
% 26.01/26.39 (82333) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, X,
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 26.01/26.39 (82334) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 26.01/26.39 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 26.01/26.39 ( tc_Int_Oint ) ) ) }.
% 26.01/26.39 (82335) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, X,
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 26.01/26.39 (82336) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 26.01/26.39 tc_Int_Oint ) ) ) }.
% 26.01/26.39 (82337) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, Y, X ), c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X )
% 26.01/26.39 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 26.01/26.39 (82338) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X )
% 26.01/26.39 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 26.01/26.39 (82339) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 26.01/26.39 (82340) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 26.01/26.39 (82341) {G0,W7,D4,L1,V1,M1} { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X
% 26.01/26.39 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) = X }.
% 26.01/26.39 (82342) {G0,W7,D4,L1,V1,M1} { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ) = X }.
% 26.01/26.39 (82343) {G0,W9,D3,L2,V2,M2} { ! class_RealVector_Oreal__normed__vector( X
% 26.01/26.39 ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 26.01/26.39 (82344) {G0,W11,D5,L1,V1,M1} { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 26.01/26.39 , c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 26.01/26.39 tc_Int_Oint ), X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 26.01/26.39 (82345) {G0,W9,D3,L2,V2,M2} { ! class_RealVector_Oreal__normed__vector( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_RealDef_Oreal ) ) }.
% 26.01/26.39 (82346) {G0,W23,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 26.01/26.39 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 26.01/26.39 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 26.01/26.39 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) )
% 26.01/26.39 }.
% 26.01/26.39 (82347) {G0,W22,D5,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 26.01/26.39 c_Polynomial_Osmult( X, T, c_Groups_Oplus__class_Oplus(
% 26.01/26.39 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 26.01/26.39 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ),
% 26.01/26.39 c_Polynomial_Osmult( X, T, Y ) ) }.
% 26.01/26.39 (82348) {G0,W22,D5,L2,V4,M2} { ! class_Rings_Ocomm__ring( X ),
% 26.01/26.39 c_Polynomial_Osmult( X, T, c_Groups_Ominus__class_Ominus(
% 26.01/26.39 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Groups_Ominus__class_Ominus(
% 26.01/26.39 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ),
% 26.01/26.39 c_Polynomial_Osmult( X, T, Y ) ) }.
% 26.01/26.39 (82349) {G0,W23,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 26.01/26.39 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 26.01/26.39 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 26.01/26.39 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 26.01/26.39 ) }.
% 26.01/26.39 (82350) {G0,W17,D4,L3,V2,M3} { !
% 26.01/26.39 class_RealVector_Oreal__normed__div__algebra( X ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ) ) =
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 26.01/26.39 (82351) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 26.01/26.39 c_Polynomial_Osmult( X, Y, c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.39 (82352) {G0,W21,D4,L2,V4,M2} { ! class_Rings_Ocomm__ring( X ),
% 26.01/26.39 c_Polynomial_Osmult( X, c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 26.01/26.39 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 26.01/26.39 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 26.01/26.39 (82353) {G0,W9,D4,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.39 c_Polynomial_Osmult( X, c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 26.01/26.39 (82354) {G0,W21,D4,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 26.01/26.39 c_Polynomial_Osmult( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) =
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 26.01/26.39 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 26.01/26.39 (82355) {G0,W19,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 26.01/26.39 c_Polynomial_Osmult( X, T, c_Polynomial_Osmult( X, Z, Y ) ) =
% 26.01/26.39 c_Polynomial_Osmult( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T
% 26.01/26.39 ), Z ), Y ) }.
% 26.01/26.39 (82356) {G0,W20,D3,L5,V3,M5} { ! class_Rings_Odivision__ring( X ), !
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = c_Groups_Ozero__class_Ozero
% 26.01/26.39 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 26.01/26.39 (82357) {G0,W12,D3,L3,V2,M3} { ! class_Rings_Odivision__ring( X ), !
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 26.01/26.39 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82358) {G0,W13,D4,L3,V2,M3} { ! class_Rings_Odivision__ring( X ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X,
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = Y }.
% 26.01/26.39 (82359) {G0,W12,D3,L3,V2,M3} { ! class_Rings_Odivision__ring( X ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Oinverse( X,
% 26.01/26.39 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82360) {G0,W12,D3,L3,V2,M3} { !
% 26.01/26.39 class_Rings_Odivision__ring__inverse__zero( X ), !
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 26.01/26.39 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82361) {G0,W12,D3,L3,V2,M3} { !
% 26.01/26.39 class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 26.01/26.39 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82362) {G0,W9,D4,L2,V1,M2} { ! class_Rings_Odivision__ring__inverse__zero
% 26.01/26.39 ( X ), c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero(
% 26.01/26.39 X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82363) {G0,W9,D4,L2,V1,M2} { ! class_Rings_Odivision__ring( X ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Oone__class_Oone( X ) ) =
% 26.01/26.39 c_Groups_Oone__class_Oone( X ) }.
% 26.01/26.39 (82364) {G0,W12,D3,L3,V2,M3} { ! class_RealVector_Oreal__normed__vector( X
% 26.01/26.39 ), ! c_RealVector_Onorm__class_Onorm( X, Y ) =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82365) {G0,W12,D3,L3,V2,M3} { ! class_RealVector_Oreal__normed__vector( X
% 26.01/26.39 ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_RealDef_Oreal ) }.
% 26.01/26.39 (82366) {G0,W9,D4,L2,V1,M2} { ! class_RealVector_Oreal__normed__vector( X
% 26.01/26.39 ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.39 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 26.01/26.39 (82367) {G0,W13,D3,L3,V2,M3} { ! class_RealVector_Oreal__normed__vector( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82368) {G0,W13,D3,L3,V2,M3} { ! class_RealVector_Oreal__normed__vector( X
% 26.01/26.39 ), Y = c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 26.01/26.39 (82369) {G0,W13,D3,L3,V2,M3} { ! class_RealVector_Oreal__normed__vector( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82370) {G0,W13,D3,L3,V2,M3} { ! class_RealVector_Oreal__normed__vector( X
% 26.01/26.39 ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_RealDef_Oreal ) ) }.
% 26.01/26.39 (82371) {G0,W19,D6,L2,V3,M2} { !
% 26.01/26.39 class_Rings_Odivision__ring__inverse__zero( X ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 26.01/26.39 ) ), Y ) }.
% 26.01/26.39 (82372) {G0,W21,D6,L2,V3,M2} { !
% 26.01/26.39 class_RealVector_Oreal__normed__div__algebra( X ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 26.01/26.39 (82373) {G0,W22,D6,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.39 X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 26.01/26.39 (82374) {G0,W30,D6,L4,V5,M4} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.39 X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 26.01/26.39 (82375) {G0,W18,D4,L2,V3,M2} { ! class_RealVector_Oreal__normed__vector( X
% 26.01/26.39 ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 26.01/26.39 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 26.01/26.39 ( X, Y ) ) ) }.
% 26.01/26.39 (82376) {G0,W18,D4,L2,V3,M2} { ! class_RealVector_Oreal__normed__vector( X
% 26.01/26.39 ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 26.01/26.39 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 26.01/26.39 (82377) {G0,W26,D4,L4,V5,M4} { ! class_RealVector_Oreal__normed__vector( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 26.01/26.39 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 26.01/26.39 (82378) {G0,W9,D4,L2,V1,M2} { ! class_RealVector_Oreal__normed__algebra__1
% 26.01/26.39 ( X ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X )
% 26.01/26.39 ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 26.01/26.39 (82379) {G0,W15,D4,L2,V3,M2} { ! class_RealVector_Oreal__normed__vector( X
% 26.01/26.39 ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X
% 26.01/26.39 , Z, Y ) ) = c_RealVector_Onorm__class_Onorm( X,
% 26.01/26.39 c_Groups_Ominus__class_Ominus( X, Y, Z ) ) }.
% 26.01/26.39 (82380) {G0,W18,D4,L2,V3,M2} { ! class_RealVector_Oreal__normed__vector( X
% 26.01/26.39 ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 26.01/26.39 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 26.01/26.39 ( X, Y ) ) ) }.
% 26.01/26.39 (82381) {G0,W18,D4,L2,V3,M2} { ! class_RealVector_Oreal__normed__vector( X
% 26.01/26.39 ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 26.01/26.39 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 26.01/26.39 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 26.01/26.39 (82382) {G0,W19,D6,L2,V3,M2} { !
% 26.01/26.39 class_RealVector_Oreal__normed__div__algebra( X ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 26.01/26.39 (82383) {G0,W20,D6,L2,V3,M2} { !
% 26.01/26.39 class_RealVector_Oreal__normed__algebra__1( X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 26.01/26.39 (82384) {G0,W16,D5,L1,V2,M1} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y
% 26.01/26.39 ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 26.01/26.39 (82385) {G0,W9,D4,L2,V2,M2} { ! class_Rings_Odivision__ring__inverse__zero
% 26.01/26.39 ( X ), c_Rings_Oinverse__class_Oinverse( X,
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = Y }.
% 26.01/26.39 (82386) {G0,W15,D4,L3,V2,M3} { !
% 26.01/26.39 class_RealVector_Oreal__normed__div__algebra( X ), !
% 26.01/26.39 class_Rings_Odivision__ring__inverse__zero( X ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 26.01/26.39 Y ) ) = c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 26.01/26.39 (82387) {G0,W12,D3,L3,V3,M3} { !
% 26.01/26.39 class_Rings_Odivision__ring__inverse__zero( X ), !
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 26.01/26.39 (82388) {G0,W12,D3,L3,V3,M3} { !
% 26.01/26.39 class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 26.01/26.39 (82389) {G0,W12,D3,L3,V3,M3} { !
% 26.01/26.39 class_Rings_Odivision__ring__inverse__zero( X ), !
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 26.01/26.39 (82390) {G0,W9,D3,L1,V2,M1} { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y
% 26.01/26.39 , X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 26.01/26.39 (82391) {G0,W15,D4,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, X,
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X }.
% 26.01/26.39 (82392) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 26.01/26.39 tc_Int_Oint ) ) ) }.
% 26.01/26.39 (82393) {G0,W11,D4,L2,V2,M2} { ! Y = X, c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, X,
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 26.01/26.39 (82394) {G0,W15,D4,L1,V3,M1} { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z
% 26.01/26.39 , c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus
% 26.01/26.39 ( tc_Int_Oint, Z, X ) ) }.
% 26.01/26.39 (82395) {G0,W15,D4,L1,V3,M1} { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ), X ) =
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 26.01/26.39 ( tc_Int_Oint, Y, X ) ) }.
% 26.01/26.39 (82396) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, Z ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }.
% 26.01/26.39 (82397) {G0,W11,D2,L3,V2,M3} { c_Orderings_Oord__class_Oless( tc_Int_Oint
% 26.01/26.39 , Y, X ), Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 26.01/26.39 (82398) {G0,W29,D6,L4,V3,M4} { ! class_Rings_Odivision__ring( X ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 26.01/26.39 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 26.01/26.39 (82399) {G0,W16,D5,L3,V3,M3} { ! class_Rings_Odivision__ring( X ), ! hAPP
% 26.01/26.39 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 26.01/26.39 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Z )
% 26.01/26.39 = Y }.
% 26.01/26.39 (82400) {G0,W23,D6,L3,V3,M3} { ! class_Rings_Odivision__ring( X ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X,
% 26.01/26.39 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 26.01/26.39 ) ), Z ) }.
% 26.01/26.39 (82401) {G0,W30,D5,L2,V5,M2} { ! class_RealVector_Oreal__normed__vector( X
% 26.01/26.39 ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 26.01/26.39 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 26.01/26.39 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 26.01/26.39 ( X, T, Y ) ) ) ) }.
% 26.01/26.39 (82402) {G0,W19,D4,L4,V3,M4} { ! class_Rings_Oidom( X ), !
% 26.01/26.39 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.39 (82403) {G0,W14,D4,L3,V3,M3} { ! class_Rings_Oidom( X ), ! Z =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), c_Polynomial_Osmult( X, Z, Y ) =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.39 (82404) {G0,W15,D4,L3,V3,M3} { ! class_Rings_Oidom( X ), ! Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 26.01/26.39 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.39 (82405) {G0,W11,D4,L2,V2,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 26.01/26.39 c_Polynomial_Osmult( X, c_Groups_Ozero__class_Ozero( X ), Y ) =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.39 (82406) {G0,W21,D5,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 26.01/26.39 ( c_Polynomial_Opoly( X, c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP(
% 26.01/26.39 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly(
% 26.01/26.39 X, Z ), Y ) ) }.
% 26.01/26.39 (82407) {G0,W22,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 26.01/26.39 c_Polynomial_Osmult( X, T, c_Polynomial_OpCons( X, Z, Y ) ) =
% 26.01/26.39 c_Polynomial_OpCons( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T
% 26.01/26.39 ), Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 26.01/26.39 (82408) {G0,W22,D4,L3,V4,M3} { ! class_Rings_Ocomm__semiring__0( X ), !
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 26.01/26.39 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.39 (82409) {G0,W16,D4,L3,V4,M3} { ! class_Rings_Ocomm__semiring__0( X ), !
% 26.01/26.39 c_Polynomial_Osmult( X, T, Y ) = c_Polynomial_OpCons( X, Z, Y ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.39 (82410) {G0,W19,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 26.01/26.39 c_Polynomial_Osmult( X, T, c_Polynomial_Omonom( X, Z, Y ) ) =
% 26.01/26.39 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T
% 26.01/26.39 ), Z ), Y ) }.
% 26.01/26.39 (82411) {G0,W37,D7,L4,V3,M4} { ! class_Rings_Odivision__ring( X ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Oinverse( X, Y )
% 26.01/26.39 , c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 26.01/26.39 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 26.01/26.39 (82412) {G0,W17,D5,L3,V2,M3} { ! class_Rings_Odivision__ring( X ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Y ), c_Rings_Oinverse__class_Oinverse
% 26.01/26.39 ( X, Y ) ) = c_Groups_Oone__class_Oone( X ) }.
% 26.01/26.39 (82413) {G0,W17,D5,L3,V2,M3} { ! class_Rings_Odivision__ring( X ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 26.01/26.39 Y ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 26.01/26.39 (82414) {G0,W37,D7,L4,V3,M4} { ! class_Rings_Odivision__ring( X ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.39 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 26.01/26.39 ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 26.01/26.39 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 26.01/26.39 (82415) {G0,W31,D8,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 26.01/26.39 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 26.01/26.39 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 26.01/26.39 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 26.01/26.39 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) )
% 26.01/26.39 }.
% 26.01/26.39 (82416) {G0,W31,D8,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 26.01/26.39 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 26.01/26.39 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 26.01/26.39 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 26.01/26.39 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) )
% 26.01/26.39 }.
% 26.01/26.39 (82417) {G0,W30,D9,L2,V0,M2} { !
% 26.01/26.39 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 26.01/26.39 v_pa____ ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), c_Orderings_Oord__class_Oless
% 26.01/26.39 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 26.01/26.39 , hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 26.01/26.39 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 26.01/26.39 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 26.01/26.39 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 26.01/26.39 v_q____ ) ), skol12 ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 26.01/26.39 }.
% 26.01/26.39 (82418) {G0,W7,D3,L1,V0,M1} {
% 26.01/26.39 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 26.01/26.39 skol13 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 26.01/26.39 tc_Complex_Ocomplex, v_pa____ ) }.
% 26.01/26.39 (82419) {G0,W14,D4,L1,V1,M1} { hAPP( c_Polynomial_Opoly(
% 26.01/26.39 tc_Complex_Ocomplex, skol13 ), X ) = hAPP( c_Polynomial_Opoly(
% 26.01/26.39 tc_Complex_Ocomplex, v_pa____ ), c_Groups_Oplus__class_Oplus(
% 26.01/26.39 tc_Complex_Ocomplex, v_c____, X ) ) }.
% 26.01/26.39 (82420) {G0,W31,D8,L1,V0,M1} { ! hAPP( c_Polynomial_Opoly(
% 26.01/26.39 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ),
% 26.01/26.39 skol14 ) = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 26.01/26.39 c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ),
% 26.01/26.39 skol28 ) }.
% 26.01/26.39 (82421) {G0,W16,D4,L2,V0,M2} { ! hAPP( c_Polynomial_Opoly(
% 26.01/26.39 tc_Complex_Ocomplex, v_pa____ ), v_c____ ) = c_Groups_Ozero__class_Ozero
% 26.01/26.39 ( tc_Complex_Ocomplex ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 26.01/26.39 v_pa____ ), skol15 ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex )
% 26.01/26.39 }.
% 26.01/26.39 (82422) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 26.01/26.39 , Y ), Y = X }.
% 26.01/26.39 (82423) {G0,W12,D2,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 26.01/26.39 , Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 26.01/26.39 (82424) {G0,W8,D2,L2,V2,M2} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y
% 26.01/26.39 ) }.
% 26.01/26.39 (82425) {G0,W4,D2,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, X, X ) }.
% 26.01/26.39 (82426) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 26.01/26.39 (82427) {G0,W42,D5,L4,V4,M4} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), T ), hAPP(
% 26.01/26.39 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ), Z ) ) }.
% 26.01/26.39 (82428) {G0,W42,D5,L4,V4,M4} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ) ) }.
% 26.01/26.39 (82429) {G0,W20,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 26.01/26.39 (82430) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 26.01/26.39 (82431) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 26.01/26.39 (82432) {G0,W5,D3,L1,V0,M1} { ! c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_RealDef_Oreal ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 26.01/26.39 (82433) {G0,W7,D4,L1,V0,M1} { c_Rings_Oinverse__class_Oinverse(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 26.01/26.39 (82434) {G0,W9,D5,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_RealDef_Oreal ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X )
% 26.01/26.39 = X }.
% 26.01/26.39 (82435) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_RealDef_Oreal ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y )
% 26.01/26.39 ), X ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 26.01/26.39 (82436) {G0,W21,D6,L2,V2,M2} { ! c_Groups_Oplus__class_Oplus(
% 26.01/26.39 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_RealDef_Oreal ), X ), X ) ) = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 26.01/26.39 }.
% 26.01/26.39 (82437) {G0,W21,D6,L2,V2,M2} { ! c_Groups_Oplus__class_Oplus(
% 26.01/26.39 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_RealDef_Oreal ), X ), X ) ) = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 26.01/26.39 }.
% 26.01/26.39 (82438) {G0,W25,D6,L3,V2,M3} { ! Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_RealDef_Oreal ), ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 26.01/26.39 , c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 26.01/26.39 (82439) {G0,W15,D5,L2,V1,M2} { X = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_RealDef_Oreal ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_RealDef_Oreal ), c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X
% 26.01/26.39 ) ), X ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 26.01/26.39 (82440) {G0,W20,D5,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_RealDef_Oreal ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.39 ( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 26.01/26.39 (82441) {G0,W20,D5,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.39 ( tc_RealDef_Oreal ), Y ), X ) }.
% 26.01/26.39 (82442) {G0,W20,D5,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_RealDef_Oreal ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.39 ( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 26.01/26.39 (82443) {G0,W20,D5,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.39 ( tc_RealDef_Oreal ), X ), Y ) }.
% 26.01/26.39 (82444) {G0,W23,D7,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_RealDef_Oreal ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_RealDef_Oreal ), Z ), Y ) ), X ) = hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 26.01/26.39 (82445) {G0,W13,D5,L1,V2,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_RealDef_Oreal ), Y ), X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.39 ( tc_RealDef_Oreal ), X ), Y ) }.
% 26.01/26.39 (82446) {G0,W23,D4,L4,V3,M4} { !
% 26.01/26.39 class_RealVector_Oreal__normed__div__algebra( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Y ) ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 26.01/26.39 Y ) ), c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Z ) ) }.
% 26.01/26.39 (82447) {G0,W25,D6,L4,V3,M4} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! X =
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 26.01/26.39 ( tc_Int_Oint ), Y ) }.
% 26.01/26.39 (82448) {G0,W26,D6,L4,V3,M4} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! X =
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 26.01/26.39 (82449) {G0,W27,D6,L4,V3,M4} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 26.01/26.39 (82450) {G0,W28,D6,L4,V3,M4} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 26.01/26.39 (82451) {G0,W37,D6,L5,V5,M5} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 26.01/26.39 (82452) {G0,W54,D6,L7,V6,M7} { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 26.01/26.39 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T )
% 26.01/26.39 = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 26.01/26.39 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 26.01/26.39 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 26.01/26.39 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 26.01/26.39 (82453) {G0,W37,D6,L5,V5,M5} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 26.01/26.39 (82454) {G0,W54,D6,L7,V6,M7} { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 26.01/26.39 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T )
% 26.01/26.39 = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 26.01/26.39 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 26.01/26.39 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 26.01/26.39 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 26.01/26.39 (82455) {G0,W24,D5,L4,V4,M4} { ! class_RealVector_Oreal__normed__vector( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82456) {G0,W19,D3,L4,V2,M4} { ! class_Fields_Olinordered__field( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 26.01/26.39 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 26.01/26.39 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 26.01/26.39 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 26.01/26.39 (82457) {G0,W19,D3,L4,V2,M4} { !
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 26.01/26.39 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 26.01/26.39 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 26.01/26.39 (82458) {G0,W14,D3,L3,V2,M3} { !
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.39 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 26.01/26.39 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 26.01/26.39 (82459) {G0,W14,D3,L3,V2,M3} { !
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 26.01/26.39 ), c_Groups_Oone__class_Oone( X ) ) }.
% 26.01/26.39 (82460) {G0,W9,D4,L2,V1,M2} { ! class_Fields_Ofield__inverse__zero( X ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82461) {G0,W21,D6,L2,V3,M2} { ! class_Fields_Ofield__inverse__zero( X ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 26.01/26.39 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 26.01/26.39 (82462) {G0,W12,D3,L3,V2,M3} { ! class_Fields_Ofield__inverse__zero( X ),
% 26.01/26.39 ! c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X
% 26.01/26.39 ), Y = c_Groups_Oone__class_Oone( X ) }.
% 26.01/26.39 (82463) {G0,W12,D3,L3,V2,M3} { ! class_Fields_Ofield__inverse__zero( X ),
% 26.01/26.39 ! Y = c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X
% 26.01/26.39 , Y ) = c_Groups_Oone__class_Oone( X ) }.
% 26.01/26.39 (82464) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Nat_Onat, Y, X ), X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 26.01/26.39 skol16( X, Y ) ) }.
% 26.01/26.39 (82465) {G0,W10,D3,L2,V3,M2} { ! X = c_Groups_Oplus__class_Oplus(
% 26.01/26.39 tc_Nat_Onat, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 26.01/26.39 ) }.
% 26.01/26.39 (82466) {G0,W14,D3,L3,V2,M3} { !
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 26.01/26.39 ) }.
% 26.01/26.39 (82467) {G0,W14,D3,L3,V2,M3} { !
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 26.01/26.39 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 26.01/26.39 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 26.01/26.39 (82468) {G0,W14,D3,L3,V2,M3} { !
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 26.01/26.39 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.39 ) }.
% 26.01/26.39 (82469) {G0,W14,D3,L3,V2,M3} { !
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.39 ), c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 26.01/26.39 ) ) }.
% 26.01/26.39 (82470) {G0,W14,D3,L3,V2,M3} { !
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 26.01/26.39 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 26.01/26.39 (82471) {G0,W14,D3,L3,V2,M3} { !
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 26.01/26.39 (82472) {G0,W14,D3,L3,V2,M3} { !
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 26.01/26.39 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 26.01/26.39 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.39 (82473) {G0,W14,D3,L3,V2,M3} { !
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 26.01/26.39 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.39 (82474) {G0,W14,D3,L3,V2,M3} { ! class_Fields_Olinordered__field( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 26.01/26.39 (82475) {G0,W18,D3,L4,V2,M4} { ! class_Fields_Olinordered__field( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 26.01/26.39 (82476) {G0,W14,D3,L3,V2,M3} { ! class_Fields_Olinordered__field( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 26.01/26.39 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.39 (82477) {G0,W19,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 26.01/26.39 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 26.01/26.39 ( X, c_Rings_Oinverse__class_Oinverse( X, Y ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 26.01/26.39 (82478) {G0,W19,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 26.01/26.39 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 26.01/26.39 ( X, c_Rings_Oinverse__class_Oinverse( X, Y ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 26.01/26.39 (82479) {G0,W18,D3,L4,V2,M4} { ! class_Fields_Olinordered__field( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 26.01/26.39 ), c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 X ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 26.01/26.39 ) ) }.
% 26.01/26.39 (82480) {G0,W19,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Z
% 26.01/26.39 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 26.01/26.39 (82481) {G0,W19,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Z
% 26.01/26.39 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 26.01/26.39 (82482) {G0,W19,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 26.01/26.39 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 26.01/26.39 (82483) {G0,W19,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 26.01/26.39 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 26.01/26.39 (82484) {G0,W19,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 26.01/26.39 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 26.01/26.39 (82485) {G0,W19,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 26.01/26.39 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 26.01/26.39 (82486) {G0,W19,D3,L4,V2,M4} { !
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 26.01/26.39 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.39 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 26.01/26.39 , Y ) }.
% 26.01/26.39 (82487) {G0,W14,D3,L3,V2,M3} { !
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.39 ), c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 26.01/26.39 ) }.
% 26.01/26.39 (82488) {G0,W14,D3,L3,V2,M3} { !
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 26.01/26.39 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 26.01/26.39 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 26.01/26.39 (82489) {G0,W37,D7,L4,V3,M4} { ! class_Fields_Ofield( X ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Oinverse( X, Y )
% 26.01/26.39 , c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 26.01/26.39 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 26.01/26.39 (82490) {G0,W19,D3,L4,V2,M4} { ! class_Fields_Olinordered__field( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 26.01/26.39 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 26.01/26.39 (82491) {G0,W14,D3,L3,V2,M3} { !
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 26.01/26.39 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 26.01/26.39 (82492) {G0,W14,D3,L3,V2,M3} { !
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 26.01/26.39 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 26.01/26.39 (82493) {G0,W19,D3,L4,V2,M4} { !
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 26.01/26.39 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 26.01/26.39 (82494) {G0,W17,D5,L3,V2,M3} { ! class_Fields_Ofield( X ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 26.01/26.39 Y ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 26.01/26.39 (82495) {G0,W14,D3,L3,V2,M3} { !
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 26.01/26.39 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 26.01/26.39 (82496) {G0,W14,D3,L3,V2,M3} { !
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 26.01/26.39 }.
% 26.01/26.39 (82497) {G0,W19,D3,L4,V2,M4} { !
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 26.01/26.39 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 26.01/26.39 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 26.01/26.39 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 26.01/26.39 (82498) {G0,W16,D5,L1,V2,M1} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 26.01/26.39 (82499) {G0,W31,D8,L3,V2,M3} { X = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Complex_Ocomplex ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol17( X, Y ) ), Y
% 26.01/26.39 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 26.01/26.39 (82500) {G0,W15,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 26.01/26.39 (82501) {G0,W6,D3,L1,V0,M1} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 26.01/26.39 (82502) {G0,W6,D3,L1,V0,M1} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 26.01/26.39 (82503) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 26.01/26.39 tc_Int_Oint, X, Y ) ) }.
% 26.01/26.39 (82504) {G0,W20,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 26.01/26.39 (82505) {G0,W14,D5,L2,V1,M2} { c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP(
% 26.01/26.39 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 26.01/26.39 (82506) {G0,W14,D5,L2,V1,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_RealDef_Oreal ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 26.01/26.39 (82507) {G0,W29,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 26.01/26.39 c_Polynomial_Opcompose( X, c_Polynomial_OpCons( X, T, Z ), Y ) =
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 26.01/26.39 c_Polynomial_OpCons( X, T, c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ), Y ), c_Polynomial_Opcompose( X, Z, Y ) ) )
% 26.01/26.39 }.
% 26.01/26.39 (82508) {G0,W22,D4,L4,V3,M4} { ! class_Rings_Oidom( X ), ! hAPP(
% 26.01/26.39 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 26.01/26.39 c_Polynomial_Oorder( X, Y, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 26.01/26.39 ) }.
% 26.01/26.39 (82509) {G0,W15,D4,L3,V3,M3} { ! class_Rings_Oidom( X ), ! Z =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP(
% 26.01/26.39 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82510) {G0,W17,D4,L3,V3,M3} { ! class_Rings_Oidom( X ),
% 26.01/26.39 c_Polynomial_Oorder( X, Y, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 26.01/26.39 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 X ) }.
% 26.01/26.39 (82511) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 26.01/26.39 c_Polynomial_Opcompose( X, c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.39 (82512) {G0,W20,D5,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 26.01/26.39 ( c_Polynomial_Opoly( X, c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP
% 26.01/26.39 ( c_Polynomial_Opoly( X, T ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 26.01/26.39 (82513) {G0,W4,D3,L1,V0,M1} { ! skol18 = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Complex_Ocomplex ) }.
% 26.01/26.39 (82514) {G0,W4,D3,L1,V0,M1} { ! skol29 = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Nat_Onat ) }.
% 26.01/26.39 (82515) {G0,W24,D7,L1,V0,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 26.01/26.39 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 26.01/26.39 skol31 ), skol29 ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 26.01/26.39 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 26.01/26.39 c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 26.01/26.39 (82516) {G0,W52,D9,L1,V1,M1} { hAPP( c_Polynomial_Opoly(
% 26.01/26.39 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ), X )
% 26.01/26.39 = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 26.01/26.39 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 26.01/26.39 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 26.01/26.39 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 26.01/26.39 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ), hAPP(
% 26.01/26.39 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), skol29 ) ),
% 26.01/26.39 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 26.01/26.39 tc_Complex_Ocomplex, skol18, skol31 ) ), X ) ) ) }.
% 26.01/26.39 (82517) {G0,W6,D2,L2,V2,M2} { ! class_Orderings_Opreorder( X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, Y ) }.
% 26.01/26.39 (82518) {G0,W25,D5,L2,V3,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z,
% 26.01/26.39 c_Polynomial_Osmult( X, Y, c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) =
% 26.01/26.39 c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Z ), Y ),
% 26.01/26.39 c_Polynomial_Osynthetic__div( X, Z, Y ) ) }.
% 26.01/26.39 (82519) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 26.01/26.39 c_Polynomial_Osynthetic__div( X, c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.39 (82520) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 26.01/26.39 (82521) {G0,W16,D3,L3,V5,M3} { ! class_Orderings_Oord( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ), hAPP( Y, U ) ) }.
% 26.01/26.39 (82522) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 26.01/26.39 (82523) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 26.01/26.39 (82524) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Opreorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 26.01/26.39 (82525) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 26.01/26.39 (82526) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! Z = T,
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 26.01/26.39 (82527) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oord( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! Y = T,
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 26.01/26.39 (82528) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 26.01/26.39 (82529) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oord( X ), ! Z = Y, !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 26.01/26.39 (82530) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 26.01/26.39 (82531) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! Y = Z,
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 26.01/26.39 (82532) {G0,W16,D3,L3,V5,M3} { ! class_Orderings_Oord( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ), hAPP( Y, U ) ) }.
% 26.01/26.39 (82533) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 26.01/26.39 (82534) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), ! Z = Y,
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 26.01/26.39 (82535) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), ! Z = Y,
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 26.01/26.39 (82536) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 26.01/26.39 (82537) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 26.01/26.39 (82538) {G0,W16,D3,L3,V5,M3} { ! class_Orderings_Oord( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ), hAPP( Y, U ) ) }.
% 26.01/26.39 (82539) {G0,W22,D4,L3,V4,M3} { ! class_Orderings_Oord( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, skol19( X, Y, Z ) ), hAPP
% 26.01/26.39 ( Y, skol19( X, Y, Z ) ) ), c_Orderings_Oord__class_Oless__eq( tc_fun( T
% 26.01/26.39 , X ), Z, Y ) }.
% 26.01/26.39 (82540) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y,
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 26.01/26.39 (82541) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 26.01/26.39 ( X, Y, Z ) }.
% 26.01/26.39 (82542) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 26.01/26.39 ( X, T, Z ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 26.01/26.39 (82543) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Opreorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 26.01/26.39 ( X, Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 26.01/26.39 (82544) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Z = T,
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 26.01/26.39 (82545) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oord( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Y = T,
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 26.01/26.39 (82546) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 26.01/26.39 X, T, Z ) }.
% 26.01/26.39 (82547) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oord( X ), ! Z = Y, !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, T ), c_Orderings_Oord__class_Oless(
% 26.01/26.39 X, Z, T ) }.
% 26.01/26.39 (82548) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 26.01/26.39 ( X, Y, Z ) }.
% 26.01/26.39 (82549) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 26.01/26.39 ( X, Y, Z ) }.
% 26.01/26.39 (82550) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Y = Z }.
% 26.01/26.39 (82551) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Z = Y }.
% 26.01/26.39 (82552) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 26.01/26.39 ( X, Y, Z ) }.
% 26.01/26.39 (82553) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 26.01/26.39 ( X, Y, Z ) }.
% 26.01/26.39 (82554) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Z = Y }.
% 26.01/26.39 (82555) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ), Z = Y,
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 26.01/26.39 X, Y, Z ) }.
% 26.01/26.39 (82556) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 26.01/26.39 X, Y, Z ), Y = Z }.
% 26.01/26.39 (82557) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Y = Z, !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 26.01/26.39 (82558) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y,
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 26.01/26.39 (82559) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 26.01/26.39 X, Y, Z ), Z = Y }.
% 26.01/26.39 (82560) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, Z ), ! c_Orderings_Oord__class_Oless
% 26.01/26.39 ( X, Z, Y ) }.
% 26.01/26.39 (82561) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 26.01/26.39 (82562) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ), Z = Y,
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 26.01/26.39 X, Y, Z ) }.
% 26.01/26.39 (82563) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Z = Y }.
% 26.01/26.39 (82564) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, Z ), ! Z = Y }.
% 26.01/26.39 (82565) {G0,W6,D2,L2,V2,M2} { ! class_Orderings_Opreorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, Y ) }.
% 26.01/26.39 (82566) {G0,W21,D5,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 26.01/26.39 c_Polynomial_Osynthetic__div( X, c_Polynomial_OpCons( X, T, Z ), Y ) =
% 26.01/26.39 c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Z ), Y ),
% 26.01/26.39 c_Polynomial_Osynthetic__div( X, Z, Y ) ) }.
% 26.01/26.39 (82567) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 26.01/26.39 X, T, Y ) }.
% 26.01/26.39 (82568) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Opreorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, T ), c_Orderings_Oord__class_Oless(
% 26.01/26.39 X, Z, T ) }.
% 26.01/26.39 (82569) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 26.01/26.39 (82570) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Opreorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 26.01/26.39 (82571) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Y = Z,
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 26.01/26.39 (82572) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y,
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 26.01/26.39 (82573) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 26.01/26.39 (82574) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 26.01/26.39 (82575) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! Z = Y, !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 26.01/26.39 (82576) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 26.01/26.39 (82577) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 26.01/26.39 (82578) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), Z = Y, !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 26.01/26.39 (82579) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), Z = Y, !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 26.01/26.39 (82580) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 26.01/26.39 (82581) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Z = Y,
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 26.01/26.39 (82582) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 26.01/26.39 (82583) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 26.01/26.39 (82584) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 26.01/26.39 (82585) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 26.01/26.39 (82586) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), ! Z = Y,
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 26.01/26.39 (82587) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 26.01/26.39 (82588) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 26.01/26.39 (82589) {G0,W14,D2,L4,V3,M4} { ! class_Orderings_Opreorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 26.01/26.39 (82590) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 26.01/26.39 (82591) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Z = Y }.
% 26.01/26.39 (82592) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y,
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 26.01/26.39 (82593) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 26.01/26.39 (82594) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 26.01/26.39 (82595) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 26.01/26.39 (82596) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 26.01/26.39 (82597) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 26.01/26.39 (82598) {G0,W22,D4,L3,V5,M3} { ! class_Rings_Ocomm__semiring__0( X ), !
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), U,
% 26.01/26.39 c_Polynomial_Osmult( X, T, Z ) ) = c_Polynomial_OpCons( X, Y, Z ), Y =
% 26.01/26.39 hAPP( c_Polynomial_Opoly( X, U ), T ) }.
% 26.01/26.39 (82599) {G0,W21,D4,L3,V5,M3} { ! class_Rings_Ocomm__semiring__0( X ), !
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), U,
% 26.01/26.39 c_Polynomial_Osmult( X, T, Z ) ) = c_Polynomial_OpCons( X, Y, Z ), Z =
% 26.01/26.39 c_Polynomial_Osynthetic__div( X, U, T ) }.
% 26.01/26.39 (82600) {G0,W38,D9,L2,V3,M2} { ! class_Rings_Ocomm__ring__1( X ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 26.01/26.39 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 26.01/26.39 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 26.01/26.39 c_Polynomial_Osynthetic__div( X, Y, Z ) ), c_Polynomial_OpCons( X, hAPP(
% 26.01/26.39 c_Polynomial_Opoly( X, Y ), Z ), c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 26.01/26.39 (82601) {G0,W32,D5,L5,V7,M5} { ! class_RealVector_Oreal__normed__vector( Y
% 26.01/26.39 ), ! class_Orderings_Oord( X ), c_Orderings_Oord__class_Oless__eq( X, T
% 26.01/26.39 , skol20( X, U, W, T ) ), ! c_Orderings_Oord__class_Oless__eq( X, T, V0 )
% 26.01/26.39 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 26.01/26.39 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 26.01/26.39 ) ) }.
% 26.01/26.39 (82602) {G0,W42,D6,L5,V5,M5} { ! class_RealVector_Oreal__normed__vector( Y
% 26.01/26.39 ), ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( Y,
% 26.01/26.39 c_Groups_Ominus__class_Ominus( Y, hAPP( Z, T ), hAPP( Z, skol20( X, Y, Z
% 26.01/26.39 , T ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 26.01/26.39 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 26.01/26.39 ) ) }.
% 26.01/26.39 (82603) {G0,W14,D3,L3,V4,M3} { ! class_Orderings_Oord( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 26.01/26.39 (82604) {G0,W14,D3,L3,V4,M3} { ! class_Orderings_Oord( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z ) }.
% 26.01/26.39 (82605) {G0,W20,D3,L4,V4,M4} { ! class_Orderings_Oord( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 26.01/26.39 (82606) {G0,W10,D4,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 26.01/26.39 (82607) {G0,W11,D4,L1,V2,M1} { c_Groups_Ominus__class_Ominus(
% 26.01/26.39 tc_Complex_Ocomplex, Y, X ) = c_Groups_Oplus__class_Oplus(
% 26.01/26.39 tc_Complex_Ocomplex, Y, c_Groups_Ouminus__class_Ouminus(
% 26.01/26.39 tc_Complex_Ocomplex, X ) ) }.
% 26.01/26.39 (82608) {G0,W9,D4,L1,V1,M1} { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ), X ) =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 26.01/26.39 (82609) {G0,W12,D4,L2,V2,M2} { ! c_Groups_Oplus__class_Oplus(
% 26.01/26.39 tc_RealDef_Oreal, Y, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X
% 26.01/26.39 ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 26.01/26.39 (82610) {G0,W12,D4,L2,V2,M2} { ! Y = X, c_Groups_Oplus__class_Oplus(
% 26.01/26.39 tc_RealDef_Oreal, Y, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X
% 26.01/26.39 ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 26.01/26.39 (82611) {G0,W12,D3,L2,V2,M2} { ! c_Groups_Oplus__class_Oplus(
% 26.01/26.39 tc_RealDef_Oreal, Y, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 26.01/26.39 ), X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 26.01/26.39 (82612) {G0,W12,D3,L2,V2,M2} { ! X = c_Groups_Ouminus__class_Ouminus(
% 26.01/26.39 tc_RealDef_Oreal, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 26.01/26.39 X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 26.01/26.39 (82613) {G0,W11,D4,L1,V2,M1} { c_Groups_Ominus__class_Ominus( tc_Int_Oint
% 26.01/26.39 , Y, X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 26.01/26.39 (82614) {G0,W11,D4,L1,V2,M1} { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y
% 26.01/26.39 , c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 26.01/26.39 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 26.01/26.39 (82615) {G0,W11,D4,L1,V2,M1} { c_Groups_Ominus__class_Ominus(
% 26.01/26.39 tc_RealDef_Oreal, Y, X ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal
% 26.01/26.39 , Y, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 26.01/26.39 (82616) {G0,W11,D4,L1,V2,M1} { c_Groups_Ominus__class_Ominus(
% 26.01/26.39 tc_RealDef_Oreal, Y, X ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal
% 26.01/26.39 , Y, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 26.01/26.39 (82617) {G0,W21,D5,L4,V2,M4} { ! class_Rings_Oring__1__no__zero__divisors
% 26.01/26.39 ( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 26.01/26.39 c_Groups_Oone__class_Oone( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 26.01/26.39 (82618) {G0,W15,D5,L3,V2,M3} { ! class_Rings_Oring__1__no__zero__divisors
% 26.01/26.39 ( X ), ! Y = c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 26.01/26.39 ( X ) }.
% 26.01/26.39 (82619) {G0,W17,D5,L3,V2,M3} { ! class_Rings_Oring__1__no__zero__divisors
% 26.01/26.39 ( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X,
% 26.01/26.39 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 26.01/26.39 ( X ) }.
% 26.01/26.39 (82620) {G0,W15,D6,L2,V2,M2} { ! class_Rings_Ocomm__ring__1( X ),
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ) = hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X,
% 26.01/26.39 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 26.01/26.39 (82621) {G0,W13,D4,L2,V3,M2} { ! class_Rings_Ocomm__ring__1( X ),
% 26.01/26.39 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Oplus__class_Oplus( X
% 26.01/26.39 , Z, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 26.01/26.39 (82622) {G0,W13,D4,L2,V3,M2} { ! class_Groups_Ogroup__add( X ),
% 26.01/26.39 c_Groups_Ominus__class_Ominus( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 26.01/26.39 Y ) ) = c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 26.01/26.39 (82623) {G0,W13,D4,L2,V3,M2} { ! class_Groups_Oab__group__add( X ),
% 26.01/26.39 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Oplus__class_Oplus( X
% 26.01/26.39 , Z, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 26.01/26.39 (82624) {G0,W13,D4,L2,V3,M2} { ! class_Groups_Ogroup__add( X ),
% 26.01/26.39 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Oplus__class_Oplus( X
% 26.01/26.39 , Z, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 26.01/26.39 (82625) {G0,W17,D4,L3,V2,M3} { ! class_Rings_Odivision__ring( X ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Oinverse( X,
% 26.01/26.39 Y ) ) }.
% 26.01/26.39 (82626) {G0,W18,D6,L2,V3,M2} { ! class_Rings_Ocomm__ring( X ), hAPP(
% 26.01/26.39 c_Polynomial_Opoly( X, c_Groups_Ouminus__class_Ouminus(
% 26.01/26.39 tc_Polynomial_Opoly( X ), Z ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X
% 26.01/26.39 , hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 26.01/26.39 (82627) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), !
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 26.01/26.39 ( X, Y ), Z = Y }.
% 26.01/26.39 (82628) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), ! Z = Y,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 26.01/26.39 ( X, Y ) }.
% 26.01/26.39 (82629) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), !
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Z ) = Y,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 26.01/26.39 (82630) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), !
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ) = Z,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 26.01/26.39 (82631) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), ! Z =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ), Y =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 26.01/26.39 (82632) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), ! Y =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Z ), Z =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 26.01/26.39 (82633) {G0,W9,D4,L2,V2,M2} { ! class_Groups_Ogroup__add( X ),
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 26.01/26.39 ) ) = Y }.
% 26.01/26.39 (82634) {G0,W16,D4,L2,V3,M2} { ! class_Groups_Oab__group__add( X ),
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 26.01/26.39 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 26.01/26.39 (82635) {G0,W19,D5,L2,V3,M2} { ! class_Groups_Oab__group__add( X ),
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 26.01/26.39 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 26.01/26.39 ( tc_Polynomial_Opoly( X ), Y ) ) }.
% 26.01/26.39 (82636) {G0,W19,D5,L2,V3,M2} { ! class_Groups_Oab__group__add( X ),
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 26.01/26.39 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 26.01/26.39 ( tc_Polynomial_Opoly( X ), Y ) ) }.
% 26.01/26.39 (82637) {G0,W11,D4,L2,V2,M2} { ! class_Groups_Ogroup__add( X ),
% 26.01/26.39 c_Groups_Ominus__class_Ominus( X, c_Groups_Ozero__class_Ozero( X ), Y ) =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 26.01/26.39 (82638) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), !
% 26.01/26.39 c_Groups_Oplus__class_Oplus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X )
% 26.01/26.39 , Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 26.01/26.39 (82639) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), ! Y =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 26.01/26.39 Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82640) {G0,W11,D4,L2,V2,M2} { ! class_Groups_Ogroup__add( X ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Ouminus__class_Ouminus( X, Y
% 26.01/26.39 ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82641) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), ! Z =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Oplus__class_Oplus( X,
% 26.01/26.39 Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82642) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), !
% 26.01/26.39 c_Groups_Oplus__class_Oplus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X )
% 26.01/26.39 , Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 26.01/26.39 (82643) {G0,W11,D4,L2,V2,M2} { ! class_Groups_Ogroup__add( X ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 26.01/26.39 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82644) {G0,W11,D4,L2,V2,M2} { ! class_Groups_Oab__group__add( X ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 26.01/26.39 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82645) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), !
% 26.01/26.39 c_Groups_Oplus__class_Oplus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X )
% 26.01/26.39 , c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 26.01/26.39 (82646) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.39 ( X ), ! c_Orderings_Oord__class_Oless( X,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 26.01/26.39 }.
% 26.01/26.39 (82647) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.39 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 26.01/26.39 ), Y ), c_Orderings_Oord__class_Oless( X,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) }.
% 26.01/26.39 (82648) {G0,W14,D3,L3,V2,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus(
% 26.01/26.39 X, Y ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 26.01/26.39 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 26.01/26.39 (82649) {G0,W14,D3,L3,V2,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.39 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 26.01/26.39 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.39 (82650) {G0,W14,D3,L3,V2,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.39 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 26.01/26.39 }.
% 26.01/26.39 (82651) {G0,W14,D3,L3,V2,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 26.01/26.39 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.39 , c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 26.01/26.39 (82652) {G0,W13,D3,L3,V2,M3} { ! class_Rings_Olinordered__idom( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 26.01/26.39 Y ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero(
% 26.01/26.39 X ) ) }.
% 26.01/26.39 (82653) {G0,W13,D3,L3,V2,M3} { ! class_Rings_Olinordered__idom( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 26.01/26.39 Y ) ) }.
% 26.01/26.39 (82654) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.39 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 26.01/26.39 ) }.
% 26.01/26.39 (82655) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.39 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 26.01/26.39 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) }.
% 26.01/26.39 (82656) {G0,W14,D3,L3,V2,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 26.01/26.39 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 26.01/26.39 ), Y ) }.
% 26.01/26.39 (82657) {G0,W14,D3,L3,V2,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 26.01/26.39 X ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 26.01/26.39 ) }.
% 26.01/26.39 (82658) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.39 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.39 ) }.
% 26.01/26.39 (82659) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.39 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 26.01/26.39 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 26.01/26.39 (82660) {G0,W14,D3,L3,V2,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 26.01/26.39 X ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 26.01/26.39 ) }.
% 26.01/26.39 (82661) {G0,W14,D3,L3,V2,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 26.01/26.39 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 26.01/26.39 ) ) }.
% 26.01/26.39 (82662) {G0,W17,D6,L1,V2,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_Int_Oint ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 26.01/26.39 (82663) {G0,W23,D5,L4,V3,M4} { ! class_Rings_Oidom( X ), ! hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Y ), Y ), Z = Y, Z =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 26.01/26.39 (82664) {G0,W18,D5,L3,V3,M3} { ! class_Rings_Oidom( X ), ! Z = Y, hAPP(
% 26.01/26.39 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 26.01/26.39 (82665) {G0,W20,D5,L3,V3,M3} { ! class_Rings_Oidom( X ), ! Z =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 26.01/26.39 (82666) {G0,W19,D5,L2,V3,M2} { ! class_Rings_Oring( X ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 26.01/26.39 ) ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 26.01/26.39 (82667) {G0,W19,D5,L2,V3,M2} { ! class_Rings_Oring( X ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 26.01/26.39 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 26.01/26.39 (82668) {G0,W19,D6,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.39 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 26.01/26.39 (82669) {G0,W19,D6,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.39 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 26.01/26.39 (82670) {G0,W19,D6,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.39 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 26.01/26.39 (82671) {G0,W19,D6,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.39 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 26.01/26.39 (82672) {G0,W19,D6,L2,V3,M2} { ! class_Rings_Oring( X ),
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 26.01/26.39 ) ), Y ) }.
% 26.01/26.39 (82673) {G0,W19,D6,L2,V3,M2} { ! class_Rings_Oring( X ),
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 26.01/26.39 ( X, Y ) ) }.
% 26.01/26.39 (82674) {G0,W15,D4,L1,V2,M1} { c_Groups_Ouminus__class_Ouminus(
% 26.01/26.39 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 26.01/26.39 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) )
% 26.01/26.39 }.
% 26.01/26.39 (82675) {G0,W13,D4,L2,V2,M2} { !
% 26.01/26.39 class_Rings_Odivision__ring__inverse__zero( X ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 26.01/26.39 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 26.01/26.39 (82676) {G0,W11,D4,L2,V2,M2} { ! class_RealVector_Oreal__normed__vector( X
% 26.01/26.39 ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus(
% 26.01/26.39 X, Y ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 26.01/26.39 (82677) {G0,W13,D4,L2,V3,M2} { ! class_Groups_Oab__group__add( X ),
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Ominus__class_Ominus( X, Z,
% 26.01/26.39 Y ) ) = c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 26.01/26.39 (82678) {G0,W17,D4,L2,V3,M2} { ! class_Groups_Oab__group__add( X ),
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 26.01/26.39 ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X
% 26.01/26.39 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 26.01/26.39 (82679) {G0,W17,D4,L2,V3,M2} { ! class_Groups_Ogroup__add( X ),
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 26.01/26.39 ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X
% 26.01/26.39 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 26.01/26.39 (82680) {G0,W13,D5,L2,V3,M2} { ! class_Groups_Ogroup__add( X ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Oplus__class_Oplus( X,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) ) = Y }.
% 26.01/26.39 (82681) {G0,W13,D4,L2,V3,M2} { ! class_Groups_Ogroup__add( X ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = Y }.
% 26.01/26.39 (82682) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless( X, Z,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 26.01/26.39 ( X, Y, c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 26.01/26.39 (82683) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless( X, Y,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Z ) ), c_Orderings_Oord__class_Oless
% 26.01/26.39 ( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 26.01/26.39 (82684) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus(
% 26.01/26.39 X, Z ), Y ), c_Orderings_Oord__class_Oless( X,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 26.01/26.39 (82685) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus(
% 26.01/26.39 X, Y ), Z ), c_Orderings_Oord__class_Oless( X,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 26.01/26.39 (82686) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus(
% 26.01/26.39 X, Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 26.01/26.39 (82687) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 26.01/26.39 , c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 26.01/26.39 (82688) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 26.01/26.39 ( X, Z ) ) }.
% 26.01/26.39 (82689) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 26.01/26.39 ( X, Y ) ) }.
% 26.01/26.39 (82690) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 26.01/26.39 , Y ), Z ) }.
% 26.01/26.39 (82691) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 26.01/26.39 , Z ), Y ) }.
% 26.01/26.39 (82692) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless__eq( X,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 26.01/26.39 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 26.01/26.39 (82693) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 26.01/26.39 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 26.01/26.39 (82694) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 26.01/26.39 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 26.01/26.39 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 26.01/26.39 (82695) {G0,W9,D4,L2,V1,M2} { ! class_Groups_Ogroup__add( X ),
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82696) {G0,W12,D3,L3,V2,M3} { ! class_Groups_Ogroup__add( X ), !
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 26.01/26.39 ), c_Groups_Ozero__class_Ozero( X ) = Y }.
% 26.01/26.39 (82697) {G0,W12,D3,L3,V2,M3} { ! class_Groups_Ogroup__add( X ), !
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ) = Y, c_Groups_Ozero__class_Ozero( X ) =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 26.01/26.39 (82698) {G0,W11,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.39 ( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X, Y ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82699) {G0,W11,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.39 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Y =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 26.01/26.39 (82700) {G0,W12,D3,L3,V2,M3} { ! class_Groups_Ogroup__add( X ), !
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 26.01/26.39 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82701) {G0,W12,D3,L3,V2,M3} { ! class_Groups_Ogroup__add( X ), ! Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 26.01/26.39 = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82702) {G0,W11,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.39 ( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82703) {G0,W11,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 26.01/26.39 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y }.
% 26.01/26.39 (82704) {G0,W12,D5,L2,V1,M2} { ! class_Groups_Oab__group__add( X ),
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.39 (82705) {G0,W16,D4,L2,V3,M2} { ! class_Rings_Ocomm__ring( X ),
% 26.01/26.39 c_Polynomial_Osmult( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 26.01/26.39 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 26.01/26.39 (82706) {G0,W17,D5,L2,V3,M2} { ! class_Rings_Ocomm__ring( X ),
% 26.01/26.39 c_Polynomial_Osmult( X, Z, c_Groups_Ouminus__class_Ouminus(
% 26.01/26.39 tc_Polynomial_Opoly( X ), Y ) ) = c_Groups_Ouminus__class_Ouminus(
% 26.01/26.39 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 26.01/26.39 (82707) {G0,W7,D4,L1,V0,M1} { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint
% 26.01/26.39 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 26.01/26.39 (82708) {G0,W16,D6,L1,V2,M1} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP
% 26.01/26.39 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ),
% 26.01/26.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) )
% 26.01/26.39 }.
% 26.01/26.39 (82709) {G0,W14,D5,L2,V2,M2} { ! class_Groups_Oab__group__add( X ),
% 26.01/26.39 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) }.
% 26.01/26.39 (82710) {G0,W30,D8,L2,V3,M2} { ! class_Rings_Oring__1( X ), hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 26.01/26.39 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 26.01/26.39 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 26.01/26.39 (82711) {G0,W29,D6,L4,V3,M4} { ! class_Rings_Oidom( X ), ! hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 26.01/26.39 (82712) {G0,W24,D6,L3,V3,M3} { ! class_Rings_Oidom( X ), ! Z = Y, hAPP(
% 26.01/26.39 hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 26.01/26.39 (82713) {G0,W26,D6,L3,V3,M3} { ! class_Rings_Oidom( X ), ! Z =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ), hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 26.01/26.39 (82714) {G0,W14,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 26.01/26.39 (82715) {G0,W14,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, X, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y
% 26.01/26.39 ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 26.01/26.39 (82716) {G0,W14,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 26.01/26.39 (82717) {G0,W14,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y )
% 26.01/26.39 , X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 26.01/26.39 (82718) {G0,W14,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 26.01/26.39 (82719) {G0,W14,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, X, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y
% 26.01/26.39 ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 26.01/26.39 (82720) {G0,W14,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 26.01/26.39 (82721) {G0,W14,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y )
% 26.01/26.39 , X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 26.01/26.39 (82722) {G0,W39,D8,L4,V3,M4} { ! class_Rings_Odivision__ring( X ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.39 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 26.01/26.39 ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 26.01/26.39 Y ) ), c_Groups_Ominus__class_Ominus( X, Y, Z ) ) ),
% 26.01/26.39 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 26.01/26.39 (82723) {G0,W32,D8,L3,V3,M3} { ! class_Rings_Oidom( X ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 26.01/26.39 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 26.01/26.39 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 26.01/26.39 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 26.01/26.39 (82724) {G0,W33,D8,L3,V3,M3} { ! class_Rings_Oidom( X ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 26.01/26.39 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 26.01/26.39 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc
% 26.01/26.39 ( c_Polynomial_Oorder( X, Z, Y ) ) ), Y ) }.
% 26.01/26.39 (82725) {G0,W33,D8,L3,V3,M3} { ! class_Rings_Oidom( X ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 26.01/26.39 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 26.01/26.39 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc
% 26.01/26.39 ( c_Polynomial_Oorder( X, Z, Y ) ) ), Y ) }.
% 26.01/26.39 (82726) {G0,W7,D3,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 26.01/26.39 (82727) {G0,W7,D4,L1,V1,M1} { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint
% 26.01/26.39 , c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 26.01/26.39 (82728) {G0,W12,D3,L3,V3,M3} { ! class_Rings_Ocomm__ring__1( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y )
% 26.01/26.39 , c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 26.01/26.39 (82729) {G0,W12,D3,L3,V3,M3} { ! class_Rings_Ocomm__ring__1( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, Y ), c_Rings_Odvd__class_Odvd( X,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 26.01/26.39 (82730) {G0,W12,D3,L3,V3,M3} { ! class_Rings_Ocomm__ring__1( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y ) )
% 26.01/26.39 , c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 26.01/26.39 (82731) {G0,W12,D3,L3,V3,M3} { ! class_Rings_Ocomm__ring__1( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, Y ), c_Rings_Odvd__class_Odvd( X, Z,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 26.01/26.39 (82732) {G0,W20,D5,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 26.01/26.39 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) )
% 26.01/26.39 }.
% 26.01/26.39 (82733) {G0,W24,D5,L4,V5,M4} { ! class_Rings_Ocomm__semiring__1( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq
% 26.01/26.39 ( tc_Nat_Onat, U, T ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( X ), Z ), U ), hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 26.01/26.39 (82734) {G0,W24,D5,L4,V5,M4} { ! class_Rings_Ocomm__semiring__1( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 26.01/26.39 ), T ), Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z
% 26.01/26.39 ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 26.01/26.39 ( X ), T ), U ), Y ) }.
% 26.01/26.39 (82735) {G0,W15,D3,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z,
% 26.01/26.39 c_Polynomial_Osmult( X, T, Y ) ) }.
% 26.01/26.39 (82736) {G0,W15,D3,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 26.01/26.39 X, T, Z ), Y ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y
% 26.01/26.39 ) }.
% 26.01/26.39 (82737) {G0,W11,D3,L3,V2,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, c_Groups_Ozero__class_Ozero( X ), Y ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82738) {G0,W17,D3,L4,V4,M4} { ! class_Rings_Ocomm__semiring__1( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T
% 26.01/26.39 ), c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, Y, T
% 26.01/26.39 ) ) }.
% 26.01/26.39 (82739) {G0,W7,D3,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 26.01/26.39 (82740) {G0,W17,D3,L4,V4,M4} { ! class_Rings_Ocomm__ring__1( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T
% 26.01/26.39 ), c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ominus__class_Ominus( X, Y,
% 26.01/26.39 T ) ) }.
% 26.01/26.39 (82741) {G0,W20,D5,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, Y ), c_Rings_Odvd__class_Odvd( X, hAPP(
% 26.01/26.39 hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 26.01/26.39 (82742) {G0,W11,D5,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.39 ( X ), Z ), Y ) ) }.
% 26.01/26.39 (82743) {G0,W11,D5,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 26.01/26.39 ( X ), Y ), Z ) ) }.
% 26.01/26.39 (82744) {G0,W15,D5,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP
% 26.01/26.39 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 26.01/26.39 (82745) {G0,W15,D5,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP
% 26.01/26.39 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 26.01/26.39 (82746) {G0,W24,D5,L4,V5,M4} { ! class_Rings_Ocomm__semiring__1( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, U, T
% 26.01/26.39 ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 26.01/26.39 (82747) {G0,W14,D5,L3,V4,M3} { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X
% 26.01/26.39 , Y, Z ) }.
% 26.01/26.39 (82748) {G0,W15,D5,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 26.01/26.39 ), Z ), T ), Y ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 26.01/26.39 (82749) {G0,W15,D5,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 26.01/26.39 ), T ), Z ), Y ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 26.01/26.39 (82750) {G0,W24,D5,L4,V4,M4} { ! class_Rings_Oidom( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 26.01/26.39 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 26.01/26.39 , T = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 26.01/26.39 ) }.
% 26.01/26.39 (82751) {G0,W20,D5,L3,V4,M3} { ! class_Rings_Oidom( X ), ! T =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP
% 26.01/26.39 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 26.01/26.39 (82752) {G0,W20,D5,L3,V4,M3} { ! class_Rings_Oidom( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, Y ), c_Rings_Odvd__class_Odvd( X, hAPP(
% 26.01/26.39 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 26.01/26.39 (82753) {G0,W24,D5,L4,V4,M4} { ! class_Rings_Oidom( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 26.01/26.39 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 26.01/26.39 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y
% 26.01/26.39 ) }.
% 26.01/26.39 (82754) {G0,W20,D5,L3,V4,M3} { ! class_Rings_Oidom( X ), ! Z =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP
% 26.01/26.39 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 26.01/26.39 (82755) {G0,W20,D5,L3,V4,M3} { ! class_Rings_Oidom( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, T, Y ), c_Rings_Odvd__class_Odvd( X, hAPP(
% 26.01/26.39 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 26.01/26.39 (82756) {G0,W6,D2,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Y, Y ) }.
% 26.01/26.39 (82757) {G0,W14,D2,L4,V4,M4} { ! class_Rings_Ocomm__semiring__1( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T
% 26.01/26.39 ), c_Rings_Odvd__class_Odvd( X, Z, T ) }.
% 26.01/26.39 (82758) {G0,W19,D3,L4,V4,M4} { ! class_Fields_Ofield( X ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Y, Z ) ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ) }.
% 26.01/26.39 (82759) {G0,W19,D3,L4,V4,M4} { ! class_Fields_Ofield( X ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Polynomial_Opoly( X ), T, Z ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Y, Z ) ) }.
% 26.01/26.39 (82760) {G0,W19,D3,L4,V4,M4} { ! class_Fields_Ofield( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), T =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) }.
% 26.01/26.39 (82761) {G0,W19,D3,L4,V4,M4} { ! class_Fields_Ofield( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 26.01/26.39 c_Polynomial_Osmult( X, Z, Y ) ), Z = c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Y ) }.
% 26.01/26.39 (82762) {G0,W14,D3,L3,V4,M3} { ! class_Fields_Ofield( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 26.01/26.39 X, T, Z ), Y ), alpha10( X, Y, T ) }.
% 26.01/26.39 (82763) {G0,W15,D3,L3,V4,M3} { ! class_Fields_Ofield( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 26.01/26.39 X, T, Z ), Y ), alpha22( X, Y, Z, T ) }.
% 26.01/26.39 (82764) {G0,W19,D3,L4,V4,M4} { ! class_Fields_Ofield( X ), ! alpha10( X, Y
% 26.01/26.39 , T ), ! alpha22( X, Y, Z, T ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) }.
% 26.01/26.39 (82765) {G0,W14,D3,L3,V4,M3} { ! alpha22( X, Y, Z, T ), T =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 26.01/26.39 (82766) {G0,W9,D3,L2,V4,M2} { ! T = c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.39 alpha22( X, Y, Z, T ) }.
% 26.01/26.39 (82767) {G0,W10,D3,L2,V4,M2} { ! c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Polynomial_Opoly( X ), Z, Y ), alpha22( X, Y, Z, T ) }.
% 26.01/26.39 (82768) {G0,W13,D4,L3,V3,M3} { ! alpha10( X, Y, Z ), ! Z =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.39 (82769) {G0,W8,D3,L2,V3,M2} { Z = c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.39 alpha10( X, Y, Z ) }.
% 26.01/26.39 (82770) {G0,W9,D4,L2,V3,M2} { ! Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ), alpha10( X, Y, Z ) }.
% 26.01/26.39 (82771) {G0,W16,D5,L3,V3,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 26.01/26.39 (82772) {G0,W15,D5,L3,V3,M3} { ! class_Rings_Ocomm__semiring__1( X ), ! Y
% 26.01/26.39 = c_Groups_Oone__class_Oone( X ), c_Rings_Odvd__class_Odvd( X, Y, hAPP(
% 26.01/26.39 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 26.01/26.39 (82773) {G0,W26,D6,L3,V3,M3} { ! class_Rings_Oidom( X ), ! hAPP(
% 26.01/26.39 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_OpCons(
% 26.01/26.39 X, c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 26.01/26.39 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 26.01/26.39 (82774) {G0,W26,D6,L3,V3,M3} { ! class_Rings_Oidom( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_OpCons(
% 26.01/26.39 X, c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 26.01/26.39 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP( c_Polynomial_Opoly( X, Z ), Y
% 26.01/26.39 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82775) {G0,W26,D6,L3,V3,M3} { ! class_Rings_Oidom( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_OpCons(
% 26.01/26.39 X, Z, c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP(
% 26.01/26.39 c_Polynomial_Opoly( X, Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ) }.
% 26.01/26.39 (82776) {G0,W26,D6,L3,V3,M3} { ! class_Rings_Oidom( X ), ! hAPP(
% 26.01/26.39 c_Polynomial_Opoly( X, Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons
% 26.01/26.39 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 26.01/26.39 (82777) {G0,W27,D8,L2,V3,M2} { ! class_Rings_Oidom( X ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 26.01/26.39 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 26.01/26.39 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 26.01/26.39 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 26.01/26.39 (82778) {G0,W30,D7,L5,V6,M5} { ! class_Rings_Ocomm__ring( X ), !
% 26.01/26.39 class_Rings_Odvd( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 26.01/26.39 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X,
% 26.01/26.39 c_Groups_Ominus__class_Ominus( X, U, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 26.01/26.39 (82779) {G0,W30,D7,L5,V6,M5} { ! class_Rings_Ocomm__ring( X ), !
% 26.01/26.39 class_Rings_Odvd( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X,
% 26.01/26.39 c_Groups_Ominus__class_Ominus( X, U, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 26.01/26.39 }.
% 26.01/26.39 (82780) {G0,W30,D7,L5,V6,M5} { ! class_Rings_Ocomm__ring( X ), !
% 26.01/26.39 class_Rings_Odvd( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 26.01/26.39 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X,
% 26.01/26.39 c_Groups_Ominus__class_Ominus( X, U, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 26.01/26.39 (82781) {G0,W30,D7,L5,V6,M5} { ! class_Rings_Ocomm__ring( X ), !
% 26.01/26.39 class_Rings_Odvd( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X,
% 26.01/26.39 c_Groups_Ominus__class_Ominus( X, U, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 26.01/26.39 }.
% 26.01/26.39 (82782) {G0,W6,D4,L1,V1,M1} { c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 26.01/26.39 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 26.01/26.39 (82783) {G0,W19,D3,L4,V3,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z
% 26.01/26.39 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 26.01/26.39 (82784) {G0,W19,D3,L4,V3,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z
% 26.01/26.39 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 26.01/26.39 (82785) {G0,W21,D3,L5,V2,M5} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 26.01/26.39 ( tc_Int_Oint, Y, X ), X = Y }.
% 26.01/26.39 (82786) {G0,W10,D3,L2,V2,M2} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 26.01/26.39 (82787) {G0,W10,D3,L2,V2,M2} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y
% 26.01/26.39 , c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 26.01/26.39 (82788) {G0,W10,D3,L2,V2,M2} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 26.01/26.39 (82789) {G0,W10,D3,L2,V2,M2} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 26.01/26.39 (82790) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 26.01/26.39 c_Fact_Ofact__class_Ofact( tc_Nat_Onat, Y ), c_Fact_Ofact__class_Ofact(
% 26.01/26.39 tc_Nat_Onat, X ) ) }.
% 26.01/26.39 (82791) {G0,W16,D6,L2,V3,M2} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z
% 26.01/26.39 , c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 26.01/26.39 (82792) {G0,W16,D6,L2,V3,M2} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z
% 26.01/26.39 , Y ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 26.01/26.39 (82793) {G0,W26,D7,L3,V5,M3} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y
% 26.01/26.39 , X ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 26.01/26.39 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ) }.
% 26.01/26.39 (82794) {G0,W26,D7,L3,V5,M3} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y
% 26.01/26.39 , X ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 26.01/26.39 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 26.01/26.39 , Z ), X ) ), T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) }.
% 26.01/26.39 (82795) {G0,W11,D4,L2,V1,M2} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X
% 26.01/26.39 , c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 26.01/26.39 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.39 (82796) {G0,W11,D4,L2,V1,M2} { ! X = c_Nat_OSuc(
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 26.01/26.39 ) }.
% 26.01/26.39 (82797) {G0,W13,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 26.01/26.39 (82798) {G0,W22,D5,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Int_Oint ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 26.01/26.39 (82799) {G0,W22,D5,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Int_Oint ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 26.01/26.39 (82800) {G0,W11,D3,L2,V2,M2} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 26.01/26.39 (82801) {G0,W11,D3,L2,V2,M2} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 26.01/26.39 (82802) {G0,W15,D3,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus(
% 26.01/26.39 tc_Nat_Onat, X, Z ) ) }.
% 26.01/26.39 (82803) {G0,W9,D3,L2,V1,M2} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X,
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone
% 26.01/26.39 ( tc_Nat_Onat ) }.
% 26.01/26.39 (82804) {G0,W9,D3,L2,V1,M2} { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat
% 26.01/26.39 ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 26.01/26.39 tc_Nat_Onat ) ) }.
% 26.01/26.39 (82805) {G0,W15,D3,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z
% 26.01/26.39 , c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Int_Oint, Z, Y ) }.
% 26.01/26.39 (82806) {G0,W22,D5,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint,
% 26.01/26.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP
% 26.01/26.39 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Int_Oint, Y, X ) }.
% 26.01/26.39 (82807) {G0,W13,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 26.01/26.39 (82808) {G0,W22,D5,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 26.01/26.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP
% 26.01/26.39 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, Y, X ) }.
% 26.01/26.39 (82809) {G0,W18,D5,L2,V3,M2} { ! Z = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Nat_Onat ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 26.01/26.39 (82810) {G0,W18,D5,L2,V3,M2} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 26.01/26.39 (82811) {G0,W13,D3,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y
% 26.01/26.39 , X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 26.01/26.39 (82812) {G0,W13,D3,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 26.01/26.39 (82813) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 26.01/26.39 (82814) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 26.01/26.39 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y
% 26.01/26.39 ) ) }.
% 26.01/26.39 (82815) {G0,W23,D5,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 26.01/26.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP
% 26.01/26.39 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 26.01/26.39 (82816) {G0,W15,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Fact_Ofact__class_Ofact(
% 26.01/26.39 tc_Nat_Onat, Y ) ) }.
% 26.01/26.39 (82817) {G0,W18,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 26.01/26.39 (82818) {G0,W18,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! Y =
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 26.01/26.39 ), Y ), X ) }.
% 26.01/26.39 (82819) {G0,W18,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 26.01/26.39 (82820) {G0,W18,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! Y =
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 26.01/26.39 ), X ), X ) }.
% 26.01/26.39 (82821) {G0,W23,D5,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 26.01/26.39 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP(
% 26.01/26.39 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 26.01/26.39 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 26.01/26.39 ) }.
% 26.01/26.39 (82822) {G0,W20,D6,L4,V6,M4} { ! class_Rings_Odvd( X ), !
% 26.01/26.39 class_Rings_Osemiring__0( X ), ! hBOOL( hAPP( Z, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL( hAPP( Z, skol21
% 26.01/26.39 ( U, W, Z ) ) ) }.
% 26.01/26.39 (82823) {G0,W24,D6,L4,V4,M4} { ! class_Rings_Odvd( X ), !
% 26.01/26.39 class_Rings_Osemiring__0( X ), ! hBOOL( hAPP( Z, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol21( X
% 26.01/26.39 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 26.01/26.39 (82824) {G0,W28,D6,L5,V4,M5} { ! class_Rings_Odvd( X ), !
% 26.01/26.39 class_Rings_Osemiring__0( X ), ! c_Rings_Odvd__class_Odvd( X, Y,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( X, T, c_Groups_Ozero__class_Ozero( X ) ) ),
% 26.01/26.39 ! hBOOL( hAPP( Z, T ) ), hBOOL( hAPP( Z, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Y ), skol30( X, Y, Z ) ) ) ) }.
% 26.01/26.39 (82825) {G0,W48,D5,L5,V1,M5} { ! c_RealVector_Onorm__class_Onorm(
% 26.01/26.39 tc_Complex_Ocomplex, X ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 26.01/26.39 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X,
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 26.01/26.39 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X, c_Complex_Oii ) ),
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 26.01/26.39 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 26.01/26.39 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 26.01/26.39 (82826) {G0,W22,D5,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Nat_Onat ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 26.01/26.39 (82827) {G0,W22,D5,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Nat_Onat ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 26.01/26.39 (82828) {G0,W4,D2,L1,V1,M1} { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X
% 26.01/26.39 ) }.
% 26.01/26.39 (82829) {G0,W7,D2,L2,V2,M2} { ! Y = X, c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, Y, X ) }.
% 26.01/26.39 (82830) {G0,W7,D2,L2,V2,M2} { ! Y = X, c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, X, Y ) }.
% 26.01/26.39 (82831) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 26.01/26.39 (82832) {G0,W10,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), alpha11( X, Y ), Y = X }.
% 26.01/26.39 (82833) {G0,W7,D2,L2,V2,M2} { ! alpha11( X, Y ), c_Rings_Odvd__class_Odvd
% 26.01/26.39 ( tc_Nat_Onat, Y, X ) }.
% 26.01/26.39 (82834) {G0,W7,D2,L2,V2,M2} { ! Y = X, c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, Y, X ) }.
% 26.01/26.39 (82835) {G0,W7,D2,L2,V2,M2} { ! alpha11( X, Y ), c_Rings_Odvd__class_Odvd
% 26.01/26.39 ( tc_Nat_Onat, Y, X ) }.
% 26.01/26.39 (82836) {G0,W7,D2,L2,V2,M2} { ! alpha11( X, Y ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 26.01/26.39 (82837) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), alpha11( X, Y ) }.
% 26.01/26.39 (82838) {G0,W7,D2,L2,V2,M2} { ! alpha12( X, Y ), c_Rings_Odvd__class_Odvd
% 26.01/26.39 ( tc_Nat_Onat, Y, X ) }.
% 26.01/26.39 (82839) {G0,W6,D2,L2,V2,M2} { ! alpha12( X, Y ), ! Y = X }.
% 26.01/26.39 (82840) {G0,W10,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), Y = X, alpha12( X, Y ) }.
% 26.01/26.39 (82841) {G0,W7,D2,L2,V2,M2} { ! alpha12( X, Y ), c_Rings_Odvd__class_Odvd
% 26.01/26.39 ( tc_Nat_Onat, Y, X ) }.
% 26.01/26.39 (82842) {G0,W7,D2,L2,V2,M2} { ! alpha12( X, Y ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 26.01/26.39 (82843) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), alpha12( X, Y ) }.
% 26.01/26.39 (82844) {G0,W11,D2,L3,V2,M3} { Y = X, ! c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 26.01/26.39 (82845) {G0,W11,D2,L3,V2,M3} { Y = X, ! c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, Y, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 26.01/26.39 (82846) {G0,W7,D2,L2,V2,M2} { ! Y = X, c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, Y, X ) }.
% 26.01/26.39 (82847) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 26.01/26.39 (82848) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), ! X = Y, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 26.01/26.39 (82849) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X }.
% 26.01/26.39 (82850) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 26.01/26.39 (82851) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 26.01/26.39 (82852) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 26.01/26.39 (82853) {G0,W11,D2,L3,V3,M3} { ! Y = X, ! c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 26.01/26.39 (82854) {G0,W11,D2,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 26.01/26.39 (82855) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 26.01/26.39 (82856) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 26.01/26.39 (82857) {G0,W12,D2,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 26.01/26.39 (82858) {G0,W15,D2,L4,V3,M4} { ! Y = X, ! c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 26.01/26.39 (82859) {G0,W15,D2,L4,V3,M4} { ! Y = X, ! c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 26.01/26.39 (82860) {G0,W16,D2,L4,V3,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, Y, Z ) }.
% 26.01/26.39 (82861) {G0,W16,D2,L4,V3,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 26.01/26.39 ( tc_Nat_Onat, Z, Y ) }.
% 26.01/26.39 (82862) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), ! Y = X }.
% 26.01/26.39 (82863) {G0,W16,D2,L4,V2,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, Y, X ) }.
% 26.01/26.39 (82864) {G0,W12,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 26.01/26.39 (82865) {G0,W16,D2,L4,V2,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, Y, X ) }.
% 26.01/26.39 (82866) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), ! Y = X }.
% 26.01/26.39 (82867) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), ! X = Y }.
% 26.01/26.39 (82868) {G0,W15,D2,L4,V3,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), ! X = Z,
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 26.01/26.39 (82869) {G0,W15,D2,L4,V3,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), ! X = Z, !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 26.01/26.39 (82870) {G0,W16,D2,L4,V3,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, Y, Z ) }.
% 26.01/26.39 (82871) {G0,W16,D2,L4,V3,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), ! c_Rings_Odvd__class_Odvd
% 26.01/26.39 ( tc_Nat_Onat, Z, Y ) }.
% 26.01/26.39 (82872) {G0,W16,D2,L4,V2,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, Y, X ) }.
% 26.01/26.39 (82873) {G0,W20,D2,L5,V3,M5} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 26.01/26.39 (82874) {G0,W20,D2,L5,V3,M5} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 26.01/26.39 (82875) {G0,W16,D2,L4,V2,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 26.01/26.39 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, Y, X ) }.
% 26.01/26.39 (82876) {G0,W4,D3,L1,V0,M1} { ! c_Complex_Oii = c_Groups_Oone__class_Oone
% 26.01/26.39 ( tc_Complex_Ocomplex ) }.
% 26.01/26.39 (82877) {G0,W4,D3,L1,V0,M1} { ! c_Complex_Oii =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 26.01/26.39 (82878) {G0,W5,D3,L1,V1,M1} { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.01/26.39 (82879) {G0,W15,D6,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_Complex_Ocomplex ), c_Complex_Oii ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), c_Complex_Oii ), X
% 26.01/26.39 ) ) = c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) }.
% 26.01/26.39 (82880) {G0,W5,D3,L1,V1,M1} { c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 26.01/26.39 (82881) {G0,W7,D3,L1,V0,M1} { c_Rings_Oinverse__class_Oinverse(
% 26.01/26.39 tc_Complex_Ocomplex, c_Complex_Oii ) = c_Groups_Ouminus__class_Ouminus(
% 26.01/26.39 tc_Complex_Ocomplex, c_Complex_Oii ) }.
% 26.01/26.39 (82882) {G0,W11,D5,L1,V0,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_Complex_Ocomplex ), c_Complex_Oii ), c_Complex_Oii ) =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex,
% 26.01/26.39 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }.
% 26.01/26.39 (82883) {G0,W14,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Nat_Onat ), Y ) }.
% 26.01/26.39 (82884) {G0,W22,D5,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Nat_Onat ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 26.01/26.39 (82885) {G0,W22,D5,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Nat_Onat ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ),
% 26.01/26.39 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) }.
% 26.01/26.39 (82886) {G0,W22,D5,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint,
% 26.01/26.39 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP(
% 26.01/26.39 hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Int_Oint, Z, X ) }.
% 26.01/26.39 (82887) {G0,W22,D5,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 26.01/26.39 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP(
% 26.01/26.39 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 26.01/26.39 tc_Nat_Onat, Z, X ) }.
% 26.01/26.39 (82888) {G0,W7,D3,L1,V0,M1} {
% 26.01/26.39 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 26.01/26.39 skol22 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 26.01/26.39 tc_Complex_Ocomplex, v_pa____ ) }.
% 26.01/26.39 (82889) {G0,W14,D4,L1,V1,M1} { hAPP( c_Polynomial_Opoly(
% 26.01/26.39 tc_Complex_Ocomplex, skol22 ), X ) = hAPP( c_Polynomial_Opoly(
% 26.01/26.39 tc_Complex_Ocomplex, v_pa____ ), c_Groups_Oplus__class_Oplus(
% 26.01/26.39 tc_Complex_Ocomplex, v_c____, X ) ) }.
% 26.01/26.39 (82890) {G0,W9,D3,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra( X
% 26.01/26.39 ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol23( Z, T ) ) }.
% 26.01/26.39 (82891) {G0,W22,D6,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.39 X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol23( X, Y ) ) ) }.
% 26.01/26.39 (82892) {G0,W8,D3,L2,V2,M2} { ! class_RealVector_Oreal__normed__algebra( X
% 26.01/26.39 ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol24( Y ) ) }.
% 26.01/26.39 (82893) {G0,W28,D7,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.39 X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol24( X ) ) ) }.
% 26.01/26.39 (82894) {G0,W9,D3,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra( X
% 26.01/26.39 ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol25( Z, T ) ) }.
% 26.01/26.39 (82895) {G0,W22,D6,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 26.01/26.39 X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 26.01/26.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol25( X, Y ) ) ) }.
% 26.01/26.39 (82896) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, Y, X ), c_Nat__Transfer_Otsub( X, Y ) =
% 26.01/26.39 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, Y ) }.
% 26.01/26.39 (82897) {G0,W10,D3,L2,V2,M2} { c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, Y, X ), c_Nat__Transfer_Otsub( X, Y ) =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 26.01/26.39 (82898) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 26.01/26.39 (82899) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 26.01/26.39 ) }.
% 26.01/26.39 (82900) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Int_Oint, Y, X ), c_Nat__Transfer_Otsub( X, Y ) =
% 26.01/26.39 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, Y ) }.
% 26.01/26.39 (82901) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 26.01/26.39 (82902) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 26.01/26.39 (82903) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 26.01/26.39 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 26.01/26.39 (82904) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 26.01/26.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 26.01/26.39 (82905) {G0,W15,D3,L4,V3,M4} { ! class_Rings_Olinordered__idom( X ), !
% 26.01/26.39 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ),
% 26.01/26.39 c_Polynomial_Opos__poly( X, Y ), alpha13( X, Y, Z ) }.
% 26.01/26.39 (82906) {G0,W11,D3,L3,V3,M3} { ! class_Rings_Olinordered__idom( X ), !
% 26.01/26.39 c_Polynomial_Opos__poly( X, Y ), c_Polynomial_Opos__poly( X,
% 26.01/26.39 c_Polynomial_OpCons( X, Z, Y ) ) }.
% 26.01/26.39 (82907) {G0,W12,D3,L3,V3,M3} { ! class_Rings_Olinordered__idom( X ), !
% 26.01/26.39 alpha13( X, Y, Z ), c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z
% 26.01/26.39 , Y ) ) }.
% 26.01/26.39 (82908) {G0,W9,D4,L2,V3,M2} { ! alpha13( X, Y, Z ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.39 (82909) {G0,W9,D3,L2,V3,M2} { ! alpha13( X, Y, Z ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 26.01/26.39 }.
% 26.01/26.39 (82910) {G0,W14,D4,L3,V3,M3} { ! Y = c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( X ), Z ), alpha13( X, Y, Z ) }.
% 26.01/26.39 (82911) {G0,W17,D4,L2,V3,M2} { ! class_Groups_Oab__group__add( X ),
% 26.01/26.39 c_Groups_Ominus__class_Ominus( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 26.01/26.39 , c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Ominus__class_Ominus( X, Z,
% 26.01/26.39 Y ) ) }.
% 26.01/26.39 (82912) {G0,W15,D4,L4,V3,M4} { ! class_Rings_Olinordered__idom( X ), !
% 26.01/26.39 c_Polynomial_Opos__poly( X, Y ), ! c_Polynomial_Opos__poly( X, Z ),
% 26.01/26.39 c_Polynomial_Opos__poly( X, c_Groups_Oplus__class_Oplus(
% 26.01/26.39 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 26.01/26.39 (82913) {G0,W17,D6,L4,V3,M4} { ! class_Rings_Olinordered__idom( X ), !
% 26.01/26.39 c_Polynomial_Opos__poly( X, Y ), ! c_Polynomial_Opos__poly( X, Z ),
% 26.01/26.39 c_Polynomial_Opos__poly( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }.
% 26.01/26.39 (82914) {G0,W7,D4,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ), !
% 26.01/26.39 c_Polynomial_Opos__poly( X, c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Polynomial_Opoly( X ) ) ) }.
% 26.01/26.39 (82915) {G0,W17,D4,L4,V3,M4} { ! class_Rings_Olinordered__idom( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ), Z =
% 26.01/26.39 Y, c_Polynomial_Opos__poly( X, c_Groups_Ominus__class_Ominus(
% 26.01/26.39 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 26.01/26.39 (82916) {G0,W10,D3,L3,V3,M3} { ! class_Rings_Olinordered__idom( X ), ! Z =
% 26.01/26.39 Y, c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y )
% 26.01/26.39 }.
% 26.01/26.39 (82917) {G0,W14,D4,L3,V3,M3} { ! class_Rings_Olinordered__idom( X ), !
% 26.01/26.39 c_Polynomial_Opos__poly( X, c_Groups_Ominus__class_Ominus(
% 26.01/26.39 tc_Polynomial_Opoly( X ), Y, Z ) ), c_Orderings_Oord__class_Oless__eq(
% 26.01/26.39 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 26.01/26.39 (82918) {G0,W14,D4,L3,V3,M3} { ! class_Rings_Olinordered__idom( X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ),
% 26.01/26.39 c_Polynomial_Opos__poly( X, c_Groups_Ominus__class_Ominus(
% 26.01/26.39 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 26.01/26.39 (82919) {G0,W14,D4,L3,V3,M3} { ! class_Rings_Olinordered__idom( X ), !
% 26.01/26.39 c_Polynomial_Opos__poly( X, c_Groups_Ominus__class_Ominus(
% 26.01/26.39 tc_Polynomial_Opoly( X ), Y, Z ) ), c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 26.01/26.39 (82920) {G0,W16,D4,L4,V2,M4} { ! class_Rings_Olinordered__idom( X ), Y =
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 26.01/26.39 c_Polynomial_Opos__poly( X, Y ), c_Polynomial_Opos__poly( X,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 26.01/26.39 (82921) {G0,W13,D3,L2,V4,M2} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol26( T, U, W ) ) }.
% 26.01/26.39 (82922) {G0,W44,D6,L4,V4,M4} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 26.01/26.39 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, T, Z ) ) ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 26.01/26.39 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, T, Z ) ), skol26( X,
% 26.01/26.39 Y, Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 26.01/26.39 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 26.01/26.39 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), T ), hAPP(
% 26.01/26.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), Z ) ) ), X ) }.
% 26.01/26.39 (82923) {G0,W31,D6,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 26.01/26.39 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 26.01/26.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 26.01/26.39 tc_Int_Oint ), Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 26.01/26.39 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 26.01/26.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 26.01/26.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 26.01/26.39 (82924) {G0,W19,D4,L3,V3,M3} { ! class_Divides_Oring__div( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, Y ), c_Divides_Odiv__class_Odiv( X,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y, Z )
% 26.01/26.39 ) }.
% 26.01/26.39 (82925) {G0,W19,D4,L3,V3,M3} { ! class_Divides_Oring__div( X ), !
% 26.01/26.39 c_Rings_Odvd__class_Odvd( X, Z, Y ), c_Divides_Odiv__class_Odiv( X, Y,
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, Z ) ) =
% 26.01/26.39 c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y, Z )
% 26.01/26.39 ) }.
% 26.01/26.39 (82926) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ocancel__comm__monoid__add( X
% 26.01/26.39 ), class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) )
% 26.01/26.39 }.
% 26.01/26.39 (82927) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__comm__monoid__add(
% 26.01/26.39 tc_Complex_Ocomplex ) }.
% 26.01/26.39 (82928) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__comm__monoid__add(
% 26.01/26.39 tc_RealDef_Oreal ) }.
% 26.01/26.39 (82929) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__comm__monoid__add(
% 26.01/26.39 tc_Nat_Onat ) }.
% 26.01/26.39 (82930) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__comm__monoid__add(
% 26.01/26.39 tc_Int_Oint ) }.
% 26.01/26.39 (82931) {G0,W6,D3,L2,V2,M2} { ! class_Orderings_Opreorder( X ),
% 26.01/26.39 class_Orderings_Opreorder( tc_fun( Y, X ) ) }.
% 26.01/26.39 (82932) {G0,W6,D3,L2,V2,M2} { ! class_Orderings_Oorder( X ),
% 26.01/26.39 class_Orderings_Oorder( tc_fun( Y, X ) ) }.
% 26.01/26.39 (82933) {G0,W6,D3,L2,V2,M2} { ! class_Orderings_Oord( X ),
% 26.01/26.39 class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 26.01/26.39 (82934) {G0,W2,D2,L1,V0,M1} {
% 26.01/26.39 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 26.01/26.39 tc_Int_Oint ) }.
% 26.01/26.39 (82935) {G0,W2,D2,L1,V0,M1} {
% 26.01/26.39 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 26.01/26.39 (82936) {G0,W2,D2,L1,V0,M1} {
% 26.01/26.39 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 26.01/26.39 (82937) {G0,W2,D2,L1,V0,M1} {
% 26.01/26.39 class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 26.01/26.39 (82938) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring__1__strict
% 26.01/26.39 ( tc_Int_Oint ) }.
% 26.01/26.39 (82939) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring__strict(
% 26.01/26.39 tc_Int_Oint ) }.
% 26.01/26.39 (82940) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__ab__semigroup__add(
% 26.01/26.39 tc_Int_Oint ) }.
% 26.01/26.39 (82941) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__comm__monoid__add(
% 26.01/26.39 tc_Int_Oint ) }.
% 26.01/26.39 (82942) {G0,W2,D2,L1,V0,M1} { class_Groups_Olinordered__ab__group__add(
% 26.01/26.39 tc_Int_Oint ) }.
% 26.01/26.39 (82943) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__ab__semigroup__add(
% 26.01/26.39 tc_Int_Oint ) }.
% 26.01/26.39 (82944) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__1__no__zero__divisors(
% 26.01/26.39 tc_Int_Oint ) }.
% 26.01/26.39 (82945) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__cancel__semiring(
% 26.01/26.39 tc_Int_Oint ) }.
% 26.01/26.39 (82946) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__ring__strict(
% 26.01/26.39 tc_Int_Oint ) }.
% 26.01/26.39 (82947) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__no__zero__divisors(
% 26.01/26.39 tc_Int_Oint ) }.
% 26.01/26.39 (82948) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__comm__semiring(
% 26.01/26.39 tc_Int_Oint ) }.
% 26.01/26.39 (82949) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring__1(
% 26.01/26.39 tc_Int_Oint ) }.
% 26.01/26.39 (82950) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__ab__group__add(
% 26.01/26.39 tc_Int_Oint ) }.
% 26.01/26.39 (82951) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__semigroup__add(
% 26.01/26.39 tc_Int_Oint ) }.
% 26.01/26.39 (82952) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring(
% 26.01/26.39 tc_Int_Oint ) }.
% 26.01/26.39 (82953) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semidom(
% 26.01/26.39 tc_Int_Oint ) }.
% 26.01/26.39 (82954) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__mult(
% 26.01/26.39 tc_Int_Oint ) }.
% 26.01/26.39 (82955) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__mult(
% 26.01/26.39 tc_Int_Oint ) }.
% 26.01/26.39 (82956) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__add(
% 26.01/26.39 tc_Int_Oint ) }.
% 26.01/26.39 (82957) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__semiring( tc_Int_Oint
% 26.01/26.39 ) }.
% 26.01/26.39 (82958) {G0,W2,D2,L1,V0,M1} { class_Rings_Ono__zero__divisors( tc_Int_Oint
% 26.01/26.39 ) }.
% 26.01/26.39 (82959) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__add( tc_Int_Oint
% 26.01/26.39 ) }.
% 26.01/26.39 (82960) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__ring( tc_Int_Oint )
% 26.01/26.39 }.
% 26.01/26.39 (82961) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__idom( tc_Int_Oint )
% 26.01/26.39 }.
% 26.01/26.39 (82962) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__1( tc_Int_Oint
% 26.01/26.39 ) }.
% 26.01/26.39 (82963) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__0( tc_Int_Oint
% 26.01/26.39 ) }.
% 26.01/26.39 (82964) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring( tc_Int_Oint )
% 26.01/26.39 }.
% 26.01/26.39 (82965) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__group__add( tc_Int_Oint )
% 26.01/26.39 }.
% 26.01/26.39 (82966) {G0,W2,D2,L1,V0,M1} { class_Rings_Ozero__neq__one( tc_Int_Oint )
% 26.01/26.39 }.
% 26.01/26.39 (82967) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__ring( tc_Int_Oint )
% 26.01/26.39 }.
% 26.01/26.39 (82968) {G0,W2,D2,L1,V0,M1} { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 26.01/26.39 (82969) {G0,W2,D2,L1,V0,M1} { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 26.01/26.39 (82970) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__mult( tc_Int_Oint )
% 26.01/26.39 }.
% 26.01/26.39 (82971) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__ring__1( tc_Int_Oint )
% 26.01/26.39 }.
% 26.01/26.39 (82972) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 26.01/26.39 (82973) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 26.01/26.39 (82974) {G0,W2,D2,L1,V0,M1} { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 26.01/26.39 (82975) {G0,W2,D2,L1,V0,M1} { class_Divides_Oring__div( tc_Int_Oint ) }.
% 26.01/26.39 (82976) {G0,W2,D2,L1,V0,M1} { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 26.01/26.39 (82977) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 26.01/26.39 (82978) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oorder( tc_Int_Oint ) }.
% 26.01/26.39 (82979) {G0,W2,D2,L1,V0,M1} { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 26.01/26.39 (82980) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring( tc_Int_Oint ) }.
% 26.01/26.39 (82981) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oord( tc_Int_Oint ) }.
% 26.01/26.39 (82982) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__1( tc_Int_Oint ) }.
% 26.01/26.39 (82983) {G0,W2,D2,L1,V0,M1} { class_Power_Opower( tc_Int_Oint ) }.
% 26.01/26.39 (82984) {G0,W2,D2,L1,V0,M1} { class_Groups_Ozero( tc_Int_Oint ) }.
% 26.01/26.39 (82985) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring( tc_Int_Oint ) }.
% 26.01/26.39 (82986) {G0,W2,D2,L1,V0,M1} { class_Rings_Oidom( tc_Int_Oint ) }.
% 26.01/26.39 (82987) {G0,W2,D2,L1,V0,M1} { class_Groups_Oone( tc_Int_Oint ) }.
% 26.01/26.39 (82988) {G0,W2,D2,L1,V0,M1} { class_Rings_Odvd( tc_Int_Oint ) }.
% 26.01/26.39 (82989) {G0,W2,D2,L1,V0,M1} {
% 26.01/26.39 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 26.01/26.39 tc_Nat_Onat ) }.
% 26.01/26.39 (82990) {G0,W2,D2,L1,V0,M1} {
% 26.01/26.39 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 26.01/26.39 (82991) {G0,W2,D2,L1,V0,M1} {
% 26.01/26.39 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 26.01/26.39 (82992) {G0,W2,D2,L1,V0,M1} {
% 26.01/26.39 class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 26.01/26.39 (82993) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring__strict(
% 26.01/26.39 tc_Nat_Onat ) }.
% 26.01/26.39 (82994) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__ab__semigroup__add(
% 26.01/26.39 tc_Nat_Onat ) }.
% 26.01/26.39 (82995) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__comm__monoid__add(
% 26.01/26.39 tc_Nat_Onat ) }.
% 26.01/26.39 (82996) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__ab__semigroup__add(
% 26.01/26.39 tc_Nat_Onat ) }.
% 26.01/26.39 (82997) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__cancel__semiring(
% 26.01/26.39 tc_Nat_Onat ) }.
% 26.01/26.39 (82998) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__comm__semiring(
% 26.01/26.39 tc_Nat_Onat ) }.
% 26.01/26.39 (82999) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__semigroup__add(
% 26.01/26.39 tc_Nat_Onat ) }.
% 26.01/26.39 (83000) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring(
% 26.01/26.39 tc_Nat_Onat ) }.
% 26.01/26.39 (83001) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semidom(
% 26.01/26.39 tc_Nat_Onat ) }.
% 26.01/26.39 (83002) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__mult(
% 26.01/26.39 tc_Nat_Onat ) }.
% 26.01/26.39 (83003) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__mult(
% 26.01/26.39 tc_Nat_Onat ) }.
% 26.01/26.39 (83004) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__add(
% 26.01/26.39 tc_Nat_Onat ) }.
% 26.01/26.39 (83005) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__semiring( tc_Nat_Onat
% 26.01/26.39 ) }.
% 26.01/26.39 (83006) {G0,W2,D2,L1,V0,M1} { class_Rings_Ono__zero__divisors( tc_Nat_Onat
% 26.01/26.39 ) }.
% 26.01/26.39 (83007) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__add( tc_Nat_Onat
% 26.01/26.39 ) }.
% 26.01/26.39 (83008) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__1( tc_Nat_Onat
% 26.01/26.39 ) }.
% 26.01/26.39 (83009) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__0( tc_Nat_Onat
% 26.01/26.39 ) }.
% 26.01/26.39 (83010) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring( tc_Nat_Onat )
% 26.01/26.39 }.
% 26.01/26.39 (83011) {G0,W2,D2,L1,V0,M1} { class_Rings_Ozero__neq__one( tc_Nat_Onat )
% 26.01/26.39 }.
% 26.01/26.39 (83012) {G0,W2,D2,L1,V0,M1} { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 26.01/26.39 (83013) {G0,W2,D2,L1,V0,M1} { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 26.01/26.39 (83014) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__mult( tc_Nat_Onat )
% 26.01/26.39 }.
% 26.01/26.39 (83015) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 26.01/26.39 (83016) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 26.01/26.39 (83017) {G0,W2,D2,L1,V0,M1} { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 26.01/26.39 (83018) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 26.01/26.39 (83019) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 26.01/26.39 (83020) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oord( tc_Nat_Onat ) }.
% 26.01/26.39 (83021) {G0,W2,D2,L1,V0,M1} { class_Power_Opower( tc_Nat_Onat ) }.
% 26.01/26.39 (83022) {G0,W2,D2,L1,V0,M1} { class_Groups_Ozero( tc_Nat_Onat ) }.
% 26.01/26.39 (83023) {G0,W2,D2,L1,V0,M1} { class_Groups_Oone( tc_Nat_Onat ) }.
% 26.01/26.39 (83024) {G0,W2,D2,L1,V0,M1} { class_Rings_Odvd( tc_Nat_Onat ) }.
% 26.01/26.39 (83025) {G0,W2,D2,L1,V0,M1} { class_Orderings_Opreorder( tc_HOL_Obool )
% 26.01/26.39 }.
% 26.01/26.39 (83026) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 26.01/26.39 (83027) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oord( tc_HOL_Obool ) }.
% 26.01/26.39 (83028) {G0,W2,D2,L1,V0,M1} {
% 26.01/26.39 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 26.01/26.39 tc_RealDef_Oreal ) }.
% 26.01/26.39 (83029) {G0,W2,D2,L1,V0,M1} {
% 26.01/26.39 class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 26.01/26.39 (83030) {G0,W2,D2,L1,V0,M1} {
% 26.01/26.39 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal )
% 26.01/26.39 }.
% 26.01/26.39 (83031) {G0,W2,D2,L1,V0,M1} {
% 26.01/26.39 class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 26.01/26.39 (83032) {G0,W2,D2,L1,V0,M1} {
% 26.01/26.39 class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 26.01/26.39 (83033) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring__1__strict
% 26.01/26.39 ( tc_RealDef_Oreal ) }.
% 26.01/26.39 (83034) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__normed__div__algebra
% 26.01/26.39 ( tc_RealDef_Oreal ) }.
% 26.01/26.39 (83035) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring__strict(
% 26.01/26.39 tc_RealDef_Oreal ) }.
% 26.01/26.39 (83036) {G0,W2,D2,L1,V0,M1} { class_Rings_Odivision__ring__inverse__zero(
% 26.01/26.39 tc_RealDef_Oreal ) }.
% 26.01/26.39 (83037) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__normed__algebra__1(
% 26.01/26.39 tc_RealDef_Oreal ) }.
% 26.01/26.39 (83038) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__ab__semigroup__add(
% 26.01/26.39 tc_RealDef_Oreal ) }.
% 26.01/26.39 (83039) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__normed__algebra(
% 26.01/26.39 tc_RealDef_Oreal ) }.
% 26.01/26.39 (83040) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__comm__monoid__add(
% 26.01/26.39 tc_RealDef_Oreal ) }.
% 26.01/26.39 (83041) {G0,W2,D2,L1,V0,M1} { class_Groups_Olinordered__ab__group__add(
% 26.01/26.39 tc_RealDef_Oreal ) }.
% 26.01/26.39 (83042) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__ab__semigroup__add(
% 26.01/26.39 tc_RealDef_Oreal ) }.
% 26.01/26.39 (83043) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__1__no__zero__divisors(
% 26.01/26.39 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83044) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__cancel__semiring(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83045) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__normed__vector(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83046) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__ring__strict(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83047) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__no__zero__divisors(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83048) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__comm__semiring(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83049) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring__1(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83050) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__ab__group__add(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83051) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__semigroup__add(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83052) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83053) {G0,W2,D2,L1,V0,M1} { class_Fields_Ofield__inverse__zero(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83054) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semidom(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83055) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__mult(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83056) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__mult(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83057) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__add(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83058) {G0,W2,D2,L1,V0,M1} { class_Fields_Olinordered__field(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83059) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__semiring(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83060) {G0,W2,D2,L1,V0,M1} { class_Rings_Ono__zero__divisors(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83061) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__add(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83062) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__ring(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83063) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__idom(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83064) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__1(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83065) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__0(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83066) {G0,W2,D2,L1,V0,M1} { class_Rings_Odivision__ring(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83067) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83068) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__group__add(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83069) {G0,W2,D2,L1,V0,M1} { class_Rings_Ozero__neq__one(
% 26.01/26.40 tc_RealDef_Oreal ) }.
% 26.01/26.40 (83070) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__ring( tc_RealDef_Oreal
% 26.01/26.40 ) }.
% 26.01/26.40 (83071) {G0,W2,D2,L1,V0,M1} { class_Orderings_Opreorder( tc_RealDef_Oreal
% 26.01/26.40 ) }.
% 26.01/26.40 (83072) {G0,W2,D2,L1,V0,M1} { class_Orderings_Olinorder( tc_RealDef_Oreal
% 26.01/26.40 ) }.
% 26.01/26.40 (83073) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__mult( tc_RealDef_Oreal
% 26.01/26.40 ) }.
% 26.01/26.40 (83074) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal
% 26.01/26.40 ) }.
% 26.01/26.40 (83075) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__add( tc_RealDef_Oreal
% 26.01/26.40 ) }.
% 26.01/26.40 (83076) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring__0( tc_RealDef_Oreal )
% 26.01/26.40 }.
% 26.01/26.40 (83077) {G0,W2,D2,L1,V0,M1} { class_Groups_Ogroup__add( tc_RealDef_Oreal )
% 26.01/26.40 }.
% 26.01/26.40 (83078) {G0,W2,D2,L1,V0,M1} { class_Rings_Omult__zero( tc_RealDef_Oreal )
% 26.01/26.40 }.
% 26.01/26.40 (83079) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__ring( tc_RealDef_Oreal )
% 26.01/26.40 }.
% 26.01/26.40 (83080) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oorder( tc_RealDef_Oreal )
% 26.01/26.40 }.
% 26.01/26.40 (83081) {G0,W2,D2,L1,V0,M1} { class_Int_Oring__char__0( tc_RealDef_Oreal )
% 26.01/26.40 }.
% 26.01/26.40 (83082) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring( tc_RealDef_Oreal )
% 26.01/26.40 }.
% 26.01/26.40 (83083) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 26.01/26.40 (83084) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 26.01/26.40 (83085) {G0,W2,D2,L1,V0,M1} { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 26.01/26.40 (83086) {G0,W2,D2,L1,V0,M1} { class_Power_Opower( tc_RealDef_Oreal ) }.
% 26.01/26.40 (83087) {G0,W2,D2,L1,V0,M1} { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 26.01/26.40 (83088) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 26.01/26.40 (83089) {G0,W2,D2,L1,V0,M1} { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 26.01/26.40 (83090) {G0,W2,D2,L1,V0,M1} { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 26.01/26.40 (83091) {G0,W2,D2,L1,V0,M1} { class_Rings_Odvd( tc_RealDef_Oreal ) }.
% 26.01/26.40 (83092) {G0,W2,D2,L1,V0,M1} {
% 26.01/26.40 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83093) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__normed__div__algebra
% 26.01/26.40 ( tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83094) {G0,W2,D2,L1,V0,M1} { class_Rings_Odivision__ring__inverse__zero(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83095) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__normed__algebra__1(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83096) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__normed__algebra(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83097) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__ab__semigroup__add(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83098) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__1__no__zero__divisors(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83099) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__normed__vector(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83100) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__no__zero__divisors(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83101) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__semigroup__add(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83102) {G0,W2,D2,L1,V0,M1} { class_Fields_Ofield__inverse__zero(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83103) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__mult(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83104) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__mult(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83105) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__add(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83106) {G0,W2,D2,L1,V0,M1} { class_Rings_Ono__zero__divisors(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83107) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__add(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83108) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__1(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83109) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__0(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83110) {G0,W2,D2,L1,V0,M1} { class_Rings_Odivision__ring(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83111) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83112) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__group__add(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83113) {G0,W2,D2,L1,V0,M1} { class_Rings_Ozero__neq__one(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83114) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__mult(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83115) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__ring__1(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83116) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__add(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83117) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring__0(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83118) {G0,W2,D2,L1,V0,M1} { class_Groups_Ogroup__add(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83119) {G0,W2,D2,L1,V0,M1} { class_Rings_Omult__zero( tc_Complex_Ocomplex
% 26.01/26.40 ) }.
% 26.01/26.40 (83120) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__ring( tc_Complex_Ocomplex
% 26.01/26.40 ) }.
% 26.01/26.40 (83121) {G0,W2,D2,L1,V0,M1} { class_Int_Oring__char__0(
% 26.01/26.40 tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83122) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring( tc_Complex_Ocomplex )
% 26.01/26.40 }.
% 26.01/26.40 (83123) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__1( tc_Complex_Ocomplex )
% 26.01/26.40 }.
% 26.01/26.40 (83124) {G0,W2,D2,L1,V0,M1} { class_Fields_Ofield( tc_Complex_Ocomplex )
% 26.01/26.40 }.
% 26.01/26.40 (83125) {G0,W2,D2,L1,V0,M1} { class_Power_Opower( tc_Complex_Ocomplex )
% 26.01/26.40 }.
% 26.01/26.40 (83126) {G0,W2,D2,L1,V0,M1} { class_Groups_Ozero( tc_Complex_Ocomplex )
% 26.01/26.40 }.
% 26.01/26.40 (83127) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83128) {G0,W2,D2,L1,V0,M1} { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83129) {G0,W2,D2,L1,V0,M1} { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83130) {G0,W2,D2,L1,V0,M1} { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 26.01/26.40 (83131) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Oidom( X ),
% 26.01/26.40 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 26.01/26.40 tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83132) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 26.01/26.40 ) ) }.
% 26.01/26.40 (83133) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 26.01/26.40 X ) ) }.
% 26.01/26.40 (83134) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 26.01/26.40 ) }.
% 26.01/26.40 (83135) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 26.01/26.40 }.
% 26.01/26.40 (83136) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83137) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83138) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83139) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83140) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ocancel__comm__monoid__add( X
% 26.01/26.40 ), class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) )
% 26.01/26.40 }.
% 26.01/26.40 (83141) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Oidom( X ),
% 26.01/26.40 class_Rings_Oring__1__no__zero__divisors( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83142) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83143) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83144) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Oidom( X ),
% 26.01/26.40 class_Rings_Oring__no__zero__divisors( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83145) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83146) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83147) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83148) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ocancel__comm__monoid__add( X
% 26.01/26.40 ), class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83149) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Rings_Olinordered__semiring( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83150) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Rings_Olinordered__semidom( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83151) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 26.01/26.40 class_Groups_Oab__semigroup__mult( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83152) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.40 class_Groups_Ocomm__monoid__mult( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83153) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 26.01/26.40 class_Groups_Oab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83154) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Rings_Oordered__semiring( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83155) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Oidom( X ),
% 26.01/26.40 class_Rings_Ono__zero__divisors( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83156) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 26.01/26.40 class_Groups_Ocomm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83157) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Rings_Olinordered__ring( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83158) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Rings_Olinordered__idom( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83159) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.40 class_Rings_Ocomm__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83160) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 26.01/26.40 class_Rings_Ocomm__semiring__0( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83161) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 26.01/26.40 class_Rings_Ocomm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83162) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Oab__group__add( X ),
% 26.01/26.40 class_Groups_Oab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83163) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.40 class_Rings_Ozero__neq__one( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83164) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Rings_Oordered__ring( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83165) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Orderings_Opreorder( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83166) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Orderings_Olinorder( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83167) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.40 class_Groups_Omonoid__mult( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83168) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__ring__1( X ),
% 26.01/26.40 class_Rings_Ocomm__ring__1( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83169) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 26.01/26.40 class_Groups_Omonoid__add( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83170) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 26.01/26.40 class_Rings_Osemiring__0( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83171) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Oab__group__add( X ),
% 26.01/26.40 class_Groups_Ogroup__add( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83172) {G0,W5,D3,L2,V1,M2} { ! class_Fields_Ofield( X ),
% 26.01/26.40 class_Divides_Oring__div( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83173) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 26.01/26.40 class_Rings_Omult__zero( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83174) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__ring( X ),
% 26.01/26.40 class_Rings_Ocomm__ring( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83175) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Orderings_Oorder( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83176) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Int_Oring__char__0( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83177) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 26.01/26.40 class_Rings_Osemiring( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83178) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 26.01/26.40 class_Orderings_Oord( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83179) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__ring__1( X ),
% 26.01/26.40 class_Rings_Oring__1( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83180) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.40 class_Power_Opower( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83181) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ozero( X ),
% 26.01/26.40 class_Groups_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83182) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__ring( X ),
% 26.01/26.40 class_Rings_Oring( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83183) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Oidom( X ), class_Rings_Oidom
% 26.01/26.40 ( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83184) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.40 class_Groups_Oone( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83185) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 26.01/26.40 class_Rings_Odvd( tc_Polynomial_Opoly( X ) ) }.
% 26.01/26.40 (83186) {G0,W19,D8,L2,V1,M2} { ! c_Groups_Oplus__class_Oplus(
% 26.01/26.40 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.01/26.40 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 26.01/26.40 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), v_k____ )
% 26.01/26.40 ), v_a____ ) ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 26.01/26.40 v_thesis____ }.
% 26.01/26.40 (83187) {G0,W1,D1,L1,V0,M1} { ! v_thesis____ }.
% 26.01/26.40
% 26.01/26.40
% 26.01/26.40 Total Proof:
% 26.01/26.40
% 26.01/26.40 eqswap: (83192) {G0,W4,D3,L1,V0,M1} { ! c_Groups_Ozero__class_Ozero(
% 26.01/26.40 tc_Nat_Onat ) = v_k____ }.
% 26.01/26.40 parent0[0]: (81511) {G0,W4,D3,L1,V0,M1} { ! v_k____ =
% 26.01/26.40 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 26.01/26.40 substitution0:
% 26.01/26.40 end
% 26.01/26.40
% 26.01/26.40 subsumption: (2) {G0,W4,D3,L1,V0,M1} I { ! c_Groups_Ozero__class_Ozero(
% 26.01/26.40 tc_Nat_Onat ) ==> v_k____ }.
% 26.01/26.40 parent0: (83192) {G0,W4,D3,L1,V0,M1} { ! c_Groups_Ozero__class_Ozero(
% 26.01/26.40 tc_Nat_Onat ) = v_k____ }.
% 26.01/26.40 substitution0:
% 26.01/26.40 end
% 26.01/26.40 permutation0:
% 26.01/26.40 0 ==> 0
% 26.01/26.40 end
% 26.01/26.40
% 26.01/26.40 subsumption: (12) {G0,W27,D8,L1,V0,M1} I { c_Groups_Oplus__class_Oplus(
% 26.01/26.40 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.01/26.40 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), skol2 )
% 26.01/26.40 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 26.01/26.40 v_a____ ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex
% 26.01/26.40 ), skol2 ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.01/26.40 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ) ) ==>
% 26.01/26.40 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 26.01/26.40 parent0: (81521) {G0,W27,D8,L1,V0,M1} { c_Groups_Oplus__class_Oplus(
% 26.01/26.40 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.01/26.40 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), skol2 )
% 26.01/26.40 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 26.01/26.40 v_a____ ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex
% 26.01/26.40 ), skol2 ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.01/26.40 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ) ) =
% 26.01/26.40 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 26.01/26.40 substitution0:
% 26.01/26.40 end
% 26.01/26.40 permutation0:
% 26.01/26.40 0 ==> 0
% 26.01/26.40 end
% 26.01/26.40
% 26.01/26.40 eqswap: (83326) {G0,W25,D7,L2,V4,M2} { hAPP( hAPP(
% 26.01/26.40 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 26.01/26.40 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) = hAPP( hAPP(
% 26.01/26.40 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.01/26.40 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), T ), !
% 26.01/26.40 class_Rings_Ocomm__semiring__1( X ) }.
% 26.01/26.40 parent0[1]: (81545) {G0,W25,D7,L2,V4,M2} { !
% 26.01/26.40 class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 26.08/26.41 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.08/26.41 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 26.08/26.41 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 26.08/26.41 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 26.08/26.41 substitution0:
% 26.08/26.41 X := X
% 26.08/26.41 Y := T
% 26.08/26.41 Z := Z
% 26.08/26.41 T := Y
% 26.08/26.41 end
% 26.08/26.41
% 26.08/26.41 subsumption: (36) {G0,W25,D7,L2,V4,M2} I { ! class_Rings_Ocomm__semiring__1
% 26.08/26.41 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 26.08/26.41 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ==> hAPP( hAPP(
% 26.08/26.41 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.08/26.41 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 26.08/26.41 parent0: (83326) {G0,W25,D7,L2,V4,M2} { hAPP( hAPP(
% 26.08/26.41 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 26.08/26.41 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) = hAPP( hAPP(
% 26.08/26.41 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.08/26.41 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), T ), !
% 26.08/26.41 class_Rings_Ocomm__semiring__1( X ) }.
% 26.08/26.41 substitution0:
% 26.08/26.41 X := X
% 26.08/26.41 Y := T
% 26.08/26.41 Z := Z
% 26.08/26.41 T := Y
% 26.08/26.41 end
% 26.08/26.41 permutation0:
% 26.08/26.41 0 ==> 1
% 26.08/26.41 1 ==> 0
% 26.08/26.41 end
% 26.08/26.41
% 26.08/26.41 subsumption: (38) {G0,W15,D5,L2,V3,M2} I { ! class_Rings_Ocomm__semiring__1
% 26.08/26.41 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP(
% 26.08/26.41 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 26.08/26.41 parent0: (81548) {G0,W15,D5,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1(
% 26.08/26.41 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP(
% 26.08/26.41 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 26.08/26.41 substitution0:
% 26.08/26.41 X := X
% 26.08/26.41 Y := Y
% 26.08/26.41 Z := Z
% 26.08/26.41 end
% 26.08/26.41 permutation0:
% 26.08/26.41 0 ==> 0
% 26.08/26.41 1 ==> 1
% 26.08/26.41 end
% 26.08/26.41
% 26.08/26.41 subsumption: (167) {G0,W5,D3,L1,V1,M1} I { ! c_Orderings_Oord__class_Oless
% 26.08/26.41 ( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.08/26.41 parent0: (81709) {G0,W5,D3,L1,V1,M1} { ! c_Orderings_Oord__class_Oless(
% 26.08/26.41 tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 26.08/26.41 substitution0:
% 26.08/26.41 X := X
% 26.08/26.41 end
% 26.08/26.41 permutation0:
% 26.08/26.41 0 ==> 0
% 26.08/26.41 end
% 26.08/26.41
% 26.08/26.41 subsumption: (191) {G0,W15,D4,L2,V2,M2} I { !
% 26.08/26.41 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 26.08/26.41 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) ==>
% 26.08/26.41 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 26.08/26.41 parent0: (81734) {G0,W15,D4,L2,V2,M2} { !
% 26.08/26.41 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 26.08/26.41 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 26.08/26.41 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 26.08/26.41 substitution0:
% 26.08/26.41 X := X
% 26.08/26.41 Y := Y
% 26.08/26.41 end
% 26.08/26.41 permutation0:
% 26.08/26.41 0 ==> 0
% 26.08/26.41 1 ==> 1
% 26.08/26.41 end
% 26.08/26.41
% 26.08/26.41 subsumption: (210) {G0,W11,D2,L3,V2,M3} I { Y = X,
% 26.08/26.41 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 26.08/26.41 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 26.08/26.41 parent0: (81754) {G0,W11,D2,L3,V2,M3} { Y = X,
% 26.08/26.41 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 26.08/26.41 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 26.08/26.41 substitution0:
% 26.08/26.41 X := X
% 26.08/26.41 Y := Y
% 26.08/26.41 end
% 26.08/26.41 permutation0:
% 26.08/26.41 0 ==> 0
% 26.08/26.41 1 ==> 1
% 26.08/26.41 2 ==> 2
% 26.08/26.41 end
% 26.08/26.41
% 26.08/26.41 subsumption: (212) {G0,W9,D3,L2,V2,M2} I { ! c_Orderings_Oord__class_Oless
% 26.08/26.41 ( tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.08/26.41 c_Nat_OSuc( Y ), X ) }.
% 26.08/26.41 parent0: (81757) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 26.08/26.41 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 26.08/26.41 c_Nat_OSuc( Y ), X ) }.
% 26.08/26.41 substitution0:
% 26.08/26.41 X := X
% 26.08/26.41 Y := Y
% 26.08/26.41 end
% 26.08/26.41 permutation0:
% 26.08/26.41 0 ==> 0
% 26.08/26.41 1 ==> 1
% 26.08/26.41 end
% 26.08/26.41
% 26.08/26.41 eqswap: (85999) {G0,W21,D6,L2,V3,M2} { hAPP( hAPP(
% 26.08/26.41 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 26.08/26.41 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 26.08/26.41 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), !
% 26.08/26.41 class_Rings_Ocomm__semiring__1( X ) }.
% 26.08/26.41 parent0[1]: (82074) {G0,W21,D6,L2,V3,M2} { !
% 26.08/26.41 class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 26.08/26.41 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 26.08/26.41 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 26.08/26.41 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 26.08/26.41 substitution0:
% 26.08/26.41 X := X
% 26.08/26.41 Y := Z
% 26.08/26.41 Z := Y
% 26.08/26.41 end
% 26.08/26.41
% 26.08/26.41 subsumption: (464) {G0,W21,D6,L2,V3,M2} I { !
% 26.08/26.41 class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 26.08/26.41 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 26.08/26.44 c_Power_Opower__class_Opower( X ), Z ), Y ) ) ==> hAPP( hAPP(
% 26.08/26.44 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 26.08/26.44 parent0: (85999) {G0,W21,D6,L2,V3,M2} { hAPP( hAPP(
% 26.08/26.44 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 26.08/26.44 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 26.08/26.44 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), !
% 26.08/26.44 class_Rings_Ocomm__semiring__1( X ) }.
% 26.08/26.44 substitution0:
% 26.08/26.44 X := X
% 26.08/26.44 Y := Z
% 26.08/26.44 Z := Y
% 26.08/26.44 end
% 26.08/26.44 permutation0:
% 26.08/26.44 0 ==> 1
% 26.08/26.44 1 ==> 0
% 26.08/26.44 end
% 26.08/26.44
% 26.08/26.44 eqswap: (86753) {G0,W6,D4,L1,V0,M1} { c_Nat_OSuc(
% 26.08/26.44 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone
% 26.08/26.44 ( tc_Nat_Onat ) }.
% 26.08/26.44 parent0[0]: (82104) {G0,W6,D4,L1,V0,M1} { c_Groups_Oone__class_Oone(
% 26.08/26.44 tc_Nat_Onat ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 26.08/26.44 }.
% 26.08/26.44 substitution0:
% 26.08/26.44 end
% 26.08/26.44
% 26.08/26.44 subsumption: (493) {G0,W6,D4,L1,V0,M1} I { c_Nat_OSuc(
% 26.08/26.44 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ==>
% 26.08/26.44 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 26.08/26.44 parent0: (86753) {G0,W6,D4,L1,V0,M1} { c_Nat_OSuc(
% 26.08/26.45 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone
% 26.08/26.45 ( tc_Nat_Onat ) }.
% 26.08/26.45 substitution0:
% 26.08/26.45 end
% 26.08/26.45 permutation0:
% 26.08/26.45 0 ==> 0
% 26.08/26.45 end
% 26.08/26.45
% 26.08/26.45 subsumption: (509) {G0,W8,D4,L1,V1,M1} I { c_Groups_Ominus__class_Ominus(
% 26.08/26.45 tc_Nat_Onat, c_Nat_OSuc( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 26.08/26.45 ==> X }.
% 26.08/26.45 parent0: (82128) {G0,W8,D4,L1,V1,M1} { c_Groups_Ominus__class_Ominus(
% 26.08/26.45 tc_Nat_Onat, c_Nat_OSuc( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 26.08/26.45 = X }.
% 26.08/26.45 substitution0:
% 26.08/26.45 X := X
% 26.08/26.45 end
% 26.08/26.45 permutation0:
% 26.08/26.45 0 ==> 0
% 26.08/26.45 end
% 26.08/26.45
% 26.08/26.45 subsumption: (1353) {G0,W2,D2,L1,V0,M1} I { class_Rings_Ocomm__semiring__1
% 26.08/26.45 ( tc_Complex_Ocomplex ) }.
% 26.08/26.45 parent0: (83108) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__1(
% 26.08/26.45 tc_Complex_Ocomplex ) }.
% 26.08/26.45 substitution0:
% 26.08/26.45 end
% 26.08/26.45 permutation0:
% 26.08/26.45 0 ==> 0
% 26.08/26.45 end
% 26.08/26.45
% 26.08/26.45 subsumption: (1431) {G0,W19,D8,L2,V1,M2} I { ! c_Groups_Oplus__class_Oplus
% 26.08/26.45 ( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 26.08/26.45 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), v_k____ )
% 26.08/26.45 ), v_a____ ) ) ==> c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 26.08/26.45 v_thesis____ }.
% 26.08/26.45 parent0: (83186) {G0,W19,D8,L2,V1,M2} { ! c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 26.08/26.45 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), v_k____ )
% 26.08/26.45 ), v_a____ ) ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 26.08/26.45 v_thesis____ }.
% 26.08/26.45 substitution0:
% 26.08/26.45 X := X
% 26.08/26.45 end
% 26.08/26.45 permutation0:
% 26.08/26.45 0 ==> 0
% 26.08/26.45 1 ==> 1
% 26.08/26.45 end
% 26.08/26.45
% 26.08/26.45 subsumption: (1432) {G0,W1,D1,L1,V0,M1} I { ! v_thesis____ }.
% 26.08/26.45 parent0: (83187) {G0,W1,D1,L1,V0,M1} { ! v_thesis____ }.
% 26.08/26.45 substitution0:
% 26.08/26.45 end
% 26.08/26.45 permutation0:
% 26.08/26.45 0 ==> 0
% 26.08/26.45 end
% 26.08/26.45
% 26.08/26.45 eqswap: (92472) {G0,W27,D8,L1,V0,M1} { c_Groups_Ozero__class_Ozero(
% 26.08/26.45 tc_Complex_Ocomplex ) ==> c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), skol2 )
% 26.08/26.45 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 26.08/26.45 v_a____ ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex
% 26.08/26.45 ), skol2 ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ) ) }.
% 26.08/26.45 parent0[0]: (12) {G0,W27,D8,L1,V0,M1} I { c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), skol2 )
% 26.08/26.45 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 26.08/26.45 v_a____ ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex
% 26.08/26.45 ), skol2 ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ) ) ==>
% 26.08/26.45 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 26.08/26.45 substitution0:
% 26.08/26.45 end
% 26.08/26.45
% 26.08/26.45 paramod: (92476) {G1,W29,D9,L2,V0,M2} { c_Groups_Ozero__class_Ozero(
% 26.08/26.45 tc_Complex_Ocomplex ) ==> c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), skol2 )
% 26.08/26.45 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP
% 26.08/26.45 ( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol2 ),
% 26.08/26.45 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), v_a____ ) ) ), !
% 26.08/26.45 class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 26.08/26.45 parent0[1]: (38) {G0,W15,D5,L2,V3,M2} I { ! class_Rings_Ocomm__semiring__1
% 26.08/26.45 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP(
% 26.08/26.45 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 26.08/26.45 parent1[0; 12]: (92472) {G0,W27,D8,L1,V0,M1} { c_Groups_Ozero__class_Ozero
% 26.08/26.45 ( tc_Complex_Ocomplex ) ==> c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), skol2 )
% 26.08/26.45 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 26.08/26.45 v_a____ ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex
% 26.08/26.45 ), skol2 ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ) ) }.
% 26.08/26.45 substitution0:
% 26.08/26.45 X := tc_Complex_Ocomplex
% 26.08/26.45 Y := hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 26.08/26.45 skol2 ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) )
% 26.08/26.45 Z := v_a____
% 26.08/26.45 end
% 26.08/26.45 substitution1:
% 26.08/26.45 end
% 26.08/26.45
% 26.08/26.45 paramod: (92517) {G1,W31,D9,L3,V0,M3} { c_Groups_Ozero__class_Ozero(
% 26.08/26.45 tc_Complex_Ocomplex ) ==> c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 26.08/26.45 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), skol2 ), hAPP
% 26.08/26.45 ( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol2 ),
% 26.08/26.45 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ), v_a____ ) ), !
% 26.08/26.45 class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ), !
% 26.08/26.45 class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 26.08/26.45 parent0[1]: (36) {G0,W25,D7,L2,V4,M2} I { ! class_Rings_Ocomm__semiring__1
% 26.08/26.45 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 26.08/26.45 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ==> hAPP( hAPP(
% 26.08/26.45 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 26.08/26.45 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 26.08/26.45 parent1[0; 7]: (92476) {G1,W29,D9,L2,V0,M2} { c_Groups_Ozero__class_Ozero
% 26.08/26.45 ( tc_Complex_Ocomplex ) ==> c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), skol2 )
% 26.08/26.45 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP
% 26.08/26.45 ( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol2 ),
% 26.08/26.45 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), v_a____ ) ) ), !
% 26.08/26.45 class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 26.08/26.45 substitution0:
% 26.08/26.45 X := tc_Complex_Ocomplex
% 26.08/26.45 Y := v_a____
% 26.08/26.45 Z := hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 26.08/26.45 skol2 ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) )
% 26.08/26.45 T := skol2
% 26.08/26.45 end
% 26.08/26.45 substitution1:
% 26.08/26.45 end
% 26.08/26.45
% 26.08/26.45 factor: (92518) {G1,W29,D9,L2,V0,M2} { c_Groups_Ozero__class_Ozero(
% 26.08/26.45 tc_Complex_Ocomplex ) ==> c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 26.08/26.45 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), skol2 ), hAPP
% 26.08/26.45 ( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol2 ),
% 26.08/26.45 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ), v_a____ ) ), !
% 26.08/26.45 class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 26.08/26.45 parent0[1, 2]: (92517) {G1,W31,D9,L3,V0,M3} { c_Groups_Ozero__class_Ozero
% 26.08/26.45 ( tc_Complex_Ocomplex ) ==> c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 26.08/26.45 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), skol2 ), hAPP
% 26.08/26.45 ( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol2 ),
% 26.08/26.45 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ), v_a____ ) ), !
% 26.08/26.45 class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ), !
% 26.08/26.45 class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 26.08/26.45 substitution0:
% 26.08/26.45 end
% 26.08/26.45
% 26.08/26.45 paramod: (92519) {G1,W27,D9,L3,V0,M3} { c_Groups_Ozero__class_Ozero(
% 26.08/26.45 tc_Complex_Ocomplex ) ==> c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 26.08/26.45 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol2 ),
% 26.08/26.45 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ), v_a____ ) ), !
% 26.08/26.45 class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ), !
% 26.08/26.45 class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 26.08/26.45 parent0[1]: (464) {G0,W21,D6,L2,V3,M2} I { ! class_Rings_Ocomm__semiring__1
% 26.08/26.45 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 26.08/26.45 c_Power_Opower__class_Opower( X ), Z ), Y ) ) ==> hAPP( hAPP(
% 26.08/26.45 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 26.08/26.45 parent1[0; 11]: (92518) {G1,W29,D9,L2,V0,M2} { c_Groups_Ozero__class_Ozero
% 26.08/26.45 ( tc_Complex_Ocomplex ) ==> c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 26.08/26.45 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), skol2 ), hAPP
% 26.08/26.45 ( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol2 ),
% 26.08/26.45 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ), v_a____ ) ), !
% 26.08/26.45 class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 26.08/26.45 substitution0:
% 26.08/26.45 X := tc_Complex_Ocomplex
% 26.08/26.45 Y := c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 26.08/26.45 Z := skol2
% 26.08/26.45 end
% 26.08/26.45 substitution1:
% 26.08/26.45 end
% 26.08/26.45
% 26.08/26.45 factor: (92520) {G1,W25,D9,L2,V0,M2} { c_Groups_Ozero__class_Ozero(
% 26.08/26.45 tc_Complex_Ocomplex ) ==> c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 26.08/26.45 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol2 ),
% 26.08/26.45 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ), v_a____ ) ), !
% 26.08/26.45 class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 26.08/26.45 parent0[1, 2]: (92519) {G1,W27,D9,L3,V0,M3} { c_Groups_Ozero__class_Ozero
% 26.08/26.45 ( tc_Complex_Ocomplex ) ==> c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 26.08/26.45 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol2 ),
% 26.08/26.45 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ), v_a____ ) ), !
% 26.08/26.45 class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ), !
% 26.08/26.45 class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 26.08/26.45 substitution0:
% 26.08/26.45 end
% 26.08/26.45
% 26.08/26.45 resolution: (92521) {G1,W23,D9,L1,V0,M1} { c_Groups_Ozero__class_Ozero(
% 26.08/26.45 tc_Complex_Ocomplex ) ==> c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 26.08/26.45 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol2 ),
% 26.08/26.45 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ), v_a____ ) ) }.
% 26.08/26.45 parent0[1]: (92520) {G1,W25,D9,L2,V0,M2} { c_Groups_Ozero__class_Ozero(
% 26.08/26.45 tc_Complex_Ocomplex ) ==> c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 26.08/26.45 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol2 ),
% 26.08/26.45 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ), v_a____ ) ), !
% 26.08/26.45 class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 26.08/26.45 parent1[0]: (1353) {G0,W2,D2,L1,V0,M1} I { class_Rings_Ocomm__semiring__1(
% 26.08/26.45 tc_Complex_Ocomplex ) }.
% 26.08/26.45 substitution0:
% 26.08/26.45 end
% 26.08/26.45 substitution1:
% 26.08/26.45 end
% 26.08/26.45
% 26.08/26.45 eqswap: (92522) {G1,W23,D9,L1,V0,M1} { c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 26.08/26.45 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol2 ),
% 26.08/26.45 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ), v_a____ ) ) ==>
% 26.08/26.45 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 26.08/26.45 parent0[0]: (92521) {G1,W23,D9,L1,V0,M1} { c_Groups_Ozero__class_Ozero(
% 26.08/26.45 tc_Complex_Ocomplex ) ==> c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 26.08/26.45 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol2 ),
% 26.08/26.45 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ), v_a____ ) ) }.
% 26.08/26.45 substitution0:
% 26.08/26.45 end
% 26.08/26.45
% 26.08/26.45 subsumption: (5299) {G1,W23,D9,L1,V0,M1} P(38,12);d(36);d(464);r(1353) {
% 26.08/26.45 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 26.08/26.45 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 26.08/26.45 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol2 ), c_Nat_OSuc
% 26.08/26.45 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ), v_a____ ) ) ==>
% 26.08/26.45 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 26.08/26.45 parent0: (92522) {G1,W23,D9,L1,V0,M1} { c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 26.08/26.45 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol2 ),
% 26.08/26.45 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ), v_a____ ) ) ==>
% 26.08/26.45 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 26.08/26.45 substitution0:
% 26.08/26.45 end
% 26.08/26.45 permutation0:
% 26.08/26.45 0 ==> 0
% 26.08/26.45 end
% 26.08/26.45
% 26.08/26.45 resolution: (92524) {G1,W18,D8,L1,V1,M1} { ! c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 26.08/26.45 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), v_k____ )
% 26.08/26.45 ), v_a____ ) ) ==> c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex )
% 26.08/26.45 }.
% 26.08/26.45 parent0[0]: (1432) {G0,W1,D1,L1,V0,M1} I { ! v_thesis____ }.
% 26.08/26.45 parent1[1]: (1431) {G0,W19,D8,L2,V1,M2} I { ! c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 26.08/26.45 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), v_k____ )
% 26.08/26.45 ), v_a____ ) ) ==> c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 26.08/26.45 v_thesis____ }.
% 26.08/26.45 substitution0:
% 26.08/26.45 end
% 26.08/26.45 substitution1:
% 26.08/26.45 X := X
% 26.08/26.45 end
% 26.08/26.45
% 26.08/26.45 subsumption: (20339) {G1,W18,D8,L1,V1,M1} S(1431);r(1432) { !
% 26.08/26.45 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 26.08/26.45 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 26.08/26.45 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 26.08/26.45 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), v_k____ ) ),
% 26.08/26.45 v_a____ ) ) ==> c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 26.08/26.45 parent0: (92524) {G1,W18,D8,L1,V1,M1} { ! c_Groups_Oplus__class_Oplus(
% 26.08/26.45 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 26.08/26.45 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 26.08/26.45 hAPP( c_PCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------