TSTP Solution File: SWW252+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW252+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:35 EDT 2022
% Result : Timeout 291.37s 291.77s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW252+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Sun Jun 5 13:01:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.35/1.71 *** allocated 10000 integers for termspace/termends
% 1.35/1.71 *** allocated 10000 integers for clauses
% 1.35/1.71 *** allocated 10000 integers for justifications
% 1.35/1.71 *** allocated 15000 integers for termspace/termends
% 1.35/1.71 *** allocated 22500 integers for termspace/termends
% 1.35/1.71 *** allocated 33750 integers for termspace/termends
% 1.35/1.71 Bliksem 1.12
% 1.35/1.71
% 1.35/1.71
% 1.35/1.71 Automatic Strategy Selection
% 1.35/1.71
% 1.35/1.71 *** allocated 50625 integers for termspace/termends
% 1.35/1.71 *** allocated 75937 integers for termspace/termends
% 1.35/1.71 *** allocated 113905 integers for termspace/termends
% 1.35/1.71 *** allocated 170857 integers for termspace/termends
% 1.35/1.71
% 1.35/1.71 Clauses:
% 1.35/1.71
% 1.35/1.71 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.35/1.71 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.35/1.71 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.35/1.71 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.35/1.71 tc_Complex_Ocomplex, v_p ) ) }.
% 1.35/1.71 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.35/1.71 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.35/1.71 tc_Complex_Ocomplex, v_q____ ) ) }.
% 1.35/1.71 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.35/1.71 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.35/1.71 tc_Complex_Ocomplex, v_q____ ) ) }.
% 1.35/1.71 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( c_Nat_OSuc, X ) ) ) }
% 1.35/1.71 .
% 1.35/1.71 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 1.35/1.71 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.35/1.71 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.35/1.71 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.35/1.71 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.35/1.71 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.35/1.71 v_q____ ) ), X ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.35/1.71 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 1.35/1.71 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), X ),
% 1.35/1.71 hAPP( c_Nat_OSuc, X ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 hAPP( c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), X ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero(
% 1.35/1.71 tc_Nat_Onat ) ) ), c_Orderings_Oord__class_OLeast( tc_Nat_Onat, X ) =
% 1.35/1.71 hAPP( c_Nat_OSuc, c_Orderings_Oord__class_OLeast( tc_Nat_Onat, hAPP(
% 1.35/1.71 c_COMBB( tc_Nat_Onat, tc_HOL_Obool, tc_Nat_Onat, X ), c_Nat_OSuc ) ) ) }
% 1.35/1.71 .
% 1.35/1.71 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.35/1.71 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.71 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.71 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.71 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.71 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.35/1.71 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.71 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.71 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), X = hAPP( c_Nat_OSuc
% 1.35/1.71 , skol2( X ) ) }.
% 1.35/1.71 { ! X = hAPP( c_Nat_OSuc, Y ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Groups_Ozero__class_Ozero
% 1.35/1.71 ( tc_Nat_Onat ) ), X ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), X ),
% 1.35/1.71 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc,
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.35/1.71 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.35/1.71 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.35/1.71 tc_Complex_Ocomplex, v_pa____ ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.35/1.71 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.35/1.71 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.35/1.71 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.35/1.71 ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.35/1.71 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.35/1.71 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 1.35/1.71 X, T ) = hAPP( X, U ) }.
% 1.35/1.71 { ! hAPP( X, skol3( X ) ) = hAPP( X, skol66( X ) ),
% 1.35/1.71 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.35/1.71 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.35/1.71 , Y ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.35/1.71 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 1.35/1.71 ), Y ) ) }.
% 1.35/1.71 { ! hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ), Y = X }.
% 1.35/1.71 { ! hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ), Y = X }.
% 1.35/1.71 { ! Y = X, hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ) }.
% 1.35/1.71 { ! hAPP( c_Nat_OSuc, X ) = X }.
% 1.35/1.71 { ! X = hAPP( c_Nat_OSuc, X ) }.
% 1.35/1.71 { alpha51( X, Y, Z ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless(
% 1.35/1.71 tc_Nat_Onat ), Y ), Z ) ), hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.35/1.71 { alpha51( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.35/1.71 ( X, Y ), Z ) ) }.
% 1.35/1.71 { ! alpha51( X, Y, Z ), alpha56( X, Y, Z ), Z = Y }.
% 1.35/1.71 { ! alpha51( X, Y, Z ), alpha56( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.35/1.71 ) ) }.
% 1.35/1.71 { ! alpha56( X, Y, Z ), alpha51( X, Y, Z ) }.
% 1.35/1.71 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha51( X, Y, Z ) }.
% 1.35/1.71 { ! alpha56( X, Y, Z ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless(
% 1.35/1.71 tc_Nat_Onat ), Z ), Y ) ) }.
% 1.35/1.71 { ! alpha56( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Z ), Y
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha56( X, Y, Z ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ), ! Y = X }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ), ! X = Y }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), X ), X
% 1.35/1.71 ) ) }.
% 1.35/1.71 { Y = X, hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y
% 1.35/1.71 ), X ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.35/1.71 ), X ), Y ) ) }.
% 1.35/1.71 { Y = X, hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y
% 1.35/1.71 ), X ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.35/1.71 ), X ), Y ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ), ! Y = X }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), X ), Y
% 1.35/1.71 ) ), ! Y = X }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), X ), X
% 1.35/1.71 ) ) }.
% 1.35/1.71 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.35/1.71 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 1.35/1.71 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 1.35/1.71 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 1.35/1.71 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 1.35/1.71 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 1.35/1.71 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 1.35/1.71 c_Polynomial_Ocoeff( X, Y ) }.
% 1.35/1.71 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 1.35/1.71 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 1.35/1.71 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol4( X
% 1.35/1.71 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol4( X, Y, Z ) ), Z = Y
% 1.35/1.71 }.
% 1.35/1.71 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 1.35/1.71 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 1.35/1.71 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 1.35/1.71 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Groups_Ozero__class_Ozero
% 1.35/1.71 ( tc_Nat_Onat ) ), X ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), X ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.35/1.71 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Groups_Ozero__class_Ozero
% 1.35/1.71 ( tc_Nat_Onat ) ), X ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! X =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), X ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.71 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.71 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ),
% 1.35/1.71 hAPP( c_Nat_OSuc, X ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X ) ), Y = X }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 X ), Z ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.35/1.71 ), hAPP( c_Nat_OSuc, Y ) ), Z ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ), hAPP( c_Nat_OSuc, Y ) = X, hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Y ) ), X
% 1.35/1.71 ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y
% 1.35/1.71 ), hAPP( c_Nat_OSuc, X ) ) ) }.
% 1.35/1.71 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X )
% 1.35/1.71 ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y
% 1.35/1.71 ), hAPP( c_Nat_OSuc, X ) ) ), X = Y }.
% 1.35/1.71 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X )
% 1.35/1.71 ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y
% 1.35/1.71 ), hAPP( c_Nat_OSuc, X ) ) ), Y = X }.
% 1.35/1.71 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X )
% 1.35/1.71 ), ! Y = X, hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless(
% 1.35/1.71 tc_Nat_Onat ), Y ), hAPP( c_Nat_OSuc, X ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.71 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 hAPP( c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ),
% 1.35/1.71 hAPP( c_Nat_OSuc, X ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X ) ), Y = X }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y
% 1.35/1.71 ), hAPP( c_Nat_OSuc, X ) ) ) }.
% 1.35/1.71 { ! Y = X, hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat )
% 1.35/1.71 , Y ), hAPP( c_Nat_OSuc, X ) ) ) }.
% 1.35/1.71 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X )
% 1.35/1.71 ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), X )
% 1.35/1.71 , hAPP( c_Nat_OSuc, Y ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), X ),
% 1.35/1.71 hAPP( c_Nat_OSuc, Y ) ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.71 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.35/1.71 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.71 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.35/1.71 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ),
% 1.35/1.71 hAPP( c_Nat_OSuc, X ) ) ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.35/1.71 , alpha1( X, Y ) }.
% 1.35/1.71 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), hAPP( c_Nat_OSuc, X )
% 1.35/1.71 ) ) }.
% 1.35/1.71 { ! alpha1( X, Y ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless(
% 1.35/1.71 tc_Nat_Onat ), Y ), hAPP( c_Nat_OSuc, X ) ) ) }.
% 1.35/1.71 { ! alpha1( X, Y ), Y = hAPP( c_Nat_OSuc, skol5( Z, Y ) ) }.
% 1.35/1.71 { ! alpha1( X, Y ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless(
% 1.35/1.71 tc_Nat_Onat ), skol5( X, Y ) ), X ) ) }.
% 1.35/1.71 { ! Y = hAPP( c_Nat_OSuc, Z ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Z ), X ) ), alpha1( X, Y )
% 1.35/1.71 }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), X ),
% 1.35/1.71 hAPP( c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.35/1.71 tc_Nat_Onat ) ) ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X
% 1.35/1.71 = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.71 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 1.35/1.71 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 1.35/1.71 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.35/1.71 { ! class_Fields_Olinordered__field( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.35/1.71 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.71 ( c_Orderings_Oord__class_Oless( X ), Y ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.71 ) ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), Y ), Z ) )
% 1.35/1.71 }.
% 1.35/1.71 { ! class_Fields_Olinordered__field( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.35/1.71 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.71 ( c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.71 , Z ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), Y ), Z )
% 1.35/1.71 ) }.
% 1.35/1.71 { ! class_Fields_Olinordered__field( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.35/1.71 Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), Y =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 ) ) }.
% 1.35/1.71 { ! class_Fields_Olinordered__field( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 1.35/1.71 { ! class_Fields_Olinordered__field( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Z
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 1.35/1.71 { ! class_Fields_Olinordered__field( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.35/1.71 X ) ) ) }.
% 1.35/1.71 { ! class_Fields_Olinordered__field( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Y ) ) ), Y =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.71 ) ) }.
% 1.35/1.71 { ! class_Fields_Olinordered__field( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ), c_Rings_Oinverse__class_Oinverse( X,
% 1.35/1.71 Y ) ) ) }.
% 1.35/1.71 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.35/1.71 X ) ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), Y ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.71 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( X ), Y ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.35/1.71 Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.71 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.71 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.71 ) ) }.
% 1.35/1.71 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.71 ) ), Y ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ), c_Rings_Oinverse__class_Oinverse( X,
% 1.35/1.71 Y ) ) ) }.
% 1.35/1.71 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.35/1.71 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.35/1.71 tc_Complex_Ocomplex, v_pa____ ) }.
% 1.35/1.71 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.35/1.71 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.35/1.71 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.35/1.71 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.35/1.71 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.35/1.71 .
% 1.35/1.71 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.35/1.71 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.35/1.71 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.35/1.71 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.35/1.71 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.35/1.71 .
% 1.35/1.71 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.35/1.71 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.35/1.71 c_Nat_OSuc, Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.71 tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), X ), Y = X }.
% 1.35/1.71 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.35/1.71 c_Nat_OSuc, Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.71 tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), X ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.35/1.71 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 1.35/1.71 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 1.35/1.71 .
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.35/1.71 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 1.35/1.71 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 1.35/1.71 ) }.
% 1.35/1.71 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.71 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = hAPP
% 1.35/1.71 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.71 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.71 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = hAPP
% 1.35/1.71 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.71 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X
% 1.35/1.71 = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.35/1.71 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP(
% 1.35/1.71 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.71 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Groups_Ozero__class_Ozero
% 1.35/1.71 ( tc_Nat_Onat ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat
% 1.35/1.71 ), Y ), X ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.71 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP(
% 1.35/1.71 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), hBOOL(
% 1.35/1.71 hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.71 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP(
% 1.35/1.71 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), hBOOL(
% 1.35/1.71 hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.71 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.71 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP(
% 1.35/1.71 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL(
% 1.35/1.71 hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.71 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP(
% 1.35/1.71 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL(
% 1.35/1.71 hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Z ), X ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.71 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Z ), X ) ), hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.71 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z )
% 1.35/1.71 ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP
% 1.35/1.71 ( c_Nat_OSuc, Z ) ), X ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.35/1.71 c_Nat_OSuc, Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.71 tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), X ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.71 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), !
% 1.35/1.71 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.71 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), hBOOL
% 1.35/1.71 ( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), X ), hAPP(
% 1.35/1.71 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.71 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), !
% 1.35/1.71 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.71 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), hBOOL
% 1.35/1.71 ( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), X ), hAPP(
% 1.35/1.71 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.71 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), !
% 1.35/1.71 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.71 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), hBOOL
% 1.35/1.71 ( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.71 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__idom( X ), Z = Y, hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), Z ) ) }.
% 1.35/1.71 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 1.35/1.71 , Y ) ) = Y }.
% 1.35/1.71 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.35/1.71 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 1.35/1.71 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.35/1.71 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.71 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.71 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.35/1.71 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.71 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.35/1.71 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.35/1.71 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.35/1.71 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 1.35/1.71 X, Y ) ) = Y }.
% 1.35/1.71 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.35/1.71 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.35/1.71 ( X ) }.
% 1.35/1.71 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.35/1.71 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 1.35/1.71 = Y }.
% 1.35/1.71 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.35/1.71 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), alpha2( X, Y, Z, T ),
% 1.35/1.71 alpha16( X, Y, Z, T ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z, T ),
% 1.35/1.71 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z, T ),
% 1.35/1.71 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.35/1.71 { ! alpha16( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless
% 1.35/1.71 ( X ), Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.71 { ! alpha16( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless
% 1.35/1.71 ( X ), Y ), T ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), Z ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), T ) ), alpha16( X, Y, Z, T ) }.
% 1.35/1.71 { ! alpha2( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless
% 1.35/1.71 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 1.35/1.71 { ! alpha2( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless
% 1.35/1.71 ( X ), T ), Y ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), T ), Y ) ), alpha2( X, Y, Z, T ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), alpha3( X, Y, Z, T ),
% 1.35/1.71 alpha17( X, Y, Z, T ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z, T ),
% 1.35/1.71 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha17( X, Y, Z, T ),
% 1.35/1.71 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.35/1.71 { ! alpha17( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless
% 1.35/1.71 ( X ), T ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.71 { ! alpha17( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless
% 1.35/1.71 ( X ), Y ), Z ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), T ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), Z ) ), alpha17( X, Y, Z, T ) }.
% 1.35/1.71 { ! alpha3( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless
% 1.35/1.71 ( X ), c_Groups_Ozero__class_Ozero( X ) ), T ) ) }.
% 1.35/1.71 { ! alpha3( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless
% 1.35/1.71 ( X ), Z ), Y ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ), T ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), alpha3( X, Y, Z, T ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.71 ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP
% 1.35/1.71 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), T ), Z ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.71 ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), T ), Z ) )
% 1.35/1.71 , hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.71 ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.71 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.71 ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), Z ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.71 ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), Z ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.71 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), ! hBOOL(
% 1.35/1.71 hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.71 ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.71 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), ! hBOOL(
% 1.35/1.71 hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Z
% 1.35/1.71 ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP
% 1.35/1.71 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), T ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), Z ), T ) )
% 1.35/1.71 , hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), Z ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.71 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), T
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), T
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__comm__semiring__strict( X ), ! hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.71 ( c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.71 , T ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP(
% 1.35/1.71 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), T ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), T ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) ) }.
% 1.35/1.71 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 1.35/1.71 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) }.
% 1.35/1.71 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 1.35/1.71 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), v_c____ ), X ) ) }.
% 1.35/1.71 { ! class_Orderings_Owellorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), c_Orderings_Oord__class_OLeast(
% 1.35/1.71 X, Y ) ) ), ! hBOOL( hAPP( Y, Z ) ) }.
% 1.35/1.71 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.71 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.71 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 1.35/1.71 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex, X
% 1.35/1.71 ) ), c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.35/1.71 tc_Complex_Ocomplex, v_pa____ ) ) ),
% 1.35/1.71 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 1.35/1.71 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex, X ) ),
% 1.35/1.71 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol6( X ) ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Z = Y, hAPP( hAPP
% 1.35/1.71 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.71 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.71 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.71 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.71 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.35/1.71 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.35/1.71 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.35/1.71 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.71 ( X ), T ), Z ) ), Y ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.71 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 1.35/1.71 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.71 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.35/1.71 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.71 ( X ), U ), T ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y )
% 1.35/1.71 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.35/1.71 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T ), Z )
% 1.35/1.71 ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP(
% 1.35/1.71 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.35/1.71 ) }.
% 1.35/1.71 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.35/1.71 ( X ), ! Z = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Y =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.35/1.71 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.71 = Y }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.35/1.71 = Y }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, hAPP( hAPP
% 1.35/1.71 ( c_Groups_Oplus__class_Oplus( X ), T ), Z ), Y ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 1.35/1.71 c_Polynomial_Osmult( X, T, Y ) ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.35/1.71 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.35/1.71 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T )
% 1.35/1.71 , Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP(
% 1.35/1.71 c_Polynomial_Ocoeff( X, T ), Y ) ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 1.35/1.71 ) ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.71 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.35/1.71 ( X ), U = T, Z = Y, ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP
% 1.35/1.71 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.35/1.71 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.35/1.71 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! U = T }.
% 1.35/1.71 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.35/1.71 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! Z = Y }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 1.35/1.71 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.35/1.71 ( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), U = Z, T = Y }.
% 1.35/1.71 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.35/1.71 ( X ), ! U = Z, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 1.35/1.71 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.35/1.71 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.35/1.71 ( X ), ! T = Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 1.35/1.71 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.71 { ! class_Rings_Osemiring( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.35/1.71 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP(
% 1.35/1.71 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), Y ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), T ) ), Y ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.35/1.71 .
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.35/1.71 .
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.35/1.71 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, ! hAPP( hAPP
% 1.35/1.71 ( c_Groups_Oplus__class_Oplus( X ), W ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), U ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.71 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ), ! Z =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.71 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.71 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.71 ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), T ), Z ) )
% 1.35/1.71 , hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), T ), hAPP( hAPP
% 1.35/1.71 ( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.35/1.71 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.71 ( X ), c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ),
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.35/1.71 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 , Z = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.35/1.71 ) ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.35/1.71 Y ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ),
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), Z = Y, hBOOL( hAPP( hAPP
% 1.35/1.71 ( c_Orderings_Oord__class_Oless( X ), Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), T ), Z ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), T ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), T ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! Z = T, hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( X ), T ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! Y = T, hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( X ), Z ), T ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! Z = Y, ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), T ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), T ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Oord( X ), ! Z = Y, ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), T ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! Y = Z }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! Z = Y }.
% 1.35/1.71 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! Z = Y }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), Z = Y, hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), Z ) ), Y = Z }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! Y = Z, ! hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( X ), Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), Z = Y, hBOOL( hAPP( hAPP
% 1.35/1.71 ( c_Orderings_Oord__class_Oless( X ), Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), Z ) ), Z = Y }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), Z ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), ! Z = Y, ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), Z = Y, hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! Z = Y }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), Z ) ), ! Z = Y }.
% 1.35/1.71 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), Y ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.71 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.35/1.71 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.35/1.71 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.35/1.71 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.35/1.71 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.35/1.71 .
% 1.35/1.71 { ! class_Orderings_Owellorder( X ), ! hBOOL( hAPP( Y, Z ) ), hBOOL( hAPP(
% 1.35/1.71 Y, c_Orderings_Oord__class_OLeast( X, Y ) ) ) }.
% 1.35/1.71 { ! class_Groups_Ozero( X ), !
% 1.35/1.71 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.71 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.71 tc_Polynomial_Opoly( X ) ),
% 1.35/1.71 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! class_Orderings_Owellorder( X ), ! hBOOL( hAPP( Y, Z ) ), hBOOL( hAPP(
% 1.35/1.71 Y, c_Orderings_Oord__class_OLeast( X, Y ) ) ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.71 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.35/1.71 skol7 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.35/1.71 tc_Complex_Ocomplex, v_pa____ ) }.
% 1.35/1.71 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol7 ), X ) = hAPP(
% 1.35/1.71 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), v_c____ ), X ) ) }.
% 1.35/1.71 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 1.35/1.71 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), skol8 ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.35/1.71 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), Z ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero
% 1.35/1.71 ( X ) ) ) }.
% 1.35/1.71 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.71 ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.71 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.35/1.71 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.35/1.71 ( X ) ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), Y ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.71 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.35/1.71 ( X ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.35/1.71 ( X ) ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), Y ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.35/1.71 ( X ) ) ) }.
% 1.35/1.71 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.71 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ), hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.71 ) ), Y ) ) }.
% 1.35/1.71 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ) }.
% 1.35/1.71 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.35/1.71 skol9 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.35/1.71 tc_Complex_Ocomplex, v_pa____ ) }.
% 1.35/1.71 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol9 ), X ) = hAPP(
% 1.35/1.71 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), v_c____ ), X ) ) }.
% 1.35/1.71 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.35/1.71 ( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ) }.
% 1.35/1.71 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) = X }.
% 1.35/1.71 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.35/1.71 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = Y, X
% 1.35/1.71 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP(
% 1.35/1.71 c_Nat_OSuc, X ) ) = hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.71 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( c_Nat_OSuc
% 1.35/1.71 , Y ) ), X ) = hAPP( c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.71 ( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.71 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( c_Nat_OSuc
% 1.35/1.71 , Y ) ), X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y
% 1.35/1.71 ), hAPP( c_Nat_OSuc, X ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), Y ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP
% 1.35/1.71 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP
% 1.35/1.71 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y
% 1.35/1.71 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) )
% 1.35/1.71 }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y
% 1.35/1.71 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) )
% 1.35/1.71 }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), hAPP
% 1.35/1.71 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 T ), Z ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.35/1.71 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), T ) ),
% 1.35/1.71 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), X )
% 1.35/1.71 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ), hBOOL
% 1.35/1.71 ( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), T ), Z ) ) }
% 1.35/1.71 .
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), X ) ),
% 1.35/1.71 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X )
% 1.35/1.71 ) }.
% 1.35/1.71 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), X ) ) = hAPP(
% 1.35/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), Y ) ), Z ) ), X ) }.
% 1.35/1.71 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.35/1.71 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.71 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP
% 1.35/1.71 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.35/1.71 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) = Y }.
% 1.35/1.71 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Y ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T, hAPP(
% 1.35/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Z ), Y ) )
% 1.35/1.71 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 1.35/1.71 c_Polynomial_Osmult( X, T, Z ) ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T ), Z ) ), Y )
% 1.35/1.71 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 1.35/1.71 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T
% 1.35/1.71 ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 1.35/1.71 ( X ) ), Z ), Y ) ) }.
% 1.35/1.71 { ! hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = hAPP(
% 1.35/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), alpha4( X, Y
% 1.35/1.71 ), alpha18( X, Y ) }.
% 1.35/1.71 { ! alpha4( X, Y ), hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.35/1.71 tc_Nat_Onat ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.35/1.71 , Y ), X ) }.
% 1.35/1.71 { ! alpha18( X, Y ), hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.35/1.71 tc_Nat_Onat ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.35/1.71 , Y ), X ) }.
% 1.35/1.71 { ! alpha18( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! alpha18( X, Y ), X = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.35/1.71 tc_Nat_Onat ) ) }.
% 1.35/1.71 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = hAPP( c_Nat_OSuc
% 1.35/1.71 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha18( X, Y ) }.
% 1.35/1.71 { ! alpha4( X, Y ), Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.35/1.71 tc_Nat_Onat ) ) }.
% 1.35/1.71 { ! alpha4( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X
% 1.35/1.71 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha4( X, Y ) }.
% 1.35/1.71 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.35/1.71 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha5( X, Y
% 1.35/1.71 ), alpha19( X, Y ) }.
% 1.35/1.71 { ! alpha5( X, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.35/1.71 , Y ), X ) = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.35/1.71 ) }.
% 1.35/1.71 { ! alpha19( X, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.35/1.71 , Y ), X ) = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.35/1.71 ) }.
% 1.35/1.71 { ! alpha19( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! alpha19( X, Y ), X = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.35/1.71 tc_Nat_Onat ) ) }.
% 1.35/1.71 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = hAPP( c_Nat_OSuc
% 1.35/1.71 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha19( X, Y ) }.
% 1.35/1.71 { ! alpha5( X, Y ), Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.35/1.71 tc_Nat_Onat ) ) }.
% 1.35/1.71 { ! alpha5( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X
% 1.35/1.71 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha5( X, Y ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Groups_Ozero__class_Ozero
% 1.35/1.71 ( tc_Nat_Onat ) ), X ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Groups_Ozero__class_Ozero
% 1.35/1.71 ( tc_Nat_Onat ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.35/1.71 , Y ), X ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Groups_Ozero__class_Ozero
% 1.35/1.71 ( tc_Nat_Onat ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.35/1.71 , Y ), X ) ) ) }.
% 1.35/1.71 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ),
% 1.35/1.71 hAPP( c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.35/1.71 , Y ), X ) ) ) ) }.
% 1.35/1.71 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ),
% 1.35/1.71 hAPP( c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.35/1.71 , X ), Y ) ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ), X = hAPP( c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.71 tc_Nat_Onat ), Y ), skol10( X, Y ) ) ) }.
% 1.35/1.71 { ! X = hAPP( c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.71 tc_Nat_Onat ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.71 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.35/1.71 c_Nat_OSuc, Y ) ), X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.71 tc_Nat_Onat ), X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.71 tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.71 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), hAPP(
% 1.35/1.71 c_Nat_OSuc, X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.35/1.71 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X
% 1.35/1.71 ) ) }.
% 1.35/1.71 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.35/1.71 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.71 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), T ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), T ), Z = Y }.
% 1.35/1.71 { ! class_Groups_Ocancel__ab__semigroup__add( X ), ! hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.35/1.71 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.35/1.71 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), Z ), T = Y }.
% 1.35/1.71 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y, hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 1.35/1.71 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.35/1.71 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y, hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Y ) }.
% 1.35/1.71 { ! class_Groups_Oab__semigroup__add( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.71 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 1.35/1.71 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.35/1.71 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.71 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) = Y }.
% 1.35/1.71 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.35/1.71 = Y }.
% 1.35/1.71 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), Y ), Y =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) = hAPP
% 1.35/1.71 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) }.
% 1.35/1.71 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.71 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.35/1.71 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.71 = Y }.
% 1.35/1.71 { ! class_Groups_Olinordered__ab__group__add( X ), ! hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero
% 1.35/1.71 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.71 ( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.35/1.71 ( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), T ), Y ) ) }.
% 1.35/1.71 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.35/1.71 ( hAPP( c_Orderings_Oord__class_Oless( X ), T ), Y ) ), hBOOL( hAPP( hAPP
% 1.35/1.71 ( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.35/1.71 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.35/1.71 ( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ) }.
% 1.35/1.71 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.35/1.71 ( hAPP( c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), hBOOL( hAPP( hAPP
% 1.35/1.71 ( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ) }.
% 1.35/1.71 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 1.35/1.71 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ) }.
% 1.35/1.71 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.71 ( c_Orderings_Oord__class_Oless( X ), U ), T ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), U ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 1.35/1.71 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.35/1.71 ( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ) }.
% 1.35/1.71 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.35/1.71 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) ) ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.35/1.71 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) ) }.
% 1.35/1.71 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Z ), Y ) =
% 1.35/1.71 c_Polynomial_OAbs__poly( X, hAPP( hAPP( c_COMBS( tc_Nat_Onat, X, X ),
% 1.35/1.71 hAPP( c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat,
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ) ), c_Polynomial_Ocoeff( X, Z ) ) ),
% 1.35/1.71 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 1.35/1.71 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Z, Y ) =
% 1.35/1.71 c_Polynomial_OAbs__poly( X, hAPP( c_COMBB( X, X, tc_Nat_Onat, hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ) ), c_Polynomial_Ocoeff( X, Y ) )
% 1.35/1.71 ) }.
% 1.35/1.71 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, Y ) =
% 1.35/1.71 c_Orderings_Oord__class_OLeast( tc_Nat_Onat, hAPP( c_COMBB( tc_fun(
% 1.35/1.71 tc_Nat_Onat, tc_HOL_Obool ), tc_HOL_Obool, tc_Nat_Onat, c_HOL_OAll(
% 1.35/1.71 tc_Nat_Onat ) ), c_COMBC( tc_Nat_Onat, tc_fun( tc_Nat_Onat, tc_HOL_Obool
% 1.35/1.71 ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ), hAPP( c_COMBB( tc_fun(
% 1.35/1.71 tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ), tc_fun( tc_fun(
% 1.35/1.71 tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ),
% 1.35/1.71 tc_Nat_Onat, c_COMBS( tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool ) ), hAPP(
% 1.35/1.71 c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_fun
% 1.35/1.71 ( tc_HOL_Obool, tc_HOL_Obool ) ), tc_Nat_Onat, c_COMBB( tc_HOL_Obool,
% 1.35/1.71 tc_fun( tc_HOL_Obool, tc_HOL_Obool ), tc_Nat_Onat, c_fimplies ) ),
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat ) ) ), c_COMBC( tc_Nat_Onat, X
% 1.35/1.71 , tc_HOL_Obool, hAPP( c_COMBB( X, tc_fun( X, tc_HOL_Obool ), tc_Nat_Onat
% 1.35/1.71 , c_fequal ), c_Polynomial_Ocoeff( X, Y ) ), c_Groups_Ozero__class_Ozero
% 1.35/1.71 ( X ) ) ) ) ) }.
% 1.35/1.71 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.35/1.71 skol11( X, Z ) ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.35/1.71 tc_Complex_Ocomplex, X ) }.
% 1.35/1.71 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol11( X, Y ) ), Z ) =
% 1.35/1.71 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), Y ), Z ) ) }.
% 1.35/1.71 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.35/1.71 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.35/1.71 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( X, Y ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL( hAPP( X,
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha52( X, Z, skol12( X
% 1.35/1.71 , Z ) ), hBOOL( hAPP( Z, skol12( X, Z ) ) ),
% 1.35/1.71 c_Orderings_Oord__class_OLeast( tc_Nat_Onat, X ) = hAPP( c_Nat_OSuc,
% 1.35/1.71 c_Orderings_Oord__class_OLeast( tc_Nat_Onat, Z ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( X, Y ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL( hAPP( X,
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha52( X, Z, skol12( X
% 1.35/1.71 , Z ) ), ! hBOOL( hAPP( X, hAPP( c_Nat_OSuc, skol12( X, Z ) ) ) ),
% 1.35/1.71 c_Orderings_Oord__class_OLeast( tc_Nat_Onat, X ) = hAPP( c_Nat_OSuc,
% 1.35/1.71 c_Orderings_Oord__class_OLeast( tc_Nat_Onat, Z ) ) }.
% 1.35/1.71 { ! alpha52( X, Y, Z ), hBOOL( hAPP( X, hAPP( c_Nat_OSuc, Z ) ) ) }.
% 1.35/1.71 { ! alpha52( X, Y, Z ), ! hBOOL( hAPP( Y, Z ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( X, hAPP( c_Nat_OSuc, Z ) ) ), hBOOL( hAPP( Y, Z ) ),
% 1.35/1.71 alpha52( X, Y, Z ) }.
% 1.35/1.71 { ! class_Orderings_Opreorder( X ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), Y ) ) }.
% 1.35/1.71 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), Y ), X ) ) ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) ) }.
% 1.35/1.71 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 1.35/1.71 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ), Z = X }.
% 1.35/1.71 { ! Z = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 1.35/1.71 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 1.35/1.71 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 1.35/1.71 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y = X }.
% 1.35/1.71 { ! Y = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 1.35/1.71 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) }.
% 1.35/1.71 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.35/1.71 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.71 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 1.35/1.71 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP(
% 1.35/1.71 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.35/1.71 tc_RealDef_Oreal ) ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.35/1.71 tc_RealDef_Oreal ) ) ) }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 1.35/1.71 ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Y = Z }.
% 1.35/1.71 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Z = Y }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Z = T, hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Y = T, hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Oord( X ), ! Z = Y, ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Y = Z }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Y = Z, hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 1.35/1.71 ) ) }.
% 1.35/1.71 { ! class_Orderings_Opreorder( X ), ! Z = Y, hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Z = Y }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 1.35/1.71 ) ) }.
% 1.35/1.71 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, skol13( X, Y, Z ) ) ),
% 1.35/1.71 hAPP( Y, skol13( X, Y, Z ) ) ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.35/1.71 tc_RealDef_Oreal ) ) ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 1.35/1.71 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 1.35/1.71 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, Y ) ) ), ! Y =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__algebra( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, U ) ), T ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, U ) ), T ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), U ) ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), T ) ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), T ), Z ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), T ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), T ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), T ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), T ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Y = Z, hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( X ), Z ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( X ), Z ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), Z = Y }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), Z = Y }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Z = Y, ! hBOOL( hAPP
% 1.35/1.71 ( hAPP( c_Orderings_Oord__class_Oless( X ), Z ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), Z = Y, ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), Z = Y, ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! Z = Y, hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), Z = Y }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! Z = Y }.
% 1.35/1.71 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 1.35/1.71 hAPP( c_Orderings_Oord__class_Oless( X ), Z ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Y ), Z ) ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.35/1.71 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 1.35/1.71 class_Rings_Odivision__ring__inverse__zero( X ),
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 1.35/1.71 Y ) ) = c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.35/1.71 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.35/1.71 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.35/1.71 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.35/1.71 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.35/1.71 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), U ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 1.35/1.71 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ) }.
% 1.35/1.71 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 1.35/1.71 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.35/1.71 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.35/1.71 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.35/1.71 ( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ) }.
% 1.35/1.71 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.35/1.71 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 1.35/1.71 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.35/1.71 ( c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.71 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.35/1.71 { ! class_Orderings_Owellorder( X ), ! hBOOL( hAPP( Z, Y ) ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, c_Orderings_Oord__class_OLeast( X,
% 1.35/1.71 Z ) ), Y ) ) }.
% 1.35/1.71 { ! class_Groups_Ozero( X ), c_Polynomial_OAbs__poly( X,
% 1.35/1.71 c_Polynomial_Ocoeff( X, Y ) ) = Y }.
% 1.35/1.71 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.71 { ! class_RealVector_Oreal__normed__div__algebra( X ), Y =
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( X, Y ) ) =
% 1.35/1.71 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 1.35/1.71 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring( X ), hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.71 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.71 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), alpha6( X
% 1.35/1.71 , Y, Z ), alpha20( X, Y, Z ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z ), hBOOL
% 1.35/1.71 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.35/1.71 ( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha20( X, Y, Z ), hBOOL
% 1.35/1.71 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.35/1.71 ( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.35/1.71 { ! alpha20( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.71 Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.71 { ! alpha20( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.71 Y ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.71 ) ) ), alpha20( X, Y, Z ) }.
% 1.35/1.71 { ! alpha6( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 1.35/1.71 { ! alpha6( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.71 , Y ) ), alpha6( X, Y, Z ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ) ), alpha7( X, Y, Z ), alpha21( X, Y, Z
% 1.35/1.71 ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha7( X, Y, Z ), hBOOL
% 1.35/1.71 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.71 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha21( X, Y, Z ), hBOOL
% 1.35/1.71 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.71 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.71 { ! alpha21( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.71 Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.71 { ! alpha21( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 1.35/1.71 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.71 , Y ) ), alpha21( X, Y, Z ) }.
% 1.35/1.71 { ! alpha7( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 1.35/1.71 { ! alpha7( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y
% 1.35/1.71 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.71 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.71 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) ) ), alpha7( X, Y, Z ) }.
% 1.35/1.72 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.35/1.72 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.72 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.72 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.72 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.35/1.72 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.35/1.72 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.35/1.72 { ! class_Rings_Oordered__comm__semiring( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.35/1.72 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) ) }.
% 1.35/1.72 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) ) }.
% 1.35/1.72 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.35/1.72 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.35/1.72 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.35/1.72 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.35/1.72 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.72 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero
% 1.35/1.72 ( X ) ) ) }.
% 1.35/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) )
% 1.35/1.72 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ) }.
% 1.35/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) )
% 1.35/1.72 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.35/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.35/1.72 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.35/1.72 ( X ), Z = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! Y =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.72 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.35/1.72 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.35/1.72 ( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.72 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.35/1.72 ( X ) ) ) }.
% 1.35/1.72 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ), hBOOL( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.35/1.72 ), Y ) ) }.
% 1.35/1.72 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ) }.
% 1.35/1.72 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), U ), T ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), U ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 1.35/1.72 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), U ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 1.35/1.72 { ! class_Groups_Ocomm__monoid__add( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Polynomial_Odegree( X, Z
% 1.35/1.72 ) ), Y ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless(
% 1.35/1.72 tc_Nat_Onat ), c_Polynomial_Odegree( X, T ) ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Polynomial_Odegree( X,
% 1.35/1.72 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Z )
% 1.35/1.72 , T ) ) ), Y ) ) }.
% 1.35/1.72 { ! class_Groups_Ocomm__monoid__add( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Polynomial_Odegree( X, Z
% 1.35/1.72 ) ), c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Odegree( X, hAPP(
% 1.35/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Z ), Y ) )
% 1.35/1.72 = c_Polynomial_Odegree( X, Y ) }.
% 1.35/1.72 { ! class_Groups_Ocomm__monoid__add( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Polynomial_Odegree( X, Z
% 1.35/1.72 ) ), c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Odegree( X, hAPP(
% 1.35/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Y ), Z ) )
% 1.35/1.72 = c_Polynomial_Odegree( X, Y ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.35/1.72 , Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.35/1.72 X ) ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), c_Rings_Oinverse__class_Oinverse( X,
% 1.35/1.72 Y ) ) ) }.
% 1.35/1.72 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 1.35/1.72 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.35/1.72 c_Polynomial_Odegree( X, Y ) ), c_Polynomial_Odegree( X, Z ) ) }.
% 1.35/1.72 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.72 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.72 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.72 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 1.35/1.72 c_Polynomial_Odegree( X, Y ) }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Polynomial_Odegree( X, Z
% 1.35/1.72 ) ), Y ) ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.35/1.72 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.35/1.72 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.35/1.72 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), T
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Z
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , T ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), Z ), Y )
% 1.35/1.72 ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semiring( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , T ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), Z ), Y )
% 1.35/1.72 ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Z ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), T ), Y )
% 1.35/1.72 ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semiring( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Z ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), T ), Y )
% 1.35/1.72 ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), U ), T ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Z
% 1.35/1.72 ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Z ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), U ), T ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), U ), T ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.72 ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.72 ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.72 ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ),
% 1.35/1.72 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.72 ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.72 ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ),
% 1.35/1.72 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.35/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), Z ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero
% 1.35/1.72 ( X ) ) ) }.
% 1.35/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.72 ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero
% 1.35/1.72 ( X ) ) ) }.
% 1.35/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), T ), Z
% 1.35/1.72 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), T ), hAPP(
% 1.35/1.72 hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.35/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.72 ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ),
% 1.35/1.72 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), T ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.35/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.72 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.35/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.72 ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.72 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__ring( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ), Z = c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ), Y = c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.72 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.35/1.72 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.35/1.72 ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.35/1.72 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP(
% 1.35/1.72 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z
% 1.35/1.72 ), c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.35/1.72 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.35/1.72 , Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( X ), Y ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.35/1.72 , Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ), Z )
% 1.35/1.72 ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Z
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OAbs__poly( X, c_COMBK( X,
% 1.35/1.72 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ),
% 1.35/1.72 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ),
% 1.35/1.72 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = hAPP(
% 1.35/1.72 c_Nat_OSuc, c_Polynomial_Odegree( X, Y ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__div__algebra( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, Y ) ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 1.35/1.72 Y ) ) ), c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Z ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, T ) ) ) ), Z =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.35/1.72 , U = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) )
% 1.35/1.72 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.35/1.72 Z ), T ) ), Y ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.35/1.72 , alpha30( X, Y, Z, T ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! U = hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.72 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), Z ), T ) ), Y ), ! alpha30( X, Y, Z, T ),
% 1.35/1.72 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 1.35/1.72 { ! alpha30( X, Y, Z, T ), alpha8( X, Z, T ) }.
% 1.35/1.72 { ! alpha30( X, Y, Z, T ), alpha22( X, Y, T ) }.
% 1.35/1.72 { ! alpha8( X, Z, T ), ! alpha22( X, Y, T ), alpha30( X, Y, Z, T ) }.
% 1.35/1.72 { ! alpha22( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), alpha31( X, Y, Z ) }.
% 1.35/1.72 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha22( X
% 1.35/1.72 , Y, Z ) }.
% 1.35/1.72 { ! alpha31( X, Y, Z ), alpha22( X, Y, Z ) }.
% 1.35/1.72 { ! alpha31( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Polynomial_Odegree( X, Y
% 1.35/1.72 ) ), c_Polynomial_Odegree( X, Z ) ) ) }.
% 1.35/1.72 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha31( X
% 1.35/1.72 , Y, Z ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Polynomial_Odegree( X, Y ) ), c_Polynomial_Odegree( X, Z ) ) ), alpha31
% 1.35/1.72 ( X, Y, Z ) }.
% 1.35/1.72 { ! alpha8( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.72 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha8( X, Y
% 1.35/1.72 , Z ) }.
% 1.35/1.72 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha8( X
% 1.35/1.72 , Y, Z ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.72 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y
% 1.35/1.72 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) )
% 1.35/1.72 }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.72 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y
% 1.35/1.72 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) )
% 1.35/1.72 }.
% 1.35/1.72 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.35/1.72 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.35/1.72 c_Polynomial_Odegree( X, Y ) ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.72 hAPP( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) ),
% 1.35/1.72 c_Polynomial_Opos__poly( X, Y ) }.
% 1.35/1.72 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), skol14
% 1.35/1.72 ( X, Y ) ) }.
% 1.35/1.72 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 1.35/1.72 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.35/1.72 .
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.35/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.35/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X
% 1.35/1.72 ) ) }.
% 1.35/1.72 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_fun( T, X ) ), Z ), Y ) ), hBOOL( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ) }.
% 1.35/1.72 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_fun( T, X ) ), Z ), Y ) ), ! hBOOL(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y ), Z ) ) }.
% 1.35/1.72 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y ), Z ) ),
% 1.35/1.72 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_fun( T, X ) ), Z ),
% 1.35/1.72 Y ) ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.35/1.72 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.35/1.72 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.35/1.72 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.35/1.72 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 1.35/1.72 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.72 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.35/1.72 c_Nat_OSuc, X ) ), X ) ) }.
% 1.35/1.72 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ),
% 1.35/1.72 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.35/1.72 c_Nat_OSuc, X ) ), Y ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.35/1.72 c_Nat_OSuc, X ) ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.35/1.72 ( c_Nat_OSuc, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.72 tc_Nat_Onat, Y ), X ) ), Y = hAPP( c_Nat_OSuc, X ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.35/1.72 ( c_Nat_OSuc, X ) ) ) }.
% 1.35/1.72 { ! Y = hAPP( c_Nat_OSuc, X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP( c_Nat_OSuc, X
% 1.35/1.72 ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.35/1.72 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.35/1.72 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.35/1.72 ( c_Nat_OSuc, X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.35/1.72 ( c_Nat_OSuc, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.72 tc_Nat_Onat, Y ), X ) ), Y = hAPP( c_Nat_OSuc, X ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.35/1.72 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.35/1.72 ( tc_Nat_Onat, Y ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X
% 1.35/1.72 ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.72 ) ), ! Y = X }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , Y = X, hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat )
% 1.35/1.72 , Y ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.72 ) ), Y = X }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X
% 1.35/1.72 ) ) }.
% 1.35/1.72 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 1.35/1.72 , X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X
% 1.35/1.72 ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , Y = X, hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat )
% 1.35/1.72 , Y ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X
% 1.35/1.72 ) ) }.
% 1.35/1.72 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 1.35/1.72 , X ) ) }.
% 1.35/1.72 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP(
% 1.35/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.35/1.72 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP(
% 1.35/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), skol15
% 1.35/1.72 ( X, Y ) ) }.
% 1.35/1.72 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 1.35/1.72 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.35/1.72 .
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.35/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.35/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 1.35/1.72 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.35/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), T ) ), hAPP( hAPP
% 1.35/1.72 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), X ) ), hBOOL(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 1.35/1.72 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.35/1.72 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ) ), hAPP(
% 1.35/1.72 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.35/1.72 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), hAPP(
% 1.35/1.72 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) ) }.
% 1.35/1.72 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), hAPP(
% 1.35/1.72 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 1.35/1.72 .
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.35/1.72 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 1.35/1.72 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.35/1.72 c_Nat_OSuc, Y ) ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.35/1.72 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ),
% 1.35/1.72 hAPP( c_Nat_OSuc, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.35/1.72 ( tc_Nat_Onat, Y ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ),
% 1.35/1.72 hAPP( c_Nat_OSuc, X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.35/1.72 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.35/1.72 c_Nat_OSuc, Y ) ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ),
% 1.35/1.72 hAPP( c_Nat_OSuc, X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.35/1.72 c_Nat_OSuc, Y ) ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), X )
% 1.35/1.72 , hAPP( c_Nat_OSuc, Y ) ) ), X = Y }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , ! X = Y, hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.35/1.72 ), X ), hAPP( c_Nat_OSuc, Y ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.35/1.72 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ),
% 1.35/1.72 Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.35/1.72 c_Nat_OSuc, Z ) ), X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ),
% 1.35/1.72 Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.35/1.72 c_Nat_OSuc, Z ) ), X ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.35/1.72 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.35/1.72 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.35/1.72 .
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__0( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.35/1.72 c_Polynomial_Osmult( X, Z, Y ) ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.35/1.72 { ! class_Groups_Ocomm__monoid__add( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.35/1.72 Z ) ), Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.72 tc_Nat_Onat, c_Polynomial_Odegree( X, T ) ), Y ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.35/1.72 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Z )
% 1.35/1.72 , T ) ) ), Y ) ) }.
% 1.35/1.72 { hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), X ) =
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc, X ) ) }
% 1.35/1.72 .
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.35/1.72 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.35/1.72 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.35/1.72 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), !
% 1.35/1.72 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.35/1.72 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), hBOOL
% 1.35/1.72 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 1.35/1.72 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), ! hBOOL( hAPP
% 1.35/1.72 ( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.35/1.72 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), ! hBOOL( hAPP
% 1.35/1.72 ( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), X ) ) }.
% 1.35/1.72 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), X ) )
% 1.35/1.72 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.35/1.72 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 1.35/1.72 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 1.35/1.72 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 1.35/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T
% 1.35/1.72 ), W ) ), Y ) ) }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), c_Polynomial_Odegree
% 1.35/1.72 ( X, Z ) ) ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__0( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.35/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z
% 1.35/1.72 ), Y ) ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.35/1.72 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) ) }.
% 1.35/1.72 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Oorder( X, Z
% 1.35/1.72 , Y ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.35/1.72 c_Polynomial_Opdivmod__rel( X, W, U, T, Z ), c_Polynomial_Opdivmod__rel(
% 1.35/1.72 X, W, c_Polynomial_Osmult( X, Y, U ), c_Polynomial_Osmult( X,
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ), T ), Z ) }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.35/1.72 Z ) ), Y ) ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Polynomial_Odegree( X, Z
% 1.35/1.72 ) ), Y ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ), hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ) ), hBOOL
% 1.35/1.72 ( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), hAPP(
% 1.35/1.72 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ), hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ) ), hBOOL
% 1.35/1.72 ( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), hAPP(
% 1.35/1.72 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), T ) ), hAPP(
% 1.35/1.72 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ), Z ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) ), hBOOL
% 1.35/1.72 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ) }
% 1.35/1.72 .
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ), hBOOL(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ), hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ), hBOOL
% 1.35/1.72 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ) }
% 1.35/1.72 .
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ), hBOOL(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ), hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 1.35/1.72 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP(
% 1.35/1.72 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.35/1.72 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP(
% 1.35/1.72 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.35/1.72 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y )
% 1.35/1.72 ), Y = X }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z )
% 1.35/1.72 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.35/1.72 ) }.
% 1.35/1.72 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 1.35/1.72 , X ) ) }.
% 1.35/1.72 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ),
% 1.35/1.72 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ) }
% 1.35/1.72 .
% 1.35/1.72 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), X ) ) }
% 1.35/1.72 .
% 1.35/1.72 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), X
% 1.35/1.72 ) ) }.
% 1.35/1.72 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ), X
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X
% 1.35/1.72 ), Y ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.35/1.72 X ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 1.35/1.72 , X ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.72 tc_RealDef_Oreal, Y ), Z ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.35/1.72 X ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 1.35/1.72 , X ), Y ) ), Y = X }.
% 1.35/1.72 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 1.35/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 1.35/1.72 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.35/1.72 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 1.35/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 1.35/1.72 }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.35/1.72 X ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 1.35/1.72 ), Y ), X ) ), Y = X }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), Y
% 1.35/1.72 ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.72 tc_RealDef_Oreal, Y ), X ) ) }.
% 1.35/1.72 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 1.35/1.72 , Y ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), Y
% 1.35/1.72 ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.72 tc_RealDef_Oreal, Y ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), Y
% 1.35/1.72 ), X ) ), ! Y = X }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.35/1.72 X ) ), Y = X, hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless(
% 1.35/1.72 tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.35/1.72 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 1.35/1.72 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 1.35/1.72 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 1.35/1.72 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 1.35/1.72 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 1.35/1.72 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.35/1.72 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), Y ) ),
% 1.35/1.72 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), X ) ) )
% 1.35/1.72 }.
% 1.35/1.72 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 1.35/1.72 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), Y ) ), X ) = hAPP
% 1.35/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.35/1.72 { c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), Z ), Y ) ),
% 1.35/1.72 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) )
% 1.35/1.72 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 1.35/1.72 ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) ), hBOOL
% 1.35/1.72 ( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), Z ), Y )
% 1.35/1.72 ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), Z ), Y ) ),
% 1.35/1.72 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) )
% 1.35/1.72 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X )
% 1.35/1.72 ) ) }.
% 1.35/1.72 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ), X =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.35/1.72 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol16( Z, T ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol16( X, Y ) ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol17( Z, T ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol17( X, Y ) ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol18( Y ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol18( X ) ) ) ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__0( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.35/1.72 c_Polynomial_Opcompose( X, Z, Y ) ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Polynomial_Odegree( X, Z
% 1.35/1.72 ) ), c_Polynomial_Odegree( X, Y ) ) ) ) }.
% 1.35/1.72 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ) ), hAPP( Y, Z ) ) ) }
% 1.35/1.72 .
% 1.35/1.72 { ! class_Orderings_Oorder( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol19( X, Y ) ), skol67
% 1.35/1.72 ( X, Y ) ) ), c_SEQ_Odecseq( X, Y ) }.
% 1.35/1.72 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol67( X, Y ) ) ), hAPP(
% 1.35/1.72 Y, skol19( X, Y ) ) ) ), c_SEQ_Odecseq( X, Y ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.35/1.72 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 1.35/1.72 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 1.35/1.72 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol20( Z, T ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Z ) ), Y ) ), hBOOL
% 1.35/1.72 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.35/1.72 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), Z ) ) ), skol20( X, Y ) ) )
% 1.35/1.72 }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.35/1.72 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 1.35/1.72 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 1.35/1.72 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 1.35/1.72 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.35/1.72 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.35/1.72 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 1.35/1.72 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Z ), skol21( T, U, Z ) ) )
% 1.35/1.72 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.35/1.72 c_Polynomial_Odegree( X, Y ) ), Z ) ) }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ), skol21( X
% 1.35/1.72 , Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.35/1.72 Y ) ), Z ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol22( Z, T ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol22( X, Y ) ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol23( Z, T ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol23( X, Y ) ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol24( Y ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol24( X ) ) ) ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 1.35/1.72 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 1.35/1.72 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 1.35/1.72 c_Polynomial_Opoly__gcd( X, Z, c_Divides_Odiv__class_Omod(
% 1.35/1.72 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 1.35/1.72 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.35/1.72 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.35/1.72 }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 1.35/1.72 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.35/1.72 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol25( Z, T ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.35/1.72 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ) ), skol25( X, Y ) ) )
% 1.35/1.72 }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol68( X, Y, Z ) ) ) ), Z )
% 1.35/1.72 ), c_SEQ_OBseq( X, Y ) }.
% 1.35/1.72 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ) ), hAPP( Y, T ) ) ) }
% 1.35/1.72 .
% 1.35/1.72 { ! class_Orderings_Oorder( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol26( X, Y ) ), skol69
% 1.35/1.72 ( X, Y ) ) ), c_SEQ_Oincseq( X, Y ) }.
% 1.35/1.72 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol26( X, Y ) ) ), hAPP(
% 1.35/1.72 Y, skol69( X, Y ) ) ) ), c_SEQ_Oincseq( X, Y ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.35/1.72 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 1.35/1.72 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod(
% 1.35/1.72 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.35/1.72 , c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 1.35/1.72 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 1.35/1.72 tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Polynomial_Odegree( X, Z
% 1.35/1.72 ) ), c_Polynomial_Odegree( X, Y ) ) ), c_Divides_Odiv__class_Omod(
% 1.35/1.72 tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.35/1.72 c_Polynomial_Opoly__gcd( X, Y, c_Divides_Odiv__class_Omod(
% 1.35/1.72 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.35/1.72 c_SEQ_OBseq( X, hAPP( c_COMBB( tc_Nat_Onat, X, tc_Nat_Onat, Y ), c_COMBC
% 1.35/1.72 ( tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.35/1.72 tc_Nat_Onat ), Z ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, hAPP(
% 1.35/1.72 c_COMBB( tc_Nat_Onat, X, tc_Nat_Onat, Y ), c_COMBC( tc_Nat_Onat,
% 1.35/1.72 tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z )
% 1.35/1.72 ) ), c_SEQ_OBseq( X, Y ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 1.35/1.72 tc_Polynomial_Opoly( X ), Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Polynomial_Odegree( X,
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ) ),
% 1.35/1.72 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 1.35/1.72 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 1.35/1.72 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.72 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.72 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.72 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.35/1.72 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.72 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), X ) =
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 1.35/1.72 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ), Y ) =
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 1.35/1.72 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol27( X, Y ) ) }.
% 1.35/1.72 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 1.35/1.72 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Divides_Odiv__class_Omod
% 1.35/1.72 ( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 1.35/1.72 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, hAPP( c_Nat_OSuc,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.72 { ! hAPP( c_Nat_OSuc, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X
% 1.35/1.72 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), X ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.72 { hAPP( c_Nat_OSuc, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), X ) =
% 1.35/1.72 hAPP( c_Nat_OSuc, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.72 ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 1.35/1.72 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), Y ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 1.35/1.72 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) ), Y ) =
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( c_Nat_OSuc, X ), Y ) }.
% 1.35/1.72 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 1.35/1.72 alpha9( X, Y, Z ) }.
% 1.35/1.72 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 1.35/1.72 alpha23( X, Y, Z ) }.
% 1.35/1.72 { ! alpha9( X, Y, Z ), ! alpha23( X, Y, Z ), hBOOL( hAPP( Z,
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 1.35/1.72 { ! alpha23( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.35/1.72 alpha32( X, Y, Z ) }.
% 1.35/1.72 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha23( X, Y, Z ) }.
% 1.35/1.72 { ! alpha32( X, Y, Z ), alpha23( X, Y, Z ) }.
% 1.35/1.72 { ! alpha32( X, Y, Z ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless
% 1.35/1.72 ( tc_Nat_Onat ), T ), X ) ), alpha36( X, Y, Z, T ) }.
% 1.35/1.72 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), skol28(
% 1.35/1.72 X, T, U ) ), X ) ), alpha32( X, Y, Z ) }.
% 1.35/1.72 { ! alpha36( X, Y, Z, skol28( X, Y, Z ) ), alpha32( X, Y, Z ) }.
% 1.35/1.72 { ! alpha36( X, Y, Z, T ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.72 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.35/1.72 X ), U ) ), T ), hBOOL( hAPP( Z, T ) ) }.
% 1.35/1.72 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol29( X, Y, T ) ) )
% 1.35/1.72 , T ), alpha36( X, Y, Z, T ) }.
% 1.35/1.72 { ! hBOOL( hAPP( Z, T ) ), alpha36( X, Y, Z, T ) }.
% 1.35/1.72 { ! alpha9( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.35/1.72 hBOOL( hAPP( Z, Y ) ) }.
% 1.35/1.72 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha9( X, Y, Z ) }.
% 1.35/1.72 { ! hBOOL( hAPP( Z, Y ) ), alpha9( X, Y, Z ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ) ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.35/1.72 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 1.35/1.72 X, Z, Y ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.72 }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 1.35/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 1.35/1.72 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 1.35/1.72 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.35/1.72 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.72 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.72 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 1.35/1.72 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.72 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 1.35/1.72 ), Z ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.72 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 1.35/1.72 , Y ) ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.72 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.35/1.72 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.72 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 1.35/1.72 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.72 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.35/1.72 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.72 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.72 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.35/1.72 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.72 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 1.35/1.72 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 1.35/1.72 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.35/1.72 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.35/1.72 ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), U ), Z ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( X ), c_Divides_Odiv__class_Omod( X,
% 1.35/1.72 T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), c_Divides_Odiv__class_Omod
% 1.35/1.72 ( X, Z, Y ) ), Y ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Z ), Y ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), Y ) =
% 1.35/1.72 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.35/1.72 ), c_Divides_Odiv__class_Omod( X, T, Y ) ), c_Divides_Odiv__class_Omod(
% 1.35/1.72 X, Z, Y ) ), Y ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), Y ) =
% 1.35/1.72 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.35/1.72 ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), Y ) =
% 1.35/1.72 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.35/1.72 ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Z ) =
% 1.35/1.72 c_Divides_Odiv__class_Omod( X, Y, Z ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Y ) =
% 1.35/1.72 c_Divides_Odiv__class_Omod( X, Z, Y ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol30( X, Y, Z ) ) ) ), Y )
% 1.35/1.72 ), c_SEQ_OBseq( X, Z ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.35/1.72 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol31( Z, T ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.35/1.72 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ) ), skol31( X, Y ) ) )
% 1.35/1.72 }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.35/1.72 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.35/1.72 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.72 }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.35/1.72 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.35/1.72 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.35/1.72 .
% 1.35/1.72 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.35/1.72 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.35/1.72 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.35/1.72 .
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), skol32( U, W, V0, T
% 1.35/1.72 ) ) ), c_SEQ_OBseq( X, Y ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol32( X, Y, Z, T ) ) ) ),
% 1.35/1.72 Z ) ), c_SEQ_OBseq( X, Y ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 1.35/1.72 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 1.35/1.72 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.35/1.72 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.72 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.72 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.72 = Y }.
% 1.35/1.72 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.72 = Y }.
% 1.35/1.72 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.35/1.72 = Y }.
% 1.35/1.72 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.35/1.72 = Y }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.35/1.72 = Y }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.72 = Y }.
% 1.35/1.72 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.72 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 1.35/1.72 , Y = c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.72 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 1.35/1.72 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 1.35/1.72 = c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.72 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.72 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 1.35/1.72 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 1.35/1.72 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.35/1.72 tc_Nat_Onat ) }.
% 1.35/1.72 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.35/1.72 tc_Nat_Onat ) }.
% 1.35/1.72 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.35/1.72 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.35/1.72 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.35/1.72 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.35/1.72 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.35/1.72 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.35/1.72 , Y ), X ) }.
% 1.35/1.72 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.35/1.72 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.35/1.72 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.72 ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) ), Z ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), Y ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 1.35/1.72 ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 1.35/1.72 , Z ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) = hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), c_Groups_Oone__class_Oone( X ) ) )
% 1.35/1.72 , Y ) }.
% 1.35/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.72 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 1.35/1.72 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 1.35/1.72 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( c_Nat_OSuc,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.72 { hAPP( c_Nat_OSuc, X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.72 tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.35/1.72 { hAPP( c_Nat_OSuc, X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.72 tc_Nat_Onat ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.35/1.72 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.35/1.72 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Oone__class_Oone( X )
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Oone__class_Oone( X )
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.72 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone(
% 1.35/1.72 X ) ), c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.35/1.72 , Y ) ), c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) ), Y ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Groups_Oone__class_Oone( X
% 1.35/1.72 ) ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ), Y
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Groups_Oone__class_Oone( X
% 1.35/1.72 ) ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.72 ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), Y ),
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X )
% 1.35/1.72 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.72 ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X )
% 1.35/1.72 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.35/1.72 ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) ), Y ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), Y )
% 1.35/1.72 , c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ) ) }.
% 1.35/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.72 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.72 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.35/1.72 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.72 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 1.35/1.72 ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ),
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X ) =
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.35/1.72 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), X ) =
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semiring__1( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , U ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), W ) ), ! hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), U ), W ) = c_Groups_Oone__class_Oone( X
% 1.35/1.72 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), W ), T ) ) ), Y ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.72 ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Groups_Oone__class_Oone( X
% 1.35/1.72 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.72 ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Groups_Oone__class_Oone( X
% 1.35/1.72 ) ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X )
% 1.35/1.72 ), Y ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Groups_Oone__class_Oone( X
% 1.35/1.72 ) ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.72 ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Oone__class_Oone( X )
% 1.35/1.72 ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) ), Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semiring__1__strict( X ), ! hBOOL( hAPP( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), T ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , U ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), W ) ), ! hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), U ), W ) = c_Groups_Oone__class_Oone( X
% 1.35/1.72 ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), W ), T ) ) ), Y ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), hBOOL( hAPP( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , skol33( X, T, U ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.72 X, Z ), Y ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), hBOOL( hAPP( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless( X ), skol33( X, T, U ) ),
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.35/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), skol33( X, Y, Z ) ), Z ) ), Y ) ),
% 1.35/1.72 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Z ), c_Polynomial_Odegree(
% 1.35/1.72 X, Y ) ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.35/1.72 ), Z ), skol34( T, U, Z ) ) ) }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Z ), c_Polynomial_Odegree(
% 1.35/1.72 X, Y ) ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ), skol34( X, Y, Z ) ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.72 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) =
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z ) ), Z = hAPP(
% 1.35/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), skol35( X, Y, Z ) ) )
% 1.35/1.72 }.
% 1.35/1.72 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.35/1.72 hAPP( X, Y ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless(
% 1.35/1.72 tc_Nat_Onat ), skol36( Z, Y ) ), Y ) ) }.
% 1.35/1.72 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.35/1.72 hAPP( X, Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.72 tc_Nat_Onat, Z ), skol36( X, Y ) ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 1.35/1.72 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.35/1.72 hAPP( X, Y ) ), hBOOL( hAPP( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.72 tc_Nat_Onat ), skol36( X, Y ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 1.35/1.72 ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.35/1.72 c_RComplete_Onatceiling( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.72 tc_RealDef_Oreal ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.35/1.72 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.35/1.72 c_RComplete_Onatceiling( X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 1.35/1.72 ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.35/1.72 c_RComplete_Onatfloor( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.72 tc_RealDef_Oreal ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.35/1.72 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.35/1.72 c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 1.35/1.72 }.
% 1.35/1.72 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.35/1.72 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.35/1.72 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.35/1.72 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), c_RComplete_Onatfloor( X )
% 1.35/1.72 ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.35/1.72 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.35/1.72 c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( X ) ) ) }.
% 1.35/1.72 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 1.35/1.72 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.35/1.72 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.35/1.72 c_RComplete_Onatceiling( Y ) ), c_RComplete_Onatceiling( X ) ) ) }.
% 1.35/1.72 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), c_RComplete_Onatceiling( X
% 1.35/1.72 ) ) ) }.
% 1.35/1.72 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 1.35/1.72 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ),
% 1.35/1.72 c_RComplete_Onatfloor( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.35/1.72 .
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ),
% 1.35/1.72 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.35/1.72 }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), c_RComplete_Onatfloor( X ) )
% 1.35/1.72 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 1.35/1.72 ( tc_Nat_Onat ) ), c_RComplete_Onatfloor( X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.35/1.72 c_RComplete_Onatceiling( X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X
% 1.35/1.72 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.35/1.72 X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 1.35/1.72 ), c_RComplete_Onatfloor( Y ) ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ),
% 1.35/1.72 c_RComplete_Onatceiling( X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.72 tc_Nat_Onat ), Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.35/1.72 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), skol37(
% 1.35/1.72 Z, Y ) ), Y ) ), ! hBOOL( hAPP( X, T ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), T ), Y ) ), hBOOL( hAPP( X
% 1.35/1.72 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.35/1.72 { hBOOL( hAPP( X, skol37( X, Y ) ) ), ! hBOOL( hAPP( X, Z ) ), ! hBOOL(
% 1.35/1.72 hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Z ), Y ) ),
% 1.35/1.72 hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( X, c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP(
% 1.35/1.72 c_Nat_OSuc, skol37( X, Y ) ), Y ) ) ), ! hBOOL( hAPP( X, Z ) ), ! hBOOL(
% 1.35/1.72 hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Z ), Y ) ),
% 1.35/1.72 hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.35/1.72 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.35/1.72 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), skol38 ) ) ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.35/1.72 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) ) }.
% 1.35/1.72 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, X ) ) ) }.
% 1.35/1.72 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 1.35/1.72 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 1.35/1.72 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 1.35/1.72 Y = X }.
% 1.35/1.72 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 1.35/1.72 , X ) }.
% 1.35/1.72 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.35/1.72 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.35/1.72 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.72 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_RealDef_Oreal ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) )
% 1.35/1.72 ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y )
% 1.35/1.72 , X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.72 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 1.35/1.72 ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X
% 1.35/1.72 ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) )
% 1.35/1.72 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X )
% 1.35/1.72 ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) )
% 1.35/1.72 ) }.
% 1.35/1.72 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.72 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.72 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 1.35/1.72 ( tc_Nat_Onat, X ) ) }.
% 1.35/1.72 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.72 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.72 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 1.35/1.72 ( tc_Nat_Onat, X ) ) }.
% 1.35/1.72 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 1.35/1.72 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.35/1.72 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_RealDef_Oreal ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.35/1.72 .
% 1.35/1.72 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, X ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }
% 1.35/1.72 .
% 1.35/1.72 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, hAPP( c_Nat_OSuc, X ) ) ) ) }.
% 1.35/1.72 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.35/1.72 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( c_Nat_OSuc, X ) ) = hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.35/1.72 c_RComplete_Onatfloor( X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.35/1.72 Y ) ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, X ) ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless(
% 1.35/1.72 tc_Nat_Onat ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone(
% 1.35/1.72 tc_RealDef_Oreal ) ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 1.35/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal
% 1.35/1.72 ( tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.72 , hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ) }
% 1.35/1.72 .
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ),
% 1.35/1.72 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.35/1.72 .
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.35/1.72 c_RComplete_Onatfloor( X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, Y ) ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.35/1.72 ( tc_Nat_Onat, Y ), c_RComplete_Onatfloor( X ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.35/1.72 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ) ), c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, hAPP( c_Nat_OSuc, skol39( X, Y ) ) ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol70( X, Y, Z ) ) ) ),
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, hAPP( c_Nat_OSuc, Z ) ) ) ), c_SEQ_OBseq( X
% 1.35/1.72 , Y ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.35/1.72 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ) ), c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, hAPP( c_Nat_OSuc, skol40( X, Y ) ) ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol71( X, Y, Z ) ) ) ),
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, hAPP( c_Nat_OSuc, Z ) ) ) ), c_SEQ_OBseq( X
% 1.35/1.72 , Y ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.35/1.72 X ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.72 tc_RealDef_Oreal, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), c_RealDef_Oreal
% 1.35/1.72 ( tc_Nat_Onat, Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.72 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ), Y ) ) }.
% 1.35/1.72 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), X )
% 1.35/1.72 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol41( X, Y, Z ) ) ) ), Z )
% 1.35/1.72 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ) ), c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, hAPP( c_Nat_OSuc, skol72( X, Y ) ) ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol79( X, Y, Z ) ) ) ),
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, hAPP( c_Nat_OSuc, Z ) ) ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol81( T, U ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol79( X, Y, Z ) ) ) ),
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, hAPP( c_Nat_OSuc, Z ) ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ) ), skol81( X, Y ) ) )
% 1.35/1.72 }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol42( X, Y, Z ) ) ) ), Z )
% 1.35/1.72 ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal )
% 1.35/1.72 , c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ) ), c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, hAPP( c_Nat_OSuc, skol73( X, Y ) ) ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol80( X, Y, Z ) ) ) ),
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, hAPP( c_Nat_OSuc, Z ) ) ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol82( T, U ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol80( X, Y, Z ) ) ) ),
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, hAPP( c_Nat_OSuc, Z ) ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ) ), skol82( X, Y ) ) )
% 1.35/1.72 }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), X ),
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 1.35/1.72 ), Y ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.35/1.72 c_RComplete_Onatfloor( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.72 tc_RealDef_Oreal ), X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = hAPP(
% 1.35/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_RComplete_Onatfloor(
% 1.35/1.72 X ) ), Y ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_RComplete_Onatfloor( Y )
% 1.35/1.72 ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), Y ),
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ),
% 1.35/1.72 c_RComplete_Onatfloor( X ) = Y }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.35/1.72 c_RComplete_Onatceiling( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.72 tc_RealDef_Oreal ), X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = hAPP(
% 1.35/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_RComplete_Onatceiling
% 1.35/1.72 ( X ) ), Y ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, skol43( X, Y ) ) ), X ) ), Y ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), Y ), hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, hAPP( c_Nat_OSuc, skol43( X, Y ) ) ) ), X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, hAPP( c_Nat_OSuc, skol44( X ) ) ) ) ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, skol45( X ) ) ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), X ),
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, hAPP( c_Nat_OSuc, skol45( X ) ) ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, Y ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 1.35/1.72 ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), hAPP
% 1.35/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), X ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), Y ), hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.35/1.72 tc_Nat_Onat, skol46( X, Y ) ) ), X ) ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol47( X, Y ) ) ) ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) = hAPP(
% 1.35/1.72 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__algebra__1( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.35/1.72 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.35/1.72 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.35/1.72 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.35/1.72 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.35/1.72 tc_Nat_Onat ) ) = Y }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), c_SEQ_OBseq(
% 1.35/1.72 tc_RealDef_Oreal, hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal )
% 1.35/1.72 , X ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, Z ) ) ), Y ) )
% 1.35/1.72 }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Z ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.35/1.72 ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), T ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), T ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.72 ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.72 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.72 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.35/1.72 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), hBOOL
% 1.35/1.72 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 1.35/1.72 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), X =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Groups_Ozero__class_Ozero
% 1.35/1.72 ( tc_Nat_Onat ) ), Y ) ) }.
% 1.35/1.72 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Groups_Ozero__class_Ozero
% 1.35/1.72 ( tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat
% 1.35/1.72 ), Y ), X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Groups_Ozero__class_Ozero
% 1.35/1.72 ( tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat
% 1.35/1.72 ), Y ), X ) ) ) }.
% 1.35/1.72 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.72 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( c_Nat_OSuc,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.72 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = hAPP( c_Nat_OSuc
% 1.35/1.72 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.72 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.35/1.72 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.35/1.72 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.72 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), hAPP( c_Nat_OSuc
% 1.35/1.72 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = hAPP( c_Nat_OSuc
% 1.35/1.72 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), X =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Groups_Ozero__class_Ozero
% 1.35/1.72 ( tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat
% 1.35/1.72 ), Y ), X ) ) ) }.
% 1.35/1.72 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Groups_Ozero__class_Ozero
% 1.35/1.72 ( tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat
% 1.35/1.72 ), Y ), X ) ) ) }.
% 1.35/1.72 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.35/1.72 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.72 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP
% 1.35/1.72 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.35/1.72 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 1.35/1.72 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.72 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.35/1.72 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.35/1.72 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.35/1.72 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z )
% 1.35/1.72 , Y ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.35/1.72 c_Polynomial_Odegree( X, Z ) ), Y ) ) ) }.
% 1.35/1.72 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 1.35/1.72 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.35/1.72 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 1.35/1.72 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 1.35/1.72 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.35/1.72 ( X ) }.
% 1.35/1.72 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.35/1.72 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.35/1.72 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.72 = c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.72 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.35/1.72 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.35/1.72 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 1.35/1.72 ) ), Y ) }.
% 1.35/1.72 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.35/1.72 tc_Nat_Onat ) ) = Y }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), T ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.72 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ), Y
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.35/1.72 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.35/1.72 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.35/1.72 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.35/1.72 .
% 1.35/1.72 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.35/1.72 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.35/1.72 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Nat_Onat ) }.
% 1.35/1.72 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.35/1.72 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.35/1.72 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.35/1.72 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.35/1.72 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.72 ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP(
% 1.35/1.72 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.72 ), ! T = Z, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) =
% 1.35/1.72 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.35/1.72 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.72 hAPP( c_Nat_OSuc, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.72 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) = hAPP(
% 1.35/1.72 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.35/1.72 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.35/1.72 , Z ), hAPP( c_Nat_OSuc, Y ) ) = hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.35/1.72 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.35/1.72 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.72 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.35/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.72 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.35/1.72 ) ), Z ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), T ) ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), Z ), Y )
% 1.35/1.72 ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, T ) ) = hAPP(
% 1.35/1.72 hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, T ) ), !
% 1.35/1.72 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , Y ) ), Z = Y }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, T ) ) ), hAPP(
% 1.35/1.72 hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, T ) ) ) )
% 1.35/1.72 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.72 ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.72 ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) ) }.
% 1.35/1.72 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.72 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.72 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.72 ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ),
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, Z ) ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X )
% 1.35/1.72 ), T ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP(
% 1.35/1.72 hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), T ), Y ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.72 ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), T ), Z ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.72 ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), T ), Z ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.72 ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), T
% 1.35/1.72 ), Z ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP(
% 1.35/1.72 hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) )
% 1.35/1.72 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), T ), Y ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.72 ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), Y ),
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.72 ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), Y ),
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, Z ) ) ),
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Z ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( X ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.72 ) ), T ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), T )
% 1.35/1.72 , c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), T ), Z ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.72 , T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Groups_Ozero__class_Ozero
% 1.35/1.72 ( tc_Nat_Onat ) ), Z ) ), T = Y }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.35/1.72 ), T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ),
% 1.35/1.72 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), T ), Z ) ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.72 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ) }.
% 1.35/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.72 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.35/1.72 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol48( X, Y ) ), Y
% 1.35/1.72 ) ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.35/1.72 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.35/1.72 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 1.35/1.72 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.35/1.72 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 1.35/1.72 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 1.35/1.72 X, Z ), Y ) ) }.
% 1.35/1.72 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.35/1.72 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 1.35/1.72 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 1.35/1.72 }.
% 1.35/1.72 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol49( X, Y ) ) }.
% 1.35/1.72 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 1.35/1.72 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.72 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 1.35/1.72 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 1.35/1.72 { ! Z = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ) ), X ), alpha53
% 1.35/1.72 ( X, Y ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint
% 1.35/1.72 ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), Y =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.35/1.72 tc_Int_Oint, Z, Y ) = X }.
% 1.35/1.72 { ! Z = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP
% 1.35/1.72 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ) ), X ), alpha53
% 1.35/1.72 ( X, Y ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint
% 1.35/1.72 ), Y ), X ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.72 tc_Int_Oint, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), Y =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.35/1.72 tc_Int_Oint, Z, Y ) = X }.
% 1.35/1.72 { ! alpha53( X, Y ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless(
% 1.35/1.72 tc_Int_Oint ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.35/1.72 { ! alpha53( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.72 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL
% 1.35/1.72 ( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ), Y ) ) }
% 1.35/1.72 .
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha53( X, Y ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ), Y ) ), alpha53( X, Y )
% 1.35/1.72 }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Z ), Y ) ), ! hBOOL( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ) ), Y ) ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Z ), Y ) ), ! hBOOL( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ) ), Y ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ), Z ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ) ), Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ), Z ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ) ), Y ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 1.35/1.72 alpha10( X, Y, Z ) }.
% 1.35/1.72 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 1.35/1.72 alpha24( X, Y, Z ) }.
% 1.35/1.72 { ! alpha10( X, Y, Z ), ! alpha24( X, Y, Z ), hBOOL( hAPP( Z,
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.35/1.72 { ! alpha24( X, Y, Z ), alpha33( X, Y, Z ) }.
% 1.35/1.72 { ! alpha24( X, Y, Z ), alpha37( X, Y, Z ) }.
% 1.35/1.72 { ! alpha33( X, Y, Z ), ! alpha37( X, Y, Z ), alpha24( X, Y, Z ) }.
% 1.35/1.72 { ! alpha37( X, Y, Z ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless
% 1.35/1.72 ( tc_Int_Oint ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ),
% 1.35/1.72 alpha41( X, Y, Z ) }.
% 1.35/1.72 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha37( X, Y, Z ) }.
% 1.35/1.72 { ! alpha41( X, Y, Z ), alpha37( X, Y, Z ) }.
% 1.35/1.72 { ! alpha41( X, Y, Z ), ! alpha45( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( Z, skol50( T, U, Z ) ) ), alpha41( X, Y, Z ) }.
% 1.35/1.72 { alpha45( X, Y, skol50( X, Y, Z ) ), alpha41( X, Y, Z ) }.
% 1.35/1.72 { ! alpha45( X, Y, Z ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless(
% 1.35/1.72 tc_Int_Oint ), X ), Z ) ) }.
% 1.35/1.72 { ! alpha45( X, Y, Z ), alpha49( X, Y, Z ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ), Z
% 1.35/1.72 ) ), ! alpha49( X, Y, Z ), alpha45( X, Y, Z ) }.
% 1.35/1.72 { ! alpha49( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.72 tc_Int_Oint, Z ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.35/1.72 { ! alpha49( X, Y, Z ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.72 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.35/1.72 X ), skol51( X, Y, Z ) ) ), Z ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! Y = hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ) ), Z ), alpha49( X
% 1.35/1.72 , Y, Z ) }.
% 1.35/1.72 { ! alpha33( X, Y, Z ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless
% 1.35/1.72 ( tc_Int_Oint ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ),
% 1.35/1.72 alpha38( X, Y, Z ) }.
% 1.35/1.72 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha33( X, Y, Z ) }
% 1.35/1.72 .
% 1.35/1.72 { ! alpha38( X, Y, Z ), alpha33( X, Y, Z ) }.
% 1.35/1.72 { ! alpha38( X, Y, Z ), ! alpha42( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( Z, skol52( T, U, Z ) ) ), alpha38( X, Y, Z ) }.
% 1.35/1.72 { alpha42( X, Y, skol52( X, Y, Z ) ), alpha38( X, Y, Z ) }.
% 1.35/1.72 { ! alpha42( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.72 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ) }.
% 1.35/1.72 { ! alpha42( X, Y, Z ), alpha46( X, Y, Z ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), ! alpha46( X, Y, Z )
% 1.35/1.72 , alpha42( X, Y, Z ) }.
% 1.35/1.72 { ! alpha46( X, Y, Z ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless(
% 1.35/1.72 tc_Int_Oint ), Z ), X ) ) }.
% 1.35/1.72 { ! alpha46( X, Y, Z ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.72 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.35/1.72 X ), skol53( X, Y, Z ) ) ), Z ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Z ), X
% 1.35/1.72 ) ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP
% 1.35/1.72 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ) ), Z ),
% 1.35/1.72 alpha46( X, Y, Z ) }.
% 1.35/1.72 { ! alpha10( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.35/1.72 hBOOL( hAPP( Z, Y ) ) }.
% 1.35/1.72 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha10( X, Y, Z ) }.
% 1.35/1.72 { ! hBOOL( hAPP( Z, Y ) ), alpha10( X, Y, Z ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ), X
% 1.35/1.72 ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 1.35/1.72 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 1.35/1.72 c_Polynomial_Omonom( X, Y, Z ) }.
% 1.35/1.72 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.35/1.72 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.35/1.72 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.35/1.72 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.35/1.72 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.35/1.72 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.35/1.72 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP
% 1.35/1.72 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.35/1.72 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ) ), T ) = hAPP(
% 1.35/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), ! hBOOL(
% 1.35/1.72 hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint ), T ), W ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z ), W ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), U ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ) ), Z ) ), hAPP(
% 1.35/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ) ), X ) ) ), !
% 1.35/1.72 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint ), U ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), U ), Z ) ), hBOOL(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), T ) ) }.
% 1.35/1.72 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ) ), T ) = hAPP(
% 1.35/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), ! hBOOL(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ) ), !
% 1.35/1.72 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ), Z )
% 1.35/1.72 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z ), W ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U ), Y ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ) ), Z ) ), hAPP(
% 1.35/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ) ), X ) ) ), !
% 1.35/1.72 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Z ), U ) ), ! hBOOL( hAPP
% 1.35/1.72 ( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ), U ) ), hBOOL(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ), Y ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), hAPP(
% 1.35/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ) ), !
% 1.35/1.72 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ), Z )
% 1.35/1.72 ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ), X = c_Groups_Oone__class_Oone(
% 1.35/1.72 tc_Int_Oint ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y = c_Groups_Oone__class_Oone(
% 1.35/1.72 tc_Int_Oint ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X =
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y = c_Groups_Oone__class_Oone
% 1.35/1.72 ( tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.35/1.72 , X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.35/1.72 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.35/1.72 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X = hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Z ), X ) ), hBOOL(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), Y ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X = hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.72 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.72 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.35/1.72 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.35/1.72 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.72 }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.35/1.72 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.35/1.72 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Z, Y ) )
% 1.35/1.72 ), Y ) ) }.
% 1.35/1.72 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 1.35/1.72 c_Polynomial_Omonom( X, T, Z ) ), c_Polynomial_Omonom( X, Y, Z ) ) =
% 1.35/1.72 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T )
% 1.35/1.72 , Y ), Z ) }.
% 1.35/1.72 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.35/1.72 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), hAPP( c_Nat_OSuc, X )
% 1.35/1.72 ) = hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y
% 1.35/1.72 ), X ) ) }.
% 1.35/1.72 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, Y ) =
% 1.35/1.72 c_Polynomial_OAbs__poly( X, c_COMBC( tc_Nat_Onat, X, X, c_COMBC(
% 1.35/1.72 tc_Nat_Onat, X, tc_fun( X, X ), hAPP( c_COMBB( tc_HOL_Obool, tc_fun( X,
% 1.35/1.72 tc_fun( X, X ) ), tc_Nat_Onat, c_If( X ) ), hAPP( c_fequal, Y ) ), Z ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.35/1.72 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.35/1.72 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.35/1.72 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.35/1.72 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 1.35/1.72 ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), Y )
% 1.35/1.72 ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), c_SEQ_Omonoseq(
% 1.35/1.72 tc_RealDef_Oreal, hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal )
% 1.35/1.72 , X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol54( Z, T ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol54( X, Y ) ), X ) =
% 1.35/1.72 Y }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.72 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hAPP( hAPP(
% 1.35/1.72 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 1.35/1.72 skol54( X, Y ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), hAPP(
% 1.35/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.35/1.72 tc_Int_Oint ) ), X ) ), X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 1.35/1.72 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X
% 1.35/1.72 ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.35/1.72 tc_Int_Oint ) ), X ) ), X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 1.35/1.72 ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint ), c_Groups_Ozero__class_Ozero
% 1.35/1.72 ( tc_Int_Oint ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint )
% 1.35/1.72 , c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ), X
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 1.35/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ), X
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 1.35/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ),
% 1.35/1.72 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ), X ) ), Y = X }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ), X
% 1.35/1.72 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y
% 1.35/1.72 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 1.35/1.72 { ! Y = X, hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint )
% 1.35/1.72 , Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ),
% 1.35/1.72 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.35/1.72 , hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ),
% 1.35/1.72 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint ), c_Groups_Ozero__class_Ozero
% 1.35/1.72 ( tc_Int_Oint ) ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.35/1.72 ( tc_Int_Oint ) ), X ) ) }.
% 1.35/1.72 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oone__class_Oone(
% 1.35/1.72 tc_Int_Oint ) ) ) }.
% 1.35/1.72 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.35/1.72 ( tc_Int_Oint ) }.
% 1.35/1.72 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.35/1.72 tc_Int_Oint ) ), X ) ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 1.35/1.72 }.
% 1.35/1.72 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) = hAPP(
% 1.35/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) }.
% 1.35/1.72 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), X ) ) }.
% 1.35/1.72 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.35/1.72 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) }.
% 1.35/1.72 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) = X }.
% 1.35/1.72 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) = X }.
% 1.35/1.72 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ), X )
% 1.35/1.72 ), Y = X, hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint
% 1.35/1.72 ), X ), Y ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ), X
% 1.35/1.72 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X
% 1.35/1.72 ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ), X
% 1.35/1.72 ) ), ! Y = X }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.35/1.72 , Y = X, hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint )
% 1.35/1.72 , Y ), X ) ) }.
% 1.35/1.72 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), X ) ) }
% 1.35/1.72 .
% 1.35/1.72 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ),
% 1.35/1.72 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ) }
% 1.35/1.72 .
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.35/1.72 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Z )
% 1.35/1.72 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), Z )
% 1.35/1.72 ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.35/1.72 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y )
% 1.35/1.72 ), Y = X }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.35/1.72 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 1.35/1.72 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ), X
% 1.35/1.72 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), Z ) ), hAPP
% 1.35/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Z ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ), X
% 1.35/1.72 ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T )
% 1.35/1.72 , Z ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint )
% 1.35/1.72 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), T ) ),
% 1.35/1.72 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Z ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ),
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = hAPP( hAPP(
% 1.35/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Omod
% 1.35/1.72 ( tc_Int_Oint, Y, X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Omod
% 1.35/1.72 ( tc_Int_Oint, Y, X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint ), c_Divides_Odiv__class_Omod
% 1.35/1.72 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.72 ( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ), Y ) ),
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ),
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ), X ) ),
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Omod
% 1.35/1.72 ( tc_Int_Oint, X, Y ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) ), X ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ),
% 1.35/1.72 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.35/1.72 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint ), c_Divides_Odiv__class_Omod
% 1.35/1.72 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.35/1.72 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 1.35/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.72 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.35/1.72 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.72 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), c_SEQ_Omonoseq( X
% 1.35/1.72 , Y ) }.
% 1.35/1.72 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), c_SEQ_Omonoseq( X
% 1.35/1.72 , Y ) }.
% 1.35/1.72 { ! class_Orderings_Oorder( X ), ! c_SEQ_Omonoseq( X, Y ), hBOOL( hAPP(
% 1.35/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ) ), hAPP( Y, hAPP(
% 1.35/1.72 c_Nat_OSuc, Z ) ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X
% 1.35/1.73 , hAPP( Y, hAPP( c_Nat_OSuc, T ) ) ), hAPP( Y, T ) ) ) }.
% 1.35/1.73 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol55( X, Y ) ) ), hAPP(
% 1.35/1.73 Y, hAPP( c_Nat_OSuc, skol55( X, Y ) ) ) ) ), c_SEQ_Omonoseq( X, Y ) }.
% 1.35/1.73 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, hAPP( c_Nat_OSuc, skol74(
% 1.35/1.73 X, Y ) ) ) ), hAPP( Y, skol74( X, Y ) ) ) ), c_SEQ_Omonoseq( X, Y ) }.
% 1.35/1.73 { ! class_Orderings_Oorder( X ), ! c_SEQ_Omonoseq( X, Y ), alpha11( X, Y )
% 1.35/1.73 , alpha25( X, Y ) }.
% 1.35/1.73 { ! class_Orderings_Oorder( X ), ! alpha11( X, Y ), c_SEQ_Omonoseq( X, Y )
% 1.35/1.73 }.
% 1.35/1.73 { ! class_Orderings_Oorder( X ), ! alpha25( X, Y ), c_SEQ_Omonoseq( X, Y )
% 1.35/1.73 }.
% 1.35/1.73 { ! alpha25( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.73 tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.73 X, hAPP( Y, T ) ), hAPP( Y, Z ) ) ) }.
% 1.35/1.73 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol56( X, Y
% 1.35/1.73 ) ), skol75( X, Y ) ) ), alpha25( X, Y ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol75( X,
% 1.35/1.73 Y ) ) ), hAPP( Y, skol56( X, Y ) ) ) ), alpha25( X, Y ) }.
% 1.35/1.73 { ! alpha11( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.73 tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.73 X, hAPP( Y, Z ) ), hAPP( Y, T ) ) ) }.
% 1.35/1.73 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol57( X, Y
% 1.35/1.73 ) ), skol76( X, Y ) ) ), alpha11( X, Y ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol57( X,
% 1.35/1.73 Y ) ) ), hAPP( Y, skol76( X, Y ) ) ) ), alpha11( X, Y ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.35/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 1.35/1.73 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Ozero__class_Ozero
% 1.35/1.73 ( tc_Int_Oint ) ) ) }.
% 1.35/1.73 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oone__class_Oone(
% 1.35/1.73 tc_Int_Oint ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.73 ( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol58( Z, T ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.73 ( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hAPP( hAPP(
% 1.35/1.73 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol58( X, Y ) ), X ) =
% 1.35/1.73 Y }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.35/1.73 c_Transcendental_Oln( hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.35/1.73 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.35/1.73 tc_Nat_Onat, Y ) ), c_Transcendental_Oln( X ) ) }.
% 1.35/1.73 { c_Transcendental_Oln( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Transcendental_Oln( X ) ), c_Transcendental_Oln( Y ) ) ), hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), X ), Y ) ),
% 1.35/1.73 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Transcendental_Oln( X ) ), c_Transcendental_Oln( Y ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), !
% 1.35/1.73 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ), X = Y }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! X = Y,
% 1.35/1.73 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Transcendental_Oln( X ) ), X ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 1.35/1.73 ( X ) ), c_Transcendental_Oln( Y ) ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), Y ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), Y ) ), hBOOL(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.73 c_Transcendental_Oln( X ) ), c_Transcendental_Oln( Y ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.73 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.35/1.73 X ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP( hAPP
% 1.35/1.73 ( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.35/1.73 X ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.35/1.73 X ) ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless(
% 1.35/1.73 tc_RealDef_Oreal ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X )
% 1.35/1.73 ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP( hAPP
% 1.35/1.73 ( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.35/1.73 X ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), !
% 1.35/1.73 c_Transcendental_Oln( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 1.35/1.73 ), X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! X =
% 1.35/1.73 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oln( X )
% 1.35/1.73 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Transcendental_Oln( X ) ), c_Groups_Ozero__class_Ozero(
% 1.35/1.73 tc_RealDef_Oreal ) ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless
% 1.35/1.73 ( tc_RealDef_Oreal ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 1.35/1.73 ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), X ),
% 1.35/1.73 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), c_Transcendental_Oln(
% 1.35/1.73 X ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), X ),
% 1.35/1.73 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ), c_Transcendental_Oln(
% 1.35/1.73 X ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.35/1.73 X ) ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless(
% 1.35/1.73 tc_RealDef_Oreal ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X
% 1.35/1.73 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 1.35/1.73 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.35/1.73 X ) ) ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless(
% 1.35/1.73 tc_RealDef_Oreal ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X
% 1.35/1.73 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.73 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.35/1.73 X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 1.35/1.73 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.73 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.35/1.73 X ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ),
% 1.35/1.73 c_Transcendental_Oln( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.73 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.73 ( tc_RealDef_Oreal ), c_Transcendental_Oln( X ) ), c_Transcendental_Oln(
% 1.35/1.73 Y ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 1.35/1.73 ( hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) ), X ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP( hAPP( Z,
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.35/1.73 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha12( X, Y, T,
% 1.35/1.73 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha12( X, Y, skol59( X
% 1.35/1.73 , Y, Z ), skol77( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.35/1.73 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP( hAPP( Z,
% 1.35/1.73 skol59( X, Y, Z ) ), skol77( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.35/1.73 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.35/1.73 { ! alpha12( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless
% 1.35/1.73 ( tc_Int_Oint ), X ), T ) ) }.
% 1.35/1.73 { ! alpha12( X, Y, Z, T ), alpha26( X, Y, Z, T ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ), T
% 1.35/1.73 ) ), ! alpha26( X, Y, Z, T ), alpha12( X, Y, Z, T ) }.
% 1.35/1.73 { ! alpha26( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.73 tc_Int_Oint, T ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.35/1.73 { ! alpha26( X, Y, Z, T ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.73 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.35/1.73 X ), Z ) ), T ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! Y = hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), T ), alpha26( X
% 1.35/1.73 , Y, Z, T ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.73 ( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.35/1.73 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha13( X, Y, T,
% 1.35/1.73 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha13( X, Y,
% 1.35/1.73 skol60( X, Y, Z ), skol78( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.35/1.73 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.73 ( Z, skol60( X, Y, Z ) ), skol78( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.35/1.73 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.35/1.73 { ! alpha13( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.73 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ) }.
% 1.35/1.73 { ! alpha13( X, Y, Z, T ), alpha27( X, Y, Z, T ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! alpha27( X, Y, Z,
% 1.35/1.73 T ), alpha13( X, Y, Z, T ) }.
% 1.35/1.73 { ! alpha27( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless
% 1.35/1.73 ( tc_Int_Oint ), T ), X ) ) }.
% 1.35/1.73 { ! alpha27( X, Y, Z, T ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.73 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.35/1.73 X ), Z ) ), T ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), T ), X
% 1.35/1.73 ) ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP
% 1.35/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), T ),
% 1.35/1.73 alpha27( X, Y, Z, T ) }.
% 1.35/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.35/1.73 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.35/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.35/1.73 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.35/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 1.35/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 1.35/1.73 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 1.35/1.73 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.73 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.35/1.73 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 1.35/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.73 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 1.35/1.73 }.
% 1.35/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 1.35/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.35/1.73 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.35/1.73 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.35/1.73 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.35/1.73 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 1.35/1.73 ( X ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.35/1.73 ( tc_Int_Oint, X, Y ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint ), c_Groups_Ozero__class_Ozero
% 1.35/1.73 ( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 1.35/1.73 ( tc_Int_Oint, X, Y ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }
% 1.35/1.73 .
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 1.35/1.73 ( tc_Int_Oint, Y, X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ),
% 1.35/1.73 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint ), c_Groups_Ozero__class_Ozero
% 1.35/1.73 ( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 1.35/1.73 ( tc_Int_Oint, Y, X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }
% 1.35/1.73 .
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.73 ( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.73 ( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 1.35/1.73 ( tc_Int_Oint, Y, X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }
% 1.35/1.73 .
% 1.35/1.73 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.35/1.73 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.73 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.73 }.
% 1.35/1.73 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.73 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 1.35/1.73 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.73 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 1.35/1.73 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.73 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 1.35/1.73 tc_Int_Oint ) ) = X }.
% 1.35/1.73 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ), X ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.35/1.73 tc_Int_Oint, Z, X ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) )
% 1.35/1.73 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.35/1.73 tc_Int_Oint, Z, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 1.35/1.73 , X ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.35/1.73 , ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Z )
% 1.35/1.73 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.35/1.73 , ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ), X ) ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint ), c_Groups_Ozero__class_Ozero
% 1.35/1.73 ( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), Z ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint ), c_Groups_Ozero__class_Ozero
% 1.35/1.73 ( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.35/1.73 ( tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.35/1.73 ( tc_Int_Oint, Y, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.35/1.73 ( tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.35/1.73 ( tc_Int_Oint, Y, X ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.73 ( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ), Y ) ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.73 ( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.73 ( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), Z ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.73 ( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.35/1.73 ( tc_Int_Oint, X, Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.35/1.73 ( tc_Int_Oint, Y ), X ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.73 ( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.35/1.73 ( tc_Int_Oint, X, Y ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint ), c_Groups_Ozero__class_Ozero
% 1.35/1.73 ( tc_Int_Oint ) ), Y ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ), ! hBOOL( hAPP
% 1.35/1.73 ( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint ), c_Groups_Ozero__class_Ozero
% 1.35/1.73 ( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) ) }
% 1.35/1.73 .
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.73 ( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.35/1.73 ( tc_Int_Oint, Y, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.35/1.73 ( tc_Int_Oint, X ), Y ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ), hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.35/1.73 ( tc_Int_Oint, Y, X ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.35/1.73 ( tc_Int_Oint, Y, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.35/1.73 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.35/1.73 ( tc_Int_Oint, Y, X ) ) ) }.
% 1.35/1.73 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha14( X, Y ) }.
% 1.35/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.73 { ! alpha14( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.73 { ! alpha14( X, Y ), alpha28( X, Y ), alpha34( X, Y ) }.
% 1.35/1.73 { ! alpha28( X, Y ), alpha14( X, Y ) }.
% 1.35/1.73 { ! alpha34( X, Y ), alpha14( X, Y ) }.
% 1.35/1.73 { ! alpha34( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.73 tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.35/1.73 { ! alpha34( X, Y ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless(
% 1.35/1.73 tc_Int_Oint ), X ), Y ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ), Y ) ), alpha34( X, Y )
% 1.35/1.73 }.
% 1.35/1.73 { ! alpha28( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.73 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.35/1.73 { ! alpha28( X, Y ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless(
% 1.35/1.73 tc_Int_Oint ), Y ), X ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.73 ( c_Orderings_Oord__class_Oless( tc_Int_Oint ), Y ), X ) ), alpha28( X, Y
% 1.35/1.73 ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.73 ( c_Orderings_Oord__class_Oless( tc_Int_Oint ), c_Groups_Oone__class_Oone
% 1.35/1.73 ( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 1.35/1.73 ( tc_Int_Oint, X, Y ) ), X ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.35/1.73 tc_Int_Oint, Z, Y ), X ) }.
% 1.35/1.73 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 1.35/1.73 ( tc_Int_Oint, Z, Y ) ), Y ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 1.35/1.73 Z, Y ) ) ), X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint )
% 1.35/1.73 , Z ), X ) }.
% 1.35/1.73 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) ),
% 1.35/1.73 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ) ), X ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) }.
% 1.35/1.73 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) = hAPP( hAPP
% 1.35/1.73 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.35/1.73 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.35/1.73 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.35/1.73 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 1.35/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.73 ( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y
% 1.35/1.73 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( X, T, Y ) ) }.
% 1.35/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.73 ( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y
% 1.35/1.73 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( X, T, Y ) ) }.
% 1.35/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.73 ( X ), Z ), Y ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), c_Groups_Oone__class_Oone( X ) )
% 1.35/1.73 }.
% 1.35/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.73 ( X ), Y ), Z ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), c_Groups_Oone__class_Oone( X ) )
% 1.35/1.73 }.
% 1.35/1.73 { ! class_Divides_Osemiring__div( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), c_Divides_Odiv__class_Omod( X, Z, Y ) )
% 1.35/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), Y ) ) = Z }.
% 1.35/1.73 { ! class_Divides_Osemiring__div( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), c_Divides_Odiv__class_Odiv( X, Y
% 1.35/1.73 , Z ) ) ), c_Divides_Odiv__class_Omod( X, Y, Z ) ) = Y }.
% 1.35/1.73 { ! class_Divides_Osemiring__div( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 1.35/1.73 ), Y ) ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 1.35/1.73 { ! class_Divides_Osemiring__div( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.73 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( X, Z, T ) ) ), c_Divides_Odiv__class_Omod( X
% 1.35/1.73 , Z, T ) ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y
% 1.35/1.73 ) }.
% 1.35/1.73 { ! class_Divides_Osemiring__div( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.73 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ) ),
% 1.35/1.73 c_Divides_Odiv__class_Omod( X, T, Z ) ) ), Y ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), T ), Y ) }.
% 1.35/1.73 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.35/1.73 alpha15( X, Z ) }.
% 1.35/1.73 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.35/1.73 alpha29( X, Y, Z ) }.
% 1.35/1.73 { ! alpha15( X, Z ), ! alpha29( X, Y, Z ), hBOOL( hAPP( Z,
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 1.35/1.73 { ! alpha29( X, Y, Z ), alpha35( X, Y, Z ) }.
% 1.35/1.73 { ! alpha29( X, Y, Z ), alpha39( X, Y, Z ) }.
% 1.35/1.73 { ! alpha35( X, Y, Z ), ! alpha39( X, Y, Z ), alpha29( X, Y, Z ) }.
% 1.35/1.73 { ! alpha39( X, Y, Z ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless
% 1.35/1.73 ( tc_Int_Oint ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ),
% 1.35/1.73 alpha43( X, Y, Z ) }.
% 1.35/1.73 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha39( X, Y, Z ) }.
% 1.35/1.73 { ! alpha43( X, Y, Z ), alpha39( X, Y, Z ) }.
% 1.35/1.73 { ! alpha43( X, Y, Z ), ! alpha47( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( Z, skol61( T, U, Z ) ) ), alpha43( X, Y, Z ) }.
% 1.35/1.73 { alpha47( X, Y, skol61( X, Y, Z ) ), alpha43( X, Y, Z ) }.
% 1.35/1.73 { ! alpha47( X, Y, Z ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless(
% 1.35/1.73 tc_Int_Oint ), X ), skol62( X, T, U ) ) ) }.
% 1.35/1.73 { ! alpha47( X, Y, Z ), alpha50( X, Y, Z, skol62( X, Y, Z ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ), T
% 1.35/1.73 ) ), ! alpha50( X, Y, Z, T ), alpha47( X, Y, Z ) }.
% 1.35/1.73 { ! alpha50( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.73 tc_Int_Oint, T ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.35/1.73 { ! alpha50( X, Y, Z, T ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.73 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.35/1.73 X ), Z ) ), T ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! Y = hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), T ), alpha50( X
% 1.35/1.73 , Y, Z, T ) }.
% 1.35/1.73 { ! alpha35( X, Y, Z ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless
% 1.35/1.73 ( tc_Int_Oint ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ),
% 1.35/1.73 alpha40( X, Y, Z ) }.
% 1.35/1.73 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha35( X, Y, Z ) }
% 1.35/1.73 .
% 1.35/1.73 { ! alpha40( X, Y, Z ), alpha35( X, Y, Z ) }.
% 1.35/1.73 { ! alpha40( X, Y, Z ), ! alpha44( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( Z, skol63( T, U, Z ) ) ), alpha40( X, Y, Z ) }.
% 1.35/1.73 { alpha44( X, Y, skol63( X, Y, Z ) ), alpha40( X, Y, Z ) }.
% 1.35/1.73 { ! alpha44( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.73 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol64( T, U,
% 1.35/1.73 W ) ) ) }.
% 1.35/1.73 { ! alpha44( X, Y, Z ), alpha48( X, Y, Z, skol64( X, Y, Z ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! alpha48( X, Y, Z,
% 1.35/1.73 T ), alpha44( X, Y, Z ) }.
% 1.35/1.73 { ! alpha48( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless
% 1.35/1.73 ( tc_Int_Oint ), T ), X ) ) }.
% 1.35/1.73 { ! alpha48( X, Y, Z, T ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.73 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.35/1.73 X ), Z ) ), T ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), T ), X
% 1.35/1.73 ) ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP
% 1.35/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), T ),
% 1.35/1.73 alpha48( X, Y, Z, T ) }.
% 1.35/1.73 { ! alpha15( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.35/1.73 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.35/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha15( X, Y ) }.
% 1.35/1.73 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha15
% 1.35/1.73 ( X, Y ) }.
% 1.35/1.73 { ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP
% 1.35/1.73 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), alpha54
% 1.35/1.73 ( X, Z ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint
% 1.35/1.73 ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), Z =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.35/1.73 tc_Int_Oint, T, Z ) = Y }.
% 1.35/1.73 { ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP
% 1.35/1.73 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), alpha54
% 1.35/1.73 ( X, Z ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint
% 1.35/1.73 ), Z ), X ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.73 tc_Int_Oint, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), Z =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.35/1.73 tc_Int_Oint, T, Z ) = Y }.
% 1.35/1.73 { ! alpha54( X, Y ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless(
% 1.35/1.73 tc_Int_Oint ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.35/1.73 { ! alpha54( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.35/1.73 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL
% 1.35/1.73 ( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ), Y ) ) }
% 1.35/1.73 .
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha54( X, Y ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint ), X ), Y ) ), alpha54( X, Y )
% 1.35/1.73 }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ),
% 1.35/1.73 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.35/1.73 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.35/1.73 tc_Int_Oint, Z, Y ), X ) ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z
% 1.35/1.73 , Y ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.73 ( c_Orderings_Oord__class_Oless( tc_Int_Oint ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 1.35/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol65( Z, T ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hAPP( hAPP(
% 1.35/1.73 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol65( X, Y ) ), hAPP
% 1.35/1.73 ( c_Nat_OSuc, Y ) ) = X }.
% 1.35/1.73 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Divides_Odiv__class_Odiv
% 1.35/1.73 ( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 1.35/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Y ) ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ),
% 1.35/1.73 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) ) }.
% 1.35/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), X ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ),
% 1.35/1.73 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 1.35/1.73 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.73 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.35/1.73 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, hAPP( c_Nat_OSuc,
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.73 ) ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = hAPP( c_Nat_OSuc,
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ), X ) ) }.
% 1.35/1.73 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), Y ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.73 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ) ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.73 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X ) ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X ) ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = hAPP( c_Nat_OSuc,
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ), X ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X ) ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = hAPP( c_Nat_OSuc,
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ), X ) ) }.
% 1.35/1.73 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), X ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_Divides_Odiv__class_Odiv(
% 1.35/1.73 tc_Nat_Onat, Z, X ) ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) )
% 1.35/1.73 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_Divides_Odiv__class_Omod(
% 1.35/1.73 tc_Nat_Onat, Z, X ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) )
% 1.35/1.73 , X ) ) }.
% 1.35/1.73 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Z, Y,
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ),
% 1.35/1.73 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.35/1.73 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.35/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 1.35/1.73 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Odiv(
% 1.35/1.73 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.35/1.73 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.35/1.73 , c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 1.35/1.73 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.35/1.73 tc_Nat_Onat, Z, Y ), X ) }.
% 1.35/1.73 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.35/1.73 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 1.35/1.73 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.35/1.73 ( X ), T, Z ), Y ) }.
% 1.35/1.73 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) ), Y ) ) }.
% 1.35/1.73 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) ), Y ) ),
% 1.35/1.73 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 1.35/1.73 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) ) ) }.
% 1.35/1.73 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) ) ), hBOOL(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 1.35/1.73 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) ), Y ) ) }.
% 1.35/1.73 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) ), Y ) ),
% 1.35/1.73 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 1.35/1.73 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( X ), T ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) ) ) }.
% 1.35/1.73 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( X ), T ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) ) ), hBOOL(
% 1.35/1.73 hAPP( hAPP( c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) ) }.
% 1.35/1.73 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( X
% 1.35/1.73 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.35/1.73 c_Groups_Oone__class_Oone( X ) ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 1.35/1.73 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), Y ),
% 1.35/1.73 c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 1.35/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Groups_Ozero__class_Ozero
% 1.35/1.73 ( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), c_Divides_Odiv__class_Odiv
% 1.35/1.73 ( tc_Nat_Onat, Y, X ) ), Y ) ) }.
% 1.35/1.73 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.73 , Z = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.35/1.73 Y ) ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.35/1.73 Y ) ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) ),
% 1.35/1.73 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.35/1.73 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ),
% 1.35/1.73 c_Polynomial_Omonom( X, T, Z ) ), c_Polynomial_Omonom( X, Y, Z ) ) =
% 1.35/1.73 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), T
% 1.35/1.73 ), Y ), Z ) }.
% 1.35/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP
% 1.35/1.73 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.35/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.35/1.73 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.73 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.35/1.73 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) =
% 1.35/1.73 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), Y ), Z ) ) }.
% 1.35/1.73 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP(
% 1.35/1.73 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) }.
% 1.35/1.73 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), Y
% 1.35/1.73 ) ), hAPP( c_Nat_OSuc, X ) ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.35/1.73 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat )
% 1.35/1.73 , Z ), Y ) ), X ) }.
% 1.35/1.73 { ! class_Groups_Oab__group__add( X ), ! hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), ! U = T, Z = Y }.
% 1.35/1.73 { ! class_Groups_Oab__group__add( X ), ! hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), ! Z = Y, U = T }.
% 1.35/1.73 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.35/1.73 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), X ) ), Y ) }.
% 1.35/1.73 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP(
% 1.35/1.73 hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), T ), Z )
% 1.35/1.73 ), Y ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP(
% 1.35/1.73 c_Polynomial_Ocoeff( X, T ), Y ) ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 1.35/1.73 ) ) }.
% 1.35/1.73 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), T ), Z ), Y ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ),
% 1.35/1.73 c_Polynomial_Osmult( X, T, Y ) ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.35/1.73 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X, hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), T ), Z ) ), Y
% 1.35/1.73 ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP(
% 1.35/1.73 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.35/1.73 ) }.
% 1.35/1.73 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), Z ), Y ) =
% 1.35/1.73 c_Polynomial_OAbs__poly( X, hAPP( hAPP( c_COMBS( tc_Nat_Onat, X, X ),
% 1.35/1.73 hAPP( c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat,
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ) ), c_Polynomial_Ocoeff( X, Z ) ) ),
% 1.35/1.73 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 1.35/1.73 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X )
% 1.35/1.73 ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.35/1.73 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.73 ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 1.35/1.73 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X )
% 1.35/1.73 ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.35/1.73 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.73 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) =
% 1.35/1.73 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ), Y ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.73 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ), Y ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), X ), Y ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), X ), Y
% 1.35/1.73 ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.35/1.73 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.73 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ), hAPP(
% 1.35/1.73 c_Nat_OSuc, Y ) ) ) }.
% 1.35/1.73 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.35/1.73 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.73 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.73 { ! hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.73 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.73 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP(
% 1.35/1.73 c_Nat_OSuc, X ) ), Y ) = hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Z ),
% 1.35/1.73 hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ),
% 1.35/1.73 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.73 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), hAPP(
% 1.35/1.73 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) ),
% 1.35/1.73 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Z ),
% 1.35/1.73 hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ) }
% 1.35/1.73 .
% 1.35/1.73 { hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X )
% 1.35/1.73 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), hAPP(
% 1.35/1.73 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) = Y }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.73 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.35/1.73 ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ),
% 1.35/1.73 hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ),
% 1.35/1.73 hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) ),
% 1.35/1.73 hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), X ), Z )
% 1.35/1.73 ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.73 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.35/1.73 ), ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), X
% 1.35/1.73 ), Z ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.35/1.73 ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) )
% 1.35/1.73 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) )
% 1.35/1.73 }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat ), Y ), X
% 1.35/1.73 ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z )
% 1.35/1.73 , Y ) ), hBOOL( hAPP( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat )
% 1.35/1.73 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), Z ) ),
% 1.35/1.73 hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Z ) ) ) }
% 1.35/1.73 .
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.73 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ), Y ) = hAPP( hAPP
% 1.35/1.73 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), Z ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.73 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), Z ) = hAPP(
% 1.35/1.73 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ), Y ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.73 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) = hAPP( hAPP
% 1.35/1.73 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.73 , ! hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) =
% 1.35/1.73 Z, X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) }
% 1.35/1.73 .
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.73 , ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 1.35/1.73 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) = Z
% 1.35/1.73 }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.73 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), Y ) = X }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.73 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 1.35/1.73 hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) ),
% 1.35/1.73 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.73 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.35/1.73 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ),
% 1.35/1.73 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), hAPP(
% 1.35/1.73 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.73 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP
% 1.35/1.73 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) = hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.73 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.35/1.73 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) = X }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.73 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), hAPP
% 1.35/1.73 ( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ), Y ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.73 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL
% 1.35/1.73 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), hAPP
% 1.35/1.73 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ), hBOOL(
% 1.35/1.73 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.35/1.73 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), hAPP(
% 1.35/1.73 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) = hAPP(
% 1.35/1.73 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) }.
% 1.35/1.73 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.73 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.35/1.73 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.73 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( X ), hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.73 c_Orderings_Oord__class_Oless( X ), Z ), Y ) ) }.
% 1.35/1.73 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP(
% 1.35/1.73 hAPP( c_Groups_Ominus__class_Ominus( X ), T ), Z ), Y ) =
% 1.35/1.73 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.35/1.73 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.35/1.73 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP(
% 1.35/1.73 hAPP( c_Groups_Ominus__class_Ominus( X ), T ), Z ), Y ) =
% 1.35/1.73 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.35/1.73 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 1.35/1.73 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP(
% 1.35/1.73 hAPP( c_Groups_Ominus__class_Ominus( X ), T ), Z ), Y ) =
% 1.35/1.73 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.35/1.73 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 1.35/1.73 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.35/1.73 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 1.35/1.73 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 1.35/1.73 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.35/1.73 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.35/1.73 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.35/1.73 c_Groups_Ominus__class_Ominus( X ), Y ), U ), Z ) }.
% 1.35/1.73 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.35/1.73 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.35/1.73 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.35/1.73 ) ) }.
% 1.35/1.73 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.35/1.73 .
% 1.35/1.73 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.35/1.73 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.35/1.73 tc_Int_Oint ) }.
% 1.35/1.73 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.35/1.73 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.35/1.73 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.35/1.73 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.35/1.73 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.35/1.73 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.35/1.73 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.35/1.73 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.35/1.73 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.35/1.73 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.35/1.73 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.35/1.73 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.35/1.73 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.35/1.73 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.35/1.73 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.35/1.73 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.35/1.73 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.35/1.73 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.35/1.73 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.35/1.73 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.35/1.73 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.35/1.73 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.35/1.73 { class_Power_Opower( tc_Int_Oint ) }.
% 1.35/1.73 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.35/1.73 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.35/1.73 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.35/1.73 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.35/1.73 tc_Nat_Onat ) }.
% 1.35/1.73 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Orderings_Owellorder( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.35/1.73 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.35/1.73 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.35/1.73 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.35/1.73 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.35/1.73 tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 1.35/1.73 .
% 1.35/1.73 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 1.35/1.73 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.35/1.73 tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 1.35/1.73 { ! class_Rings_Oidom( X ),
% 1.35/1.73 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.73 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.35/1.73 ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.73 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.35/1.73 X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.73 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.35/1.73 ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.73 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.35/1.73 }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.73 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.73 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.73 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.73 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.35/1.73 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.73 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.73 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.73 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.73 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.73 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.35/1.73 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.35/1.73 ( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.35/1.73 ( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 1.35/1.73 ( X ) ) }.
% 1.35/1.73 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.35/1.73 }.
% 1.35/1.73 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.35/1.73 .
% 1.35/1.73 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.35/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.73 { hAPP( c_COMBK( T, Z, Y ), X ) = Y }.
% 1.35/1.73 { hAPP( hAPP( c_COMBB( W, U, T, Z ), Y ), X ) = hAPP( Z, hAPP( Y, X ) ) }.
% 1.35/1.73 { hAPP( c_COMBC( W, U, T, Z, Y ), X ) = hAPP( hAPP( Z, X ), Y ) }.
% 1.35/1.73 { hAPP( hAPP( hAPP( c_COMBS( W, U, T ), Z ), Y ), X ) = hAPP( hAPP( Z, X )
% 1.35/1.73 , hAPP( Y, X ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_fequal, Y ), X ) ), Y = X }.
% 1.35/1.73 { ! Y = X, hBOOL( hAPP( hAPP( c_fequal, Y ), X ) ) }.
% 1.35/1.73 { hBOOL( X ), hBOOL( hAPP( hAPP( c_fimplies, X ), Y ) ) }.
% 1.35/1.73 { ! hBOOL( X ), hBOOL( hAPP( hAPP( c_fimplies, Y ), X ) ) }.
% 1.35/1.73 { ! hBOOL( hAPP( hAPP( c_fimplies, Y ), X ) ), ! hBOOL( Y ), hBOOL( X ) }.
% 1.35/1.73 { alpha55, ! c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.35/1.73 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.35/1.73 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 1.35/1.73 }.
% 1.35/1.73 { alpha55, alpha57, ! v_q____ = c_Groups_Ozero__class_Ozero(
% 1.35/1.73 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) }.
% 1.35/1.73 { alpha55, alpha57, ! hAPP( c_Nat_OSuc, c_Orderings_Oord__class_OLeast(
% 1.35/1.73 tc_Nat_Onat, hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool ),
% 1.35/1.73 tc_HOL_Obool, tc_Nat_Onat, c_HOL_OAll( tc_Nat_Onat ) ), c_COMBC(
% 1.35/1.73 tc_Nat_Onat, tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 1.35/1.73 tc_HOL_Obool ), hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool
% 1.35/1.73 , tc_HOL_Obool ) ), tc_fun( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun(
% 1.35/1.73 tc_Nat_Onat, tc_HOL_Obool ) ), tc_Nat_Onat, c_COMBS( tc_Nat_Onat,
% 1.35/1.73 tc_HOL_Obool, tc_HOL_Obool ) ), hAPP( c_COMBB( tc_fun( tc_Nat_Onat,
% 1.35/1.73 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool )
% 1.35/1.73 ), tc_Nat_Onat, c_COMBB( tc_HOL_Obool, tc_fun( tc_HOL_Obool,
% 1.35/1.73 tc_HOL_Obool ), tc_Nat_Onat, c_fimplies ) ),
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat ) ) ), c_COMBC( tc_Nat_Onat,
% 1.35/1.73 tc_Complex_Ocomplex, tc_HOL_Obool, hAPP( c_COMBB( tc_Complex_Ocomplex,
% 1.35/1.73 tc_fun( tc_Complex_Ocomplex, tc_HOL_Obool ), tc_Nat_Onat, c_fequal ),
% 1.35/1.73 c_Polynomial_Ocoeff( tc_Complex_Ocomplex, v_q____ ) ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ) ) ) = hAPP(
% 1.35/1.73 c_Nat_OSuc, c_Orderings_Oord__class_OLeast( tc_Nat_Onat, hAPP( c_COMBB(
% 1.35/1.73 tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_HOL_Obool, tc_Nat_Onat,
% 1.35/1.73 c_HOL_OAll( tc_Nat_Onat ) ), c_COMBC( tc_Nat_Onat, tc_fun( tc_Nat_Onat,
% 1.35/1.73 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ), hAPP( c_COMBB(
% 1.35/1.73 tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ), tc_fun(
% 1.35/1.73 tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool )
% 1.35/1.73 ), tc_Nat_Onat, c_COMBS( tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool ) ),
% 1.35/1.73 hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 1.35/1.73 tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ), tc_Nat_Onat, c_COMBB(
% 1.35/1.73 tc_HOL_Obool, tc_fun( tc_HOL_Obool, tc_HOL_Obool ), tc_Nat_Onat,
% 1.35/1.73 c_fimplies ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat ) ) ), c_COMBC
% 1.35/1.73 ( tc_Nat_Onat, tc_Complex_Ocomplex, tc_HOL_Obool, hAPP( c_COMBB(
% 1.35/1.73 tc_Complex_Ocomplex, tc_fun( tc_Complex_Ocomplex, tc_HOL_Obool ),
% 1.35/1.73 tc_Nat_Onat, c_fequal ), c_Polynomial_Ocoeff( tc_Complex_Ocomplex,
% 1.35/1.73 c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.35/1.73 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.35/1.73 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ) ) ) }.
% 1.35/1.73 { ! alpha57, v_q____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.35/1.73 tc_Complex_Ocomplex ) ) }.
% 1.35/1.73 { ! alpha57, ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP(
% 1.35/1.73 c_Nat_OSuc, c_Orderings_Oord__class_OLeast( tc_Nat_Onat, hAPP( c_COMBB(
% 1.35/1.73 tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_HOL_Obool, tc_Nat_Onat,
% 1.35/1.73 c_HOL_OAll( tc_Nat_Onat ) ), c_COMBC( tc_Nat_Onat, tc_fun( tc_Nat_Onat,
% 1.35/1.73 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ), hAPP( c_COMBB(
% 1.35/1.73 tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ), tc_fun(
% 1.35/1.73 tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool )
% 1.35/1.73 ), tc_Nat_Onat, c_COMBS( tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool ) ),
% 1.35/1.73 hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 1.35/1.73 tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ), tc_Nat_Onat, c_COMBB(
% 1.35/1.73 tc_HOL_Obool, tc_fun( tc_HOL_Obool, tc_HOL_Obool ), tc_Nat_Onat,
% 1.35/1.73 c_fimplies ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat ) ) ), c_COMBC
% 1.35/1.73 ( tc_Nat_Onat, tc_Complex_Ocomplex, tc_HOL_Obool, hAPP( c_COMBB(
% 1.35/1.73 tc_Complex_Ocomplex, tc_fun( tc_Complex_Ocomplex, tc_HOL_Obool ),
% 1.35/1.73 tc_Nat_Onat, c_fequal ), c_Polynomial_Ocoeff( tc_Complex_Ocomplex,
% 1.35/1.73 c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.35/1.73 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.35/1.73 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ) ) ) }.
% 1.35/1.73 { ! v_q____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.35/1.73 tc_Complex_Ocomplex ) ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 1.35/1.73 hAPP( c_Nat_OSuc, c_Orderings_Oord__class_OLeast( tc_Nat_Onat, hAPP(
% 1.35/1.73 c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_HOL_Obool, tc_Nat_Onat,
% 1.35/1.73 c_HOL_OAll( tc_Nat_Onat ) ), c_COMBC( tc_Nat_Onat, tc_fun( tc_Nat_Onat,
% 1.35/1.73 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ), hAPP( c_COMBB(
% 1.35/1.73 tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ), tc_fun(
% 1.35/1.73 tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool )
% 1.35/1.73 ), tc_Nat_Onat, c_COMBS( tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool ) ),
% 1.35/1.73 hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 1.35/1.73 tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ), tc_Nat_Onat, c_COMBB(
% 1.35/1.73 tc_HOL_Obool, tc_fun( tc_HOL_Obool, tc_HOL_Obool ), tc_Nat_Onat,
% 1.35/1.73 c_fimplies ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat ) ) ), c_COMBC
% 1.35/1.73 ( tc_Nat_Onat, tc_Complex_Ocomplex, tc_HOL_Obool, hAPP( c_COMBB(
% 1.35/1.73 tc_Complex_Ocomplex, tc_fun( tc_Complex_Ocomplex, tc_HOL_Obool ),
% 1.35/1.73 tc_Nat_Onat, c_fequal ), c_Polynomial_Ocoeff( tc_Complex_Ocomplex,
% 1.35/1.73 c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.35/1.73 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.35/1.73 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ) ) ), alpha57 }.
% 1.35/1.73 { ! alpha55, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.35/1.73 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.35/1.73 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 1.35/1.73 }.
% 1.35/1.73 { ! alpha55, ! v_q____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.35/1.73 tc_Complex_Ocomplex ) ) }.
% 1.35/1.73 { ! alpha55, ! hAPP( c_Nat_OSuc, c_Orderings_Oord__class_OLeast(
% 1.35/1.73 tc_Nat_Onat, hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool ),
% 1.35/1.73 tc_HOL_Obool, tc_Nat_Onat, c_HOL_OAll( tc_Nat_Onat ) ), c_COMBC(
% 1.35/1.73 tc_Nat_Onat, tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 1.35/1.73 tc_HOL_Obool ), hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool
% 1.35/1.73 , tc_HOL_Obool ) ), tc_fun( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun(
% 1.35/1.73 tc_Nat_Onat, tc_HOL_Obool ) ), tc_Nat_Onat, c_COMBS( tc_Nat_Onat,
% 1.35/1.73 tc_HOL_Obool, tc_HOL_Obool ) ), hAPP( c_COMBB( tc_fun( tc_Nat_Onat,
% 1.35/1.73 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool )
% 1.35/1.73 ), tc_Nat_Onat, c_COMBB( tc_HOL_Obool, tc_fun( tc_HOL_Obool,
% 1.35/1.73 tc_HOL_Obool ), tc_Nat_Onat, c_fimplies ) ),
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat ) ) ), c_COMBC( tc_Nat_Onat,
% 1.35/1.73 tc_Complex_Ocomplex, tc_HOL_Obool, hAPP( c_COMBB( tc_Complex_Ocomplex,
% 1.35/1.73 tc_fun( tc_Complex_Ocomplex, tc_HOL_Obool ), tc_Nat_Onat, c_fequal ),
% 1.35/1.73 c_Polynomial_Ocoeff( tc_Complex_Ocomplex, v_q____ ) ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ) ) ) =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.73 { ! c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.35/1.73 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.35/1.73 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 1.35/1.73 , v_q____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.35/1.73 tc_Complex_Ocomplex ) ), hAPP( c_Nat_OSuc, c_Orderings_Oord__class_OLeast
% 1.35/1.73 ( tc_Nat_Onat, hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool ),
% 1.35/1.73 tc_HOL_Obool, tc_Nat_Onat, c_HOL_OAll( tc_Nat_Onat ) ), c_COMBC(
% 1.35/1.73 tc_Nat_Onat, tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 1.35/1.73 tc_HOL_Obool ), hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool
% 1.35/1.73 , tc_HOL_Obool ) ), tc_fun( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun(
% 1.35/1.73 tc_Nat_Onat, tc_HOL_Obool ) ), tc_Nat_Onat, c_COMBS( tc_Nat_Onat,
% 1.35/1.73 tc_HOL_Obool, tc_HOL_Obool ) ), hAPP( c_COMBB( tc_fun( tc_Nat_Onat,
% 1.35/1.73 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool )
% 1.35/1.73 ), tc_Nat_Onat, c_COMBB( tc_HOL_Obool, tc_fun( tc_HOL_Obool,
% 1.35/1.73 tc_HOL_Obool ), tc_Nat_Onat, c_fimplies ) ),
% 1.35/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat ) ) ), c_COMBC( tc_Nat_Onat,
% 1.35/1.73 tc_Complex_Ocomplex, tc_HOL_Obool, hAPP( c_COMBB( tc_Complex_Ocomplex,
% 1.35/1.73 tc_fun( tc_Complex_Ocomplex, tc_HOL_Obool ), tc_Nat_Onat, c_fequal ),
% 1.35/1.73 c_Polynomial_Ocoeff( tc_Complex_Ocomplex, v_q____ ) ),
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ) ) ) =
% 1.35/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha55 }.
% 1.35/1.73
% 1.35/1.73 *** allocated 15000 integers for clauses
% 1.35/1.73 *** allocated 22500 integers for clauses
% 1.35/1.73 *** allocated 33750 integers for clauses
% 1.35/1.73 *** allocated 50625 integers for clauses
% 1.35/1.73 *** allocated 75937 integers for clauses
% 1.35/1.73 *** allocated 113905 integers for clauses
% 1.35/1.73 percentage equality = 0.247561, percentage horn = 0.898125
% 1.35/1.73 This is a problem with some equality
% 1.35/1.73
% 1.35/1.73
% 1.35/1.73
% 1.35/1.73 Options Used:
% 1.35/1.73
% 1.35/1.73 useres = 1
% 1.35/1.73 useparamod = 1
% 1.35/1.73 useeqrefl = 1
% 1.35/1.73 useeqfact = 1
% 1.35/1.73 usefactor = 1
% 1.35/1.73 usesimpsplitting = 0
% 1.35/1.73 usesimpdemod = 5
% 1.35/1.73 usesimpres = 3
% 1.35/1.73
% 1.35/1.73 resimpinuse = 1000
% 1.35/1.73 resimpclauses = 20000
% 1.35/1.73 substype = eqrewr
% 1.35/1.73 backwardsubs = 1
% 1.35/1.73 selectoldest = 5
% 1.35/1.73
% 1.35/1.73 litorderings [0] = split
% 1.35/1.73 litorderings [1] = extend the termordering, first sorting on arguments
% 1.35/1.73
% 1.35/1.73 termordering = kbo
% 1.35/1.73
% 1.35/1.73 litapriori = 0
% 1.35/1.73 termapriori = 1
% 1.35/1.73 litaposteriori = 0
% 1.35/1.73 termaposteriori = 0
% 1.35/1.73 demodaposteriori = 0
% 1.35/1.73 ordereqreflfact = 0
% 1.35/1.73
% 1.35/1.73 litselect = negord
% 1.35/1.73
% 1.35/1.73 maxweight = 15
% 1.35/1.73 maxdepth = 30000
% 1.35/1.73 maxlength = 115
% 1.35/1.73 maxnrvars = 195
% 1.35/1.73 excuselevel = 1
% 1.35/1.73 increasemaxweight = 1
% 1.35/1.73
% 1.35/1.73 maxselected = 10000000
% 1.35/1.73 maxnrclauses = 10000000
% 1.35/1.73
% 1.35/1.73 showgenerated = 0
% 1.35/1.73 showkept = 0
% 1.35/1.73 showselected = 0
% 1.35/1.73 showdeleted = 0
% 1.35/1.73 showresimp = 1
% 1.35/1.73 showstatus = 2000
% 1.35/1.73
% 1.35/1.73 prologoutput = 0
% 1.35/1.73 nrgoals = 5000000
% 1.35/1.73 totalproof = 1
% 1.35/1.73
% 1.35/1.73 Symbols occurring in the translation:
% 1.35/1.73
% 1.35/1.73 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.35/1.73 . [1, 2] (w:1, o:219, a:1, s:1, b:0),
% 1.35/1.73 ! [4, 1] (w:0, o:127, a:1, s:1, b:0),
% 1.35/1.73 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.35/1.73 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.35/1.73 hAPP [38, 2] (w:1, o:243, a:1, s:1, b:0),
% 1.35/1.73 tc_Complex_Ocomplex [39, 0] (w:1, o:16, a:1, s:1, b:0),
% 1.35/1.73 v_q____ [40, 0] (w:1, o:19, a:1, s:1, b:0),
% 1.35/1.73 c_Polynomial_Opoly [41, 2] (w:1, o:246, a:1, s:1, b:0),
% 1.35/1.73 c_Groups_Ozero__class_Ozero [42, 1] (w:1, o:132, a:1, s:1, b:0),
% 1.35/1.73 v_p [43, 0] (w:1, o:17, a:1, s:1, b:0),
% 1.35/1.73 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [44, 3] (w:1, o:
% 1.35/1.73 314, a:1, s:1, b:0),
% 1.35/1.73 tc_Nat_Onat [46, 0] (w:1, o:27, a:1, s:1, b:0),
% 1.35/1.73 c_Orderings_Oord__class_Oless [47, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.35/1.73 c_Nat_OSuc [48, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.35/1.73 hBOOL [49, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.35/1.73 c_Groups_Otimes__class_Otimes [51, 1] (w:1, o:135, a:1, s:1, b:0),
% 1.35/1.73 c_Rings_Oinverse__class_Oinverse [52, 2] (w:1, o:247, a:1, s:1, b:0)
% 1.35/1.73 ,
% 1.35/1.73 c_Polynomial_Osmult [53, 3] (w:1, o:315, a:1, s:1, b:0),
% 1.35/1.73 c_Orderings_Oord__class_OLeast [57, 2] (w:1, o:244, a:1, s:1, b:0),
% 1.35/1.73 tc_HOL_Obool [58, 0] (w:1, o:34, a:1, s:1, b:0),
% 1.35/1.73 c_COMBB [59, 4] (w:1, o:384, a:1, s:1, b:0),
% 1.35/1.73 class_Groups_Ozero [61, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.35/1.73 tc_Polynomial_Opoly [62, 1] (w:1, o:149, a:1, s:1, b:0),
% 1.35/1.73 c_Polynomial_Ocoeff [63, 2] (w:1, o:248, a:1, s:1, b:0),
% 1.35/1.73 class_Rings_Ocomm__semiring__0 [65, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.35/1.73 class_Rings_Oidom [68, 1] (w:1, o:153, a:1, s:1, b:0),
% 1.35/1.73 v_pa____ [71, 0] (w:1, o:18, a:1, s:1, b:0),
% 1.35/1.73 class_Int_Oring__char__0 [84, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.35/1.73 class_Rings_Odivision__ring [94, 1] (w:1, o:157, a:1, s:1, b:0),
% 1.35/1.73 class_Fields_Olinordered__field [95, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.35/1.73
% 1.35/1.73 class_Fields_Olinordered__field__inverse__zero [96, 1] (w:1, o:137
% 1.35/1.73 , a:1, s:1, b:0),
% 1.35/1.73 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [97, 2] (w:1, o:249
% 1.35/1.73 , a:1, s:1, b:0),
% 1.35/1.73 v_c____ [98, 0] (w:1, o:84, a:1, s:1, b:0),
% 1.35/1.73 class_Rings_Olinordered__idom [100, 1] (w:1, o:158, a:1, s:1, b:0),
% 1.35/1.73 class_Rings_Odivision__ring__inverse__zero [101, 1] (w:1, o:159, a:1
% 1.35/1.73 , s:1, b:0),
% 1.35/1.73 class_Rings_Omult__zero [103, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.35/1.73 class_Rings_Oring__no__zero__divisors [104, 1] (w:1, o:169, a:1, s:1
% 1.35/1.73 , b:0),
% 1.35/1.73 class_Rings_Ono__zero__divisors [105, 1] (w:1, o:170, a:1, s:1, b:0)
% 1.35/1.73 ,
% 1.35/1.73 class_Fields_Ofield__inverse__zero [106, 1] (w:1, o:138, a:1, s:1, b:
% 1.35/1.73 0),
% 1.35/1.73 class_Rings_Olinordered__ring [107, 1] (w:1, o:160, a:1, s:1, b:0),
% 1.35/1.73 class_Rings_Olinordered__ring__strict [109, 1] (w:1, o:161, a:1, s:1
% 1.35/1.73 , b:0),
% 1.35/1.73 class_Rings_Olinordered__semiring__strict [110, 1] (w:1, o:162, a:1
% 1.35/1.73 , s:1, b:0),
% 1.35/1.73 class_Rings_Olinordered__comm__semiring__strict [112, 1] (w:1, o:163
% 1.35/1.73 , a:1, s:1, b:0),
% 1.35/1.73 c_Groups_Oplus__class_Oplus [113, 1] (w:1, o:172, a:1, s:1, b:0),
% 1.35/1.73 class_Orderings_Owellorder [114, 1] (w:1, o:173, a:1, s:1, b:0),
% 1.35/1.73 c_Polynomial_Oorder [115, 3] (w:1, o:316, a:1, s:1, b:0),
% 1.35/1.73 class_Rings_Ocomm__semiring__1 [116, 1] (w:1, o:155, a:1, s:1, b:0),
% 1.35/1.73
% 1.35/1.73 class_RealVector_Oreal__normed__algebra [117, 1] (w:1, o:174, a:1, s:
% 1.35/1.73 1, b:0),
% 1.35/1.73 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.35/1.73 119, 1] (w:1, o:187, a:1, s:1, b:0),
% 1.35/1.73 class_Groups_Ocomm__monoid__add [120, 1] (w:1, o:188, a:1, s:1, b:0)
% 1.35/1.73 ,
% 1.35/1.73 class_Rings_Ocomm__semiring [129, 1] (w:1, o:156, a:1, s:1, b:0),
% 1.35/1.73 class_Rings_Osemiring [131, 1] (w:1, o:177, a:1, s:1, b:0),
% 1.35/1.73 class_Rings_Olinordered__semidom [133, 1] (w:1, o:164, a:1, s:1, b:0)
% 1.35/1.73 ,
% 1.35/1.73 class_Fields_Ofield [134, 1] (w:1, o:139, a:1, s:1, b:0),
% 1.35/1.73 class_Orderings_Olinorder [135, 1] (w:1, o:189, a:1, s:1, b:0),
% 1.35/1.73 class_Orderings_Opreorder [136, 1] (w:1, o:192, a:1, s:1, b:0),
% 1.35/1.73 class_Orderings_Oorder [137, 1] (w:1, o:190, a:1, s:1, b:0),
% 1.35/1.73 class_Orderings_Oord [138, 1] (w:1, o:191, a:1, s:1, b:0),
% 1.35/1.73 class_Groups_Oordered__comm__monoid__add [145, 1] (w:1, o:193, a:1
% 1.35/1.73 , s:1, b:0),
% 1.35/1.73 class_Groups_Olinordered__ab__group__add [146, 1] (w:1, o:194, a:1
% 1.35/1.73 , s:1, b:0),
% 1.35/1.73 class_Groups_Oordered__ab__semigroup__add__imp__le [147, 1] (w:1, o:
% 1.35/1.73 195, a:1, s:1, b:0),
% 1.35/1.73 class_Groups_Oab__semigroup__mult [151, 1] (w:1, o:196, a:1, s:1, b:0
% 1.35/1.73 ),
% 1.35/1.73 class_Groups_Ocancel__semigroup__add [152, 1] (w:1, o:197, a:1, s:1
% 1.35/1.73 , b:0),
% 1.35/1.73 class_Groups_Ocancel__ab__semigroup__add [153, 1] (w:1, o:198, a:1
% 1.35/1.73 , s:1, b:0),
% 1.35/1.73 class_Groups_Oab__semigroup__add [154, 1] (w:1, o:199, a:1, s:1, b:0)
% 1.35/1.73 ,
% 1.35/1.73 class_Groups_Omonoid__add [155, 1] (w:1, o:200, a:1, s:1, b:0),
% 1.35/1.73 class_Groups_Oordered__cancel__ab__semigroup__add [156, 1] (w:1, o:
% 1.35/1.73 201, a:1, s:1, b:0),
% 1.35/1.73 tc_RealDef_Oreal [158, 0] (w:1, o:100, a:1, s:1, b:0),
% 1.35/1.73 c_RealVector_Onorm__class_Onorm [159, 2] (w:1, o:250, a:1, s:1, b:0)
% 1.35/1.73 ,
% 1.35/1.73 c_Orderings_Oord__class_Oless__eq [160, 2] (w:1, o:245, a:1, s:1, b:0
% 1.35/1.73 ),
% 1.35/1.73 c_COMBS [161, 3] (w:1, o:317, a:1, s:1, b:0),
% 1.35/1.73 tc_fun [162, 2] (w:1, o:292, a:1, s:1, b:0),
% 1.35/1.73 c_Polynomial_OAbs__poly [163, 2] (w:1, o:293, a:1, s:1, b:0),
% 1.35/1.73 c_Polynomial_Odegree [164, 2] (w:1, o:294, a:1, s:1, b:0),
% 1.35/1.73 c_HOL_OAll [165, 1] (w:1, o:203, a:1, s:1, b:0),
% 1.35/1.73 c_fimplies [166, 0] (w:1, o:101, a:1, s:1, b:0),
% 1.35/1.73 c_fequal [167, 0] (w:1, o:102, a:1, s:1, b:0),
% 1.35/1.73 c_COMBC [168, 5] (w:1, o:398, a:1, s:1, b:0),
% 1.35/1.73 class_RealVector_Oreal__normed__vector [171, 1] (w:1, o:178, a:1, s:1
% 1.35/1.73 , b:0),
% 1.35/1.73 class_RealVector_Oreal__normed__div__algebra [172, 1] (w:1, o:179, a:
% 1.35/1.73 1, s:1, b:0),
% 1.35/1.73 class_Groups_Oordered__ab__semigroup__add [173, 1] (w:1, o:204, a:1
% 1.35/1.73 , s:1, b:0),
% 1.35/1.73 class_Rings_Oordered__cancel__semiring [174, 1] (w:1, o:180, a:1, s:1
% 1.35/1.73 , b:0),
% 1.35/1.73 class_Rings_Oordered__ring [175, 1] (w:1, o:181, a:1, s:1, b:0),
% 1.35/1.73 class_Rings_Oordered__semiring [176, 1] (w:1, o:182, a:1, s:1, b:0),
% 1.35/1.73
% 1.35/1.73 class_Rings_Oordered__comm__semiring [177, 1] (w:1, o:183, a:1, s:1
% 1.35/1.73 , b:0),
% 1.35/1.73 class_Rings_Olinordered__semiring [178, 1] (w:1, o:165, a:1, s:1, b:0
% 1.35/1.73 ),
% 1.35/1.73 c_COMBK [179, 3] (w:1, o:318, a:1, s:1, b:0),
% 1.35/1.73 c_Polynomial_Opdivmod__rel [181, 5] (w:1, o:399, a:1, s:1, b:0),
% 1.35/1.73 c_Polynomial_Opos__poly [182, 2] (w:1, o:295, a:1, s:1, b:0),
% 1.35/1.73 c_Polynomial_Opcompose [197, 3] (w:1, o:319, a:1, s:1, b:0),
% 1.35/1.73 c_SEQ_Odecseq [199, 2] (w:1, o:297, a:1, s:1, b:0),
% 1.35/1.73 c_Polynomial_Opoly__gcd [200, 3] (w:1, o:320, a:1, s:1, b:0),
% 1.35/1.73 c_Divides_Odiv__class_Omod [202, 3] (w:1, o:321, a:1, s:1, b:0),
% 1.35/1.73 c_Polynomial_Osynthetic__div [203, 3] (w:1, o:322, a:1, s:1, b:0),
% 1.35/1.73 c_SEQ_OBseq [204, 2] (w:1, o:298, a:1, s:1, b:0),
% 1.35/1.73 c_SEQ_Oincseq [205, 2] (w:1, o:299, a:1, s:1, b:0),
% 1.35/1.73 class_Divides_Osemiring__div [206, 1] (w:1, o:206, a:1, s:1, b:0),
% 1.35/1.73 c_Groups_Oone__class_Oone [208, 1] (w:1, o:171, a:1, s:1, b:0),
% 1.35/1.73 class_RealVector_Oreal__normed__algebra__1 [210, 1] (w:1, o:184, a:1
% 1.35/1.73 , s:1, b:0),
% 1.35/1.73 class_Rings_Ozero__neq__one [211, 1] (w:1, o:185, a:1, s:1, b:0),
% 1.35/1.73 class_Groups_Omonoid__mult [212, 1] (w:1, o:207, a:1, s:1, b:0),
% 1.35/1.73 class_Groups_Ocomm__monoid__mult [213, 1] (w:1, o:208, a:1, s:1, b:0)
% 1.35/1.73 ,
% 1.35/1.73 class_Groups_Oone [214, 1] (w:1, o:209, a:1, s:1, b:0),
% 1.35/1.73 class_Rings_Olinordered__semiring__1 [216, 1] (w:1, o:166, a:1, s:1
% 1.35/1.73 , b:0),
% 1.35/1.73 class_Rings_Olinordered__semiring__1__strict [217, 1] (w:1, o:167, a:
% 1.35/1.73 1, s:1, b:0),
% 1.35/1.73 c_RComplete_Onatceiling [218, 1] (w:1, o:210, a:1, s:1, b:0),
% 1.35/1.73 c_RComplete_Onatfloor [219, 1] (w:1, o:211, a:1, s:1, b:0),
% 1.35/1.73 c_RealDef_Oreal [220, 2] (w:1, o:296, a:1, s:1, b:0),
% 1.35/1.73 c_Power_Opower__class_Opower [224, 1] (w:1, o:212, a:1, s:1, b:0),
% 1.35/1.73 tc_Int_Oint [225, 0] (w:1, o:116, a:1, s:1, b:0),
% 1.35/1.73 class_Rings_Oring__1__no__zero__divisors [226, 1] (w:1, o:175, a:1
% 1.35/1.73 , s:1, b:0),
% 1.35/1.73 class_Power_Opower [227, 1] (w:1, o:213, a:1, s:1, b:0),
% 1.35/1.73 class_Rings_Osemiring__0 [228, 1] (w:1, o:186, a:1, s:1, b:0),
% 1.35/1.73 c_Power_Opower_Opower [230, 3] (w:1, o:323, a:1, s:1, b:0),
% 1.35/1.73 class_Rings_Ocomm__ring__1 [231, 1] (w:1, o:150, a:1, s:1, b:0),
% 1.35/1.73 c_Polynomial_Omonom [232, 3] (w:1, o:324, a:1, s:1, b:0),
% 1.35/1.73 c_If [238, 1] (w:1, o:214, a:1, s:1, b:0),
% 1.35/1.73 c_SEQ_Omonoseq [239, 2] (w:1, o:300, a:1, s:1, b:0),
% 1.35/1.73 c_Transcendental_Oln [243, 1] (w:1, o:215, a:1, s:1, b:0),
% 1.35/1.73 c_Divides_Odiv__class_Odiv [244, 3] (w:1, o:325, a:1, s:1, b:0),
% 1.35/1.73 c_Groups_Ominus__class_Ominus [246, 1] (w:1, o:202, a:1, s:1, b:0),
% 1.35/1.73 class_Rings_Oring__1 [248, 1] (w:1, o:176, a:1, s:1, b:0),
% 1.35/1.73 class_Groups_Oab__group__add [249, 1] (w:1, o:216, a:1, s:1, b:0),
% 1.35/1.73 class_Rings_Ocomm__ring [250, 1] (w:1, o:151, a:1, s:1, b:0),
% 1.35/1.73 class_Groups_Oordered__ab__group__add [252, 1] (w:1, o:217, a:1, s:1
% 1.35/1.73 , b:0),
% 1.35/1.73 class_Divides_Oring__div [253, 1] (w:1, o:205, a:1, s:1, b:0),
% 1.35/1.73 class_Groups_Ocancel__comm__monoid__add [255, 1] (w:1, o:218, a:1, s:
% 1.35/1.73 1, b:0),
% 1.35/1.73 alpha1 [261, 2] (w:1, o:301, a:1, s:1, b:1),
% 1.35/1.73 alpha2 [262, 4] (w:1, o:389, a:1, s:1, b:1),
% 1.35/1.73 alpha3 [263, 4] (w:1, o:392, a:1, s:1, b:1),
% 1.35/1.73 alpha4 [264, 2] (w:1, o:303, a:1, s:1, b:1),
% 1.35/1.73 alpha5 [265, 2] (w:1, o:304, a:1, s:1, b:1),
% 2.03/2.38 alpha6 [266, 3] (w:1, o:329, a:1, s:1, b:1),
% 2.03/2.38 alpha7 [267, 3] (w:1, o:330, a:1, s:1, b:1),
% 2.03/2.38 alpha8 [268, 3] (w:1, o:331, a:1, s:1, b:1),
% 2.03/2.38 alpha9 [269, 3] (w:1, o:332, a:1, s:1, b:1),
% 2.03/2.38 alpha10 [270, 3] (w:1, o:333, a:1, s:1, b:1),
% 2.03/2.38 alpha11 [271, 2] (w:1, o:305, a:1, s:1, b:1),
% 2.03/2.38 alpha12 [272, 4] (w:1, o:385, a:1, s:1, b:1),
% 2.03/2.38 alpha13 [273, 4] (w:1, o:386, a:1, s:1, b:1),
% 2.03/2.38 alpha14 [274, 2] (w:1, o:306, a:1, s:1, b:1),
% 2.03/2.38 alpha15 [275, 2] (w:1, o:307, a:1, s:1, b:1),
% 2.03/2.38 alpha16 [276, 4] (w:1, o:387, a:1, s:1, b:1),
% 2.03/2.38 alpha17 [277, 4] (w:1, o:388, a:1, s:1, b:1),
% 2.03/2.38 alpha18 [278, 2] (w:1, o:308, a:1, s:1, b:1),
% 2.03/2.38 alpha19 [279, 2] (w:1, o:309, a:1, s:1, b:1),
% 2.03/2.38 alpha20 [280, 3] (w:1, o:334, a:1, s:1, b:1),
% 2.03/2.38 alpha21 [281, 3] (w:1, o:335, a:1, s:1, b:1),
% 2.03/2.38 alpha22 [282, 3] (w:1, o:336, a:1, s:1, b:1),
% 2.03/2.38 alpha23 [283, 3] (w:1, o:337, a:1, s:1, b:1),
% 2.03/2.38 alpha24 [284, 3] (w:1, o:338, a:1, s:1, b:1),
% 2.03/2.38 alpha25 [285, 2] (w:1, o:310, a:1, s:1, b:1),
% 2.03/2.38 alpha26 [286, 4] (w:1, o:390, a:1, s:1, b:1),
% 2.03/2.38 alpha27 [287, 4] (w:1, o:391, a:1, s:1, b:1),
% 2.03/2.38 alpha28 [288, 2] (w:1, o:311, a:1, s:1, b:1),
% 2.03/2.38 alpha29 [289, 3] (w:1, o:339, a:1, s:1, b:1),
% 2.03/2.38 alpha30 [290, 4] (w:1, o:393, a:1, s:1, b:1),
% 2.03/2.38 alpha31 [291, 3] (w:1, o:340, a:1, s:1, b:1),
% 2.03/2.38 alpha32 [292, 3] (w:1, o:341, a:1, s:1, b:1),
% 2.03/2.38 alpha33 [293, 3] (w:1, o:342, a:1, s:1, b:1),
% 2.03/2.38 alpha34 [294, 2] (w:1, o:302, a:1, s:1, b:1),
% 2.03/2.38 alpha35 [295, 3] (w:1, o:343, a:1, s:1, b:1),
% 2.03/2.38 alpha36 [296, 4] (w:1, o:394, a:1, s:1, b:1),
% 2.03/2.38 alpha37 [297, 3] (w:1, o:344, a:1, s:1, b:1),
% 2.03/2.38 alpha38 [298, 3] (w:1, o:345, a:1, s:1, b:1),
% 2.03/2.38 alpha39 [299, 3] (w:1, o:346, a:1, s:1, b:1),
% 2.03/2.38 alpha40 [300, 3] (w:1, o:347, a:1, s:1, b:1),
% 2.03/2.38 alpha41 [301, 3] (w:1, o:348, a:1, s:1, b:1),
% 2.03/2.38 alpha42 [302, 3] (w:1, o:349, a:1, s:1, b:1),
% 2.03/2.38 alpha43 [303, 3] (w:1, o:350, a:1, s:1, b:1),
% 2.03/2.38 alpha44 [304, 3] (w:1, o:351, a:1, s:1, b:1),
% 2.03/2.38 alpha45 [305, 3] (w:1, o:352, a:1, s:1, b:1),
% 2.03/2.38 alpha46 [306, 3] (w:1, o:353, a:1, s:1, b:1),
% 2.03/2.38 alpha47 [307, 3] (w:1, o:354, a:1, s:1, b:1),
% 2.03/2.38 alpha48 [308, 4] (w:1, o:395, a:1, s:1, b:1),
% 2.03/2.38 alpha49 [309, 3] (w:1, o:355, a:1, s:1, b:1),
% 2.03/2.38 alpha50 [310, 4] (w:1, o:396, a:1, s:1, b:1),
% 2.03/2.38 alpha51 [311, 3] (w:1, o:326, a:1, s:1, b:1),
% 2.03/2.38 alpha52 [312, 3] (w:1, o:327, a:1, s:1, b:1),
% 2.03/2.38 alpha53 [313, 2] (w:1, o:312, a:1, s:1, b:1),
% 2.03/2.38 alpha54 [314, 2] (w:1, o:313, a:1, s:1, b:1),
% 2.03/2.38 alpha55 [315, 0] (w:1, o:125, a:1, s:1, b:1),
% 2.03/2.38 alpha56 [316, 3] (w:1, o:328, a:1, s:1, b:1),
% 2.03/2.38 alpha57 [317, 0] (w:1, o:126, a:1, s:1, b:1),
% 2.03/2.38 skol1 [318, 2] (w:1, o:251, a:1, s:1, b:1),
% 2.03/2.38 skol2 [319, 1] (w:1, o:142, a:1, s:1, b:1),
% 2.03/2.38 skol3 [320, 1] (w:1, o:144, a:1, s:1, b:1),
% 2.03/2.38 skol4 [321, 3] (w:1, o:360, a:1, s:1, b:1),
% 2.03/2.38 skol5 [322, 2] (w:1, o:258, a:1, s:1, b:1),
% 2.03/2.38 skol6 [323, 1] (w:1, o:145, a:1, s:1, b:1),
% 2.03/2.38 skol7 [324, 0] (w:1, o:12, a:1, s:1, b:1),
% 2.03/2.38 skol8 [325, 0] (w:1, o:13, a:1, s:1, b:1),
% 2.03/2.38 skol9 [326, 0] (w:1, o:14, a:1, s:1, b:1),
% 2.03/2.38 skol10 [327, 2] (w:1, o:259, a:1, s:1, b:1),
% 2.03/2.38 skol11 [328, 2] (w:1, o:260, a:1, s:1, b:1),
% 2.03/2.38 skol12 [329, 2] (w:1, o:261, a:1, s:1, b:1),
% 2.03/2.38 skol13 [330, 3] (w:1, o:361, a:1, s:1, b:1),
% 2.03/2.38 skol14 [331, 2] (w:1, o:262, a:1, s:1, b:1),
% 2.03/2.38 skol15 [332, 2] (w:1, o:263, a:1, s:1, b:1),
% 2.03/2.38 skol16 [333, 2] (w:1, o:264, a:1, s:1, b:1),
% 2.03/2.38 skol17 [334, 2] (w:1, o:265, a:1, s:1, b:1),
% 2.03/2.38 skol18 [335, 1] (w:1, o:141, a:1, s:1, b:1),
% 2.03/2.38 skol19 [336, 2] (w:1, o:266, a:1, s:1, b:1),
% 2.03/2.38 skol20 [337, 2] (w:1, o:267, a:1, s:1, b:1),
% 2.03/2.38 skol21 [338, 3] (w:1, o:362, a:1, s:1, b:1),
% 2.03/2.38 skol22 [339, 2] (w:1, o:268, a:1, s:1, b:1),
% 2.03/2.38 skol23 [340, 2] (w:1, o:269, a:1, s:1, b:1),
% 2.03/2.38 skol24 [341, 1] (w:1, o:143, a:1, s:1, b:1),
% 2.03/2.38 skol25 [342, 2] (w:1, o:270, a:1, s:1, b:1),
% 2.03/2.38 skol26 [343, 2] (w:1, o:271, a:1, s:1, b:1),
% 21.33/21.67 skol27 [344, 2] (w:1, o:272, a:1, s:1, b:1),
% 21.33/21.67 skol28 [345, 3] (w:1, o:363, a:1, s:1, b:1),
% 21.33/21.67 skol29 [346, 3] (w:1, o:364, a:1, s:1, b:1),
% 21.33/21.67 skol30 [347, 3] (w:1, o:356, a:1, s:1, b:1),
% 21.33/21.67 skol31 [348, 2] (w:1, o:273, a:1, s:1, b:1),
% 21.33/21.67 skol32 [349, 4] (w:1, o:397, a:1, s:1, b:1),
% 21.33/21.67 skol33 [350, 3] (w:1, o:357, a:1, s:1, b:1),
% 21.33/21.67 skol34 [351, 3] (w:1, o:358, a:1, s:1, b:1),
% 21.33/21.67 skol35 [352, 3] (w:1, o:359, a:1, s:1, b:1),
% 21.33/21.67 skol36 [353, 2] (w:1, o:274, a:1, s:1, b:1),
% 21.33/21.67 skol37 [354, 2] (w:1, o:275, a:1, s:1, b:1),
% 21.33/21.67 skol38 [355, 0] (w:1, o:15, a:1, s:1, b:1),
% 21.33/21.67 skol39 [356, 2] (w:1, o:276, a:1, s:1, b:1),
% 21.33/21.67 skol40 [357, 2] (w:1, o:252, a:1, s:1, b:1),
% 21.33/21.67 skol41 [358, 3] (w:1, o:365, a:1, s:1, b:1),
% 21.33/21.67 skol42 [359, 3] (w:1, o:366, a:1, s:1, b:1),
% 21.33/21.67 skol43 [360, 2] (w:1, o:253, a:1, s:1, b:1),
% 21.33/21.67 skol44 [361, 1] (w:1, o:146, a:1, s:1, b:1),
% 21.33/21.67 skol45 [362, 1] (w:1, o:147, a:1, s:1, b:1),
% 21.33/21.67 skol46 [363, 2] (w:1, o:254, a:1, s:1, b:1),
% 21.33/21.67 skol47 [364, 2] (w:1, o:255, a:1, s:1, b:1),
% 21.33/21.67 skol48 [365, 2] (w:1, o:256, a:1, s:1, b:1),
% 21.33/21.67 skol49 [366, 2] (w:1, o:257, a:1, s:1, b:1),
% 21.33/21.67 skol50 [367, 3] (w:1, o:367, a:1, s:1, b:1),
% 21.33/21.67 skol51 [368, 3] (w:1, o:368, a:1, s:1, b:1),
% 21.33/21.67 skol52 [369, 3] (w:1, o:369, a:1, s:1, b:1),
% 21.33/21.67 skol53 [370, 3] (w:1, o:370, a:1, s:1, b:1),
% 21.33/21.67 skol54 [371, 2] (w:1, o:277, a:1, s:1, b:1),
% 21.33/21.67 skol55 [372, 2] (w:1, o:278, a:1, s:1, b:1),
% 21.33/21.67 skol56 [373, 2] (w:1, o:279, a:1, s:1, b:1),
% 21.33/21.67 skol57 [374, 2] (w:1, o:280, a:1, s:1, b:1),
% 21.33/21.67 skol58 [375, 2] (w:1, o:281, a:1, s:1, b:1),
% 21.33/21.67 skol59 [376, 3] (w:1, o:371, a:1, s:1, b:1),
% 21.33/21.67 skol60 [377, 3] (w:1, o:372, a:1, s:1, b:1),
% 21.33/21.67 skol61 [378, 3] (w:1, o:373, a:1, s:1, b:1),
% 21.33/21.67 skol62 [379, 3] (w:1, o:374, a:1, s:1, b:1),
% 21.33/21.67 skol63 [380, 3] (w:1, o:375, a:1, s:1, b:1),
% 21.33/21.67 skol64 [381, 3] (w:1, o:376, a:1, s:1, b:1),
% 21.33/21.67 skol65 [382, 2] (w:1, o:282, a:1, s:1, b:1),
% 21.33/21.67 skol66 [383, 1] (w:1, o:148, a:1, s:1, b:1),
% 21.33/21.67 skol67 [384, 2] (w:1, o:283, a:1, s:1, b:1),
% 21.33/21.67 skol68 [385, 3] (w:1, o:377, a:1, s:1, b:1),
% 21.33/21.67 skol69 [386, 2] (w:1, o:284, a:1, s:1, b:1),
% 21.33/21.67 skol70 [387, 3] (w:1, o:378, a:1, s:1, b:1),
% 21.33/21.67 skol71 [388, 3] (w:1, o:379, a:1, s:1, b:1),
% 21.33/21.67 skol72 [389, 2] (w:1, o:285, a:1, s:1, b:1),
% 21.33/21.67 skol73 [390, 2] (w:1, o:286, a:1, s:1, b:1),
% 21.33/21.67 skol74 [391, 2] (w:1, o:287, a:1, s:1, b:1),
% 21.33/21.67 skol75 [392, 2] (w:1, o:288, a:1, s:1, b:1),
% 21.33/21.67 skol76 [393, 2] (w:1, o:289, a:1, s:1, b:1),
% 21.33/21.67 skol77 [394, 3] (w:1, o:380, a:1, s:1, b:1),
% 21.33/21.67 skol78 [395, 3] (w:1, o:381, a:1, s:1, b:1),
% 21.33/21.67 skol79 [396, 3] (w:1, o:382, a:1, s:1, b:1),
% 21.33/21.67 skol80 [397, 3] (w:1, o:383, a:1, s:1, b:1),
% 21.33/21.67 skol81 [398, 2] (w:1, o:290, a:1, s:1, b:1),
% 21.33/21.67 skol82 [399, 2] (w:1, o:291, a:1, s:1, b:1).
% 21.33/21.67
% 21.33/21.67
% 21.33/21.67 Starting Search:
% 21.33/21.67
% 21.33/21.67 *** allocated 170857 integers for clauses
% 21.33/21.67 Resimplifying inuse:
% 21.33/21.67 Done
% 21.33/21.67
% 21.33/21.67
% 21.33/21.67 Intermediate Status:
% 21.33/21.67 Generated: 2889
% 21.33/21.67 Kept: 2002
% 21.33/21.67 Inuse: 39
% 21.33/21.67 Deleted: 2
% 21.33/21.67 Deletedinuse: 0
% 21.33/21.67
% 21.33/21.67 *** allocated 256285 integers for clauses
% 21.33/21.67 Resimplifying inuse:
% 21.33/21.67 Done
% 21.33/21.67
% 21.33/21.67 *** allocated 384427 integers for clauses
% 21.33/21.67
% 21.33/21.67 Intermediate Status:
% 21.33/21.67 Generated: 7522
% 21.33/21.67 Kept: 4021
% 21.33/21.67 Inuse: 185
% 21.33/21.67 Deleted: 6
% 21.33/21.67 Deletedinuse: 0
% 21.33/21.67
% 21.33/21.67 Resimplifying inuse:
% 21.33/21.67 Done
% 21.33/21.67
% 21.33/21.67 *** allocated 256285 integers for termspace/termends
% 21.33/21.67 Resimplifying inuse:
% 21.33/21.67 Done
% 21.33/21.67
% 21.33/21.67
% 21.33/21.67 Intermediate Status:
% 21.33/21.67 Generated: 14290
% 21.33/21.67 Kept: 6251
% 21.33/21.67 Inuse: 230
% 21.33/21.67 Deleted: 6
% 21.33/21.67 Deletedinuse: 0
% 21.33/21.67
% 21.33/21.67 Resimplifying inuse:
% 21.33/21.67 Done
% 21.33/21.67
% 21.33/21.67 *** allocated 576640 integers for clauses
% 21.33/21.67 Resimplifying inuse:
% 21.33/21.67 Done
% 21.33/21.67
% 21.33/21.67 *** allocated 384427 integers for termspace/termends
% 21.33/21.67
% 21.33/21.67 Intermediate Status:
% 21.33/21.67 Generated: 19047
% 21.33/21.67 Kept: 8363
% 21.33/21.67 Inuse: 264
% 21.33/21.67 Deleted: 7
% 21.33/21.67 Deletedinuse: 0
% 21.33/21.67
% 21.33/21.67 Resimplifying inuse:
% 21.33/21.67 Done
% 21.33/21.67
% 21.33/21.67
% 21.33/21.67 Intermediate Status:
% 21.33/21.67 Generated: 24170
% 21.33/21.67 Kept: 10386
% 21.33/21.67 Inuse: 299
% 21.33/21.67 Deleted: 7
% 21.33/21.67 Deletedinuse: 0
% 21.33/21.67
% 21.33/21.67 Resimplifying inuse:
% 21.33/21.67 Done
% 21.33/21.67
% 21.33/21.67 *** allocated 864960 integers for clauses
% 21.33/21.67
% 21.33/21.67 Intermediate Status:
% 21.33/21.67 Generated: 31968
% 88.97/89.33 Kept: 12453
% 88.97/89.33 Inuse: 333
% 88.97/89.33 Deleted: 8
% 88.97/89.33 Deletedinuse: 0
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33 *** allocated 576640 integers for termspace/termends
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 37574
% 88.97/89.33 Kept: 14465
% 88.97/89.33 Inuse: 362
% 88.97/89.33 Deleted: 8
% 88.97/89.33 Deletedinuse: 0
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 42897
% 88.97/89.33 Kept: 16551
% 88.97/89.33 Inuse: 393
% 88.97/89.33 Deleted: 8
% 88.97/89.33 Deletedinuse: 0
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33 *** allocated 1297440 integers for clauses
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 51150
% 88.97/89.33 Kept: 18565
% 88.97/89.33 Inuse: 417
% 88.97/89.33 Deleted: 9
% 88.97/89.33 Deletedinuse: 0
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33 *** allocated 864960 integers for termspace/termends
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33 Resimplifying clauses:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 63787
% 88.97/89.33 Kept: 20652
% 88.97/89.33 Inuse: 437
% 88.97/89.33 Deleted: 243
% 88.97/89.33 Deletedinuse: 0
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 80711
% 88.97/89.33 Kept: 23246
% 88.97/89.33 Inuse: 452
% 88.97/89.33 Deleted: 243
% 88.97/89.33 Deletedinuse: 0
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 89224
% 88.97/89.33 Kept: 25511
% 88.97/89.33 Inuse: 487
% 88.97/89.33 Deleted: 243
% 88.97/89.33 Deletedinuse: 0
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33 *** allocated 1297440 integers for termspace/termends
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 98314
% 88.97/89.33 Kept: 27521
% 88.97/89.33 Inuse: 507
% 88.97/89.33 Deleted: 244
% 88.97/89.33 Deletedinuse: 1
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33 *** allocated 1946160 integers for clauses
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 115369
% 88.97/89.33 Kept: 31140
% 88.97/89.33 Inuse: 532
% 88.97/89.33 Deleted: 244
% 88.97/89.33 Deletedinuse: 1
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 128022
% 88.97/89.33 Kept: 33351
% 88.97/89.33 Inuse: 547
% 88.97/89.33 Deleted: 244
% 88.97/89.33 Deletedinuse: 1
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 133458
% 88.97/89.33 Kept: 35364
% 88.97/89.33 Inuse: 568
% 88.97/89.33 Deleted: 244
% 88.97/89.33 Deletedinuse: 1
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 140307
% 88.97/89.33 Kept: 38334
% 88.97/89.33 Inuse: 577
% 88.97/89.33 Deleted: 244
% 88.97/89.33 Deletedinuse: 1
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 171673
% 88.97/89.33 Kept: 40443
% 88.97/89.33 Inuse: 587
% 88.97/89.33 Deleted: 244
% 88.97/89.33 Deletedinuse: 1
% 88.97/89.33
% 88.97/89.33 Resimplifying clauses:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 177360
% 88.97/89.33 Kept: 42458
% 88.97/89.33 Inuse: 611
% 88.97/89.33 Deleted: 333
% 88.97/89.33 Deletedinuse: 1
% 88.97/89.33
% 88.97/89.33 *** allocated 1946160 integers for termspace/termends
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33 *** allocated 2919240 integers for clauses
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 184068
% 88.97/89.33 Kept: 44745
% 88.97/89.33 Inuse: 642
% 88.97/89.33 Deleted: 333
% 88.97/89.33 Deletedinuse: 1
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 190652
% 88.97/89.33 Kept: 46945
% 88.97/89.33 Inuse: 672
% 88.97/89.33 Deleted: 333
% 88.97/89.33 Deletedinuse: 1
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 197278
% 88.97/89.33 Kept: 49052
% 88.97/89.33 Inuse: 692
% 88.97/89.33 Deleted: 333
% 88.97/89.33 Deletedinuse: 1
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 206641
% 88.97/89.33 Kept: 51479
% 88.97/89.33 Inuse: 712
% 88.97/89.33 Deleted: 333
% 88.97/89.33 Deletedinuse: 1
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 214216
% 88.97/89.33 Kept: 53486
% 88.97/89.33 Inuse: 727
% 88.97/89.33 Deleted: 333
% 88.97/89.33 Deletedinuse: 1
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 222665
% 88.97/89.33 Kept: 55568
% 88.97/89.33 Inuse: 742
% 88.97/89.33 Deleted: 333
% 88.97/89.33 Deletedinuse: 1
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 230881
% 88.97/89.33 Kept: 57569
% 88.97/89.33 Inuse: 761
% 88.97/89.33 Deleted: 333
% 88.97/89.33 Deletedinuse: 1
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33 *** allocated 2919240 integers for termspace/termends
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 239676
% 88.97/89.33 Kept: 59658
% 88.97/89.33 Inuse: 777
% 88.97/89.33 Deleted: 333
% 88.97/89.33 Deletedinuse: 1
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33 Resimplifying clauses:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 88.97/89.33
% 88.97/89.33 Intermediate Status:
% 88.97/89.33 Generated: 250700
% 88.97/89.33 Kept: 61666
% 88.97/89.33 Inuse: 809
% 88.97/89.33 Deleted: 462
% 88.97/89.33 Deletedinuse: 1
% 88.97/89.33
% 88.97/89.33 Resimplifying inuse:
% 88.97/89.33 Done
% 88.97/89.33
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 259572
% 176.92/177.25 Kept: 64404
% 176.92/177.25 Inuse: 822
% 176.92/177.25 Deleted: 462
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 269881
% 176.92/177.25 Kept: 66528
% 176.92/177.25 Inuse: 852
% 176.92/177.25 Deleted: 462
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25 *** allocated 4378860 integers for clauses
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 306116
% 176.92/177.25 Kept: 70832
% 176.92/177.25 Inuse: 862
% 176.92/177.25 Deleted: 462
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 318874
% 176.92/177.25 Kept: 72925
% 176.92/177.25 Inuse: 882
% 176.92/177.25 Deleted: 462
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 332023
% 176.92/177.25 Kept: 75821
% 176.92/177.25 Inuse: 897
% 176.92/177.25 Deleted: 462
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 347341
% 176.92/177.25 Kept: 79400
% 176.92/177.25 Inuse: 902
% 176.92/177.25 Deleted: 462
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 384365
% 176.92/177.25 Kept: 82936
% 176.92/177.25 Inuse: 912
% 176.92/177.25 Deleted: 462
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25 Resimplifying clauses:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25 *** allocated 4378860 integers for termspace/termends
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 393278
% 176.92/177.25 Kept: 84970
% 176.92/177.25 Inuse: 917
% 176.92/177.25 Deleted: 532
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 402245
% 176.92/177.25 Kept: 87017
% 176.92/177.25 Inuse: 922
% 176.92/177.25 Deleted: 532
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 436358
% 176.92/177.25 Kept: 91855
% 176.92/177.25 Inuse: 937
% 176.92/177.25 Deleted: 532
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 467585
% 176.92/177.25 Kept: 95306
% 176.92/177.25 Inuse: 942
% 176.92/177.25 Deleted: 532
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 482067
% 176.92/177.25 Kept: 97721
% 176.92/177.25 Inuse: 957
% 176.92/177.25 Deleted: 532
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 *** allocated 6568290 integers for clauses
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 490125
% 176.92/177.25 Kept: 99729
% 176.92/177.25 Inuse: 980
% 176.92/177.25 Deleted: 532
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 499500
% 176.92/177.25 Kept: 101875
% 176.92/177.25 Inuse: 1012
% 176.92/177.25 Deleted: 532
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25 Resimplifying clauses:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 515866
% 176.92/177.25 Kept: 106283
% 176.92/177.25 Inuse: 1042
% 176.92/177.25 Deleted: 645
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 527392
% 176.92/177.25 Kept: 108830
% 176.92/177.25 Inuse: 1077
% 176.92/177.25 Deleted: 645
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 533034
% 176.92/177.25 Kept: 110841
% 176.92/177.25 Inuse: 1092
% 176.92/177.25 Deleted: 645
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 539355
% 176.92/177.25 Kept: 112841
% 176.92/177.25 Inuse: 1112
% 176.92/177.25 Deleted: 645
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25 *** allocated 6568290 integers for termspace/termends
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 552502
% 176.92/177.25 Kept: 117569
% 176.92/177.25 Inuse: 1137
% 176.92/177.25 Deleted: 645
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 560055
% 176.92/177.25 Kept: 120955
% 176.92/177.25 Inuse: 1142
% 176.92/177.25 Deleted: 645
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 567153
% 176.92/177.25 Kept: 124264
% 176.92/177.25 Inuse: 1147
% 176.92/177.25 Deleted: 645
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25 Resimplifying clauses:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 573695
% 176.92/177.25 Kept: 126297
% 176.92/177.25 Inuse: 1167
% 176.92/177.25 Deleted: 707
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 580696
% 176.92/177.25 Kept: 128536
% 176.92/177.25 Inuse: 1182
% 176.92/177.25 Deleted: 707
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25
% 176.92/177.25 Intermediate Status:
% 176.92/177.25 Generated: 591003
% 176.92/177.25 Kept: 131132
% 176.92/177.25 Inuse: 1197
% 176.92/177.25 Deleted: 707
% 176.92/177.25 Deletedinuse: 1
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 176.92/177.25 Done
% 176.92/177.25
% 176.92/177.25 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 601012
% 291.37/291.77 Kept: 133284
% 291.37/291.77 Inuse: 1217
% 291.37/291.77 Deleted: 710
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 615020
% 291.37/291.77 Kept: 138162
% 291.37/291.77 Inuse: 1237
% 291.37/291.77 Deleted: 710
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 621580
% 291.37/291.77 Kept: 141652
% 291.37/291.77 Inuse: 1242
% 291.37/291.77 Deleted: 710
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 628158
% 291.37/291.77 Kept: 145153
% 291.37/291.77 Inuse: 1247
% 291.37/291.77 Deleted: 710
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77 Resimplifying clauses:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 634758
% 291.37/291.77 Kept: 148665
% 291.37/291.77 Inuse: 1252
% 291.37/291.77 Deleted: 1111
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77 *** allocated 9852435 integers for clauses
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 658182
% 291.37/291.77 Kept: 152431
% 291.37/291.77 Inuse: 1282
% 291.37/291.77 Deleted: 1111
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 672164
% 291.37/291.77 Kept: 154452
% 291.37/291.77 Inuse: 1288
% 291.37/291.77 Deleted: 1111
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 686269
% 291.37/291.77 Kept: 156472
% 291.37/291.77 Inuse: 1294
% 291.37/291.77 Deleted: 1111
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 697351
% 291.37/291.77 Kept: 158603
% 291.37/291.77 Inuse: 1317
% 291.37/291.77 Deleted: 1111
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 705635
% 291.37/291.77 Kept: 160920
% 291.37/291.77 Inuse: 1322
% 291.37/291.77 Deleted: 1111
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 714885
% 291.37/291.77 Kept: 163115
% 291.37/291.77 Inuse: 1342
% 291.37/291.77 Deleted: 1111
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 723006
% 291.37/291.77 Kept: 165854
% 291.37/291.77 Inuse: 1357
% 291.37/291.77 Deleted: 1111
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77 Resimplifying clauses:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 729845
% 291.37/291.77 Kept: 167873
% 291.37/291.77 Inuse: 1367
% 291.37/291.77 Deleted: 1167
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 738286
% 291.37/291.77 Kept: 170092
% 291.37/291.77 Inuse: 1382
% 291.37/291.77 Deleted: 1167
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 749658
% 291.37/291.77 Kept: 172225
% 291.37/291.77 Inuse: 1392
% 291.37/291.77 Deleted: 1167
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 760142
% 291.37/291.77 Kept: 174529
% 291.37/291.77 Inuse: 1407
% 291.37/291.77 Deleted: 1167
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 767507
% 291.37/291.77 Kept: 176939
% 291.37/291.77 Inuse: 1427
% 291.37/291.77 Deleted: 1167
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 785704
% 291.37/291.77 Kept: 180320
% 291.37/291.77 Inuse: 1437
% 291.37/291.77 Deleted: 1167
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77 *** allocated 9852435 integers for termspace/termends
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 804849
% 291.37/291.77 Kept: 183065
% 291.37/291.77 Inuse: 1447
% 291.37/291.77 Deleted: 1167
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 818163
% 291.37/291.77 Kept: 185221
% 291.37/291.77 Inuse: 1472
% 291.37/291.77 Deleted: 1167
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 828118
% 291.37/291.77 Kept: 188093
% 291.37/291.77 Inuse: 1477
% 291.37/291.77 Deleted: 1167
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77 Resimplifying clauses:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 848857
% 291.37/291.77 Kept: 191892
% 291.37/291.77 Inuse: 1497
% 291.37/291.77 Deleted: 1264
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 857386
% 291.37/291.77 Kept: 193921
% 291.37/291.77 Inuse: 1519
% 291.37/291.77 Deleted: 1264
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 864599
% 291.37/291.77 Kept: 195984
% 291.37/291.77 Inuse: 1537
% 291.37/291.77 Deleted: 1264
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 Resimplifying inuse:
% 291.37/291.77 Done
% 291.37/291.77
% 291.37/291.77
% 291.37/291.77 Intermediate Status:
% 291.37/291.77 Generated: 878167
% 291.37/291.77 Kept: 202382
% 291.37/291.77 Inuse: 1552
% 291.37/291.77 Deleted: 1264
% 291.37/291.77 Deletedinuse: 4
% 291.37/291.77
% 291.37/291.77 ResimpCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------