TSTP Solution File: SWV672-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV672-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n005.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 16:27:41 EDT 2022
% Result : Timeout 296.48s 296.90s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV672-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : bliksem %s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Tue Jun 14 20:19:24 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.26/1.68 *** allocated 10000 integers for termspace/termends
% 1.26/1.68 *** allocated 10000 integers for clauses
% 1.26/1.68 *** allocated 10000 integers for justifications
% 1.26/1.68 *** allocated 15000 integers for termspace/termends
% 1.26/1.68 *** allocated 22500 integers for termspace/termends
% 1.26/1.68 *** allocated 33750 integers for termspace/termends
% 1.26/1.68 *** allocated 50625 integers for termspace/termends
% 1.26/1.68 Bliksem 1.12
% 1.26/1.68
% 1.26/1.68
% 1.26/1.68 Automatic Strategy Selection
% 1.26/1.68
% 1.26/1.68 Clauses:
% 1.26/1.68 [
% 1.26/1.68 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.26/1.68 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.26/1.68 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.26/1.68 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.26/1.68 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.26/1.68 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.26/1.68 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.26/1.68 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.26/1.68 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.26/1.68 ) ],
% 1.26/1.68 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.26/1.68 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.26/1.68 ) ],
% 1.26/1.68 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.26/1.68 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.26/1.68 ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.26/1.68 'c_HOL_Oabs__class_Oabs'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.26/1.68 , Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.26/1.68 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ), ~(
% 1.26/1.68 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ) )
% 1.26/1.68 , ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.26/1.68 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ), ~(
% 1.26/1.68 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ) )
% 1.26/1.68 , ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.26/1.68 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.26/1.68 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.26/1.68 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.26/1.68 ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ),
% 1.26/1.68 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.26/1.68 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.26/1.68 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.26/1.68 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.26/1.68 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.26/1.68 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.26/1.68 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.26/1.68 , V0, V1, V2 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.26/1.68 T, X, U, W, Y, V0 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.26/1.68 T, X, U, Y, W, V0 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.26/1.68 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.26/1.68 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.26/1.68 , V0, V1, V2 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.26/1.68 X, T, U, Y, W, V0 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.26/1.68 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.26/1.68 , V0, V1, V2 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.26/1.68 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.26/1.68 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.26/1.68 , V0, V1, V2 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.26/1.68 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.26/1.68 W, V0, V1, V2 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.26/1.68 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.26/1.68 W, V0, V1, V2 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.26/1.68 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.26/1.68 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.26/1.68 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.26/1.68 W, V0, V1, V2 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.26/1.68 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.26/1.68 , V0, V1, V2 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.26/1.68 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.26/1.68 W, V0, V1, V2 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.26/1.68 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.26/1.68 , V0, V1, V2 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.26/1.68 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.26/1.68 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.26/1.68 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.26/1.68 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.26/1.68 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.26/1.68 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.26/1.68 T, X, U, W, Z, V0 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.26/1.68 T, X, U, W, Y, V0 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.26/1.68 T, X, U, Z, W, V0 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.26/1.68 T, X, U, Y, W, V0 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.26/1.68 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.26/1.68 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.26/1.68 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.26/1.68 X, T, U, Z, W, V0 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.26/1.68 X, T, U, Y, W, V0 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.26/1.68 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.26/1.68 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.26/1.68 , V0, U, V1 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.26/1.68 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.26/1.68 , V0, U, V1 ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.26/1.68 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.26/1.68 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.68 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.26/1.68 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.68 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.26/1.68 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.26/1.68 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.26/1.68 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.26/1.68 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.68 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.26/1.68 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.26/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.68 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.26/1.68 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.26/1.68 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.26/1.68 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.26/1.68 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.26/1.68 'c_HOL_Oone__class_Oone'( X ) ) ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.26/1.68 Z, X ) ) ],
% 1.26/1.68 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.26/1.68 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.68 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.26/1.68 'c_HOL_Oone__class_Oone'( X ) ) ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.68 Y, Z, X ) ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.68 'c_HOL_Ominus__class_Ominus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.26/1.68 , hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.26/1.68 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.26/1.68 hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.26/1.68 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.26/1.68 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Z, X ) ) ],
% 1.26/1.68 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.26/1.68 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.26/1.68 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ],
% 1.26/1.68 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.26/1.68 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.26/1.68 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ],
% 1.26/1.68 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), ~(
% 1.26/1.68 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.26/1.68 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.26/1.68 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ),
% 1.26/1.68 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.26/1.68 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.26/1.68 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.68 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.68 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ), 'c_HOL_Oone__class_Oone'( X
% 1.26/1.68 ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.26/1.68 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ),
% 1.26/1.68 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.26/1.68 ,
% 1.26/1.68 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.26/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.26/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.26/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.26/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.26/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ],
% 1.26/1.68 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.68 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.26/1.68 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.26/1.68 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), ~( 'c_lessequals'( Y,
% 1.26/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.26/1.68 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.26/1.68 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.26/1.68 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.26/1.68 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.26/1.68 ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ), T, X ) ) ],
% 1.26/1.68 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.26/1.68 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.26/1.68 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.26/1.68 ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.26/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.26/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.26/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.68 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.26/1.68 'tc_nat' ), X ), Y ), hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.26/1.68 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.26/1.68 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.26/1.68 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.26/1.68 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.26/1.68 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.26/1.68 ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.26/1.68 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.26/1.68 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.26/1.68 ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.26/1.68 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.26/1.68 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.26/1.68 Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc',
% 1.26/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ),
% 1.26/1.68 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.68 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ),
% 1.26/1.68 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.68 'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.26/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.26/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.26/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.26/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.68 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.26/1.68 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.26/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.68 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.26/1.68 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.26/1.68 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.68 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.26/1.68 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.26/1.68 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.26/1.68 X ), Y ), T ) ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ), X ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.26/1.68 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.26/1.68 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.68 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.26/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.26/1.68 ,
% 1.26/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.26/1.68 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.68 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) )
% 1.26/1.68 ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.26/1.68 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.26/1.68 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.26/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.26/1.68 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ) )
% 1.26/1.68 ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.26/1.68 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.26/1.68 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.26/1.68 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.68 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) )
% 1.26/1.68 ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.26/1.68 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.26/1.68 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.26/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.26/1.68 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ) )
% 1.26/1.68 ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.26/1.68 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.26/1.68 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.68 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.68 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.26/1.68 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.68 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.26/1.68 ) ) ) ],
% 1.26/1.68 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.68 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.68 X ), Y ) ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z
% 1.26/1.68 ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.26/1.68 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.26/1.68 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.26/1.68 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.26/1.68 X ) ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.26/1.68 'c_HOL_Oabs__class_Oabs'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) )
% 1.26/1.68 , hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ) ],
% 1.26/1.68 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.68 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.26/1.68 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.26/1.68 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), W ) ],
% 1.26/1.68 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.68 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.26/1.68 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.26/1.68 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ],
% 1.26/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.68 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.26/1.68 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.26/1.68 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.26/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.68 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.26/1.68 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.26/1.68 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.26/1.68 ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.26/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.26/1.68 'c_HOL_Oabs__class_Oabs'( X ), Y ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.68 X ) ) ],
% 1.26/1.68 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.26/1.68 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.26/1.68 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.26/1.68 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.26/1.68 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.26/1.68 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.26/1.68 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.26/1.68 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), hAPP(
% 1.26/1.68 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 1.26/1.68 ,
% 1.26/1.68 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X
% 1.26/1.68 , Y, 'tc_nat' ) ), Y ) ) ) ],
% 1.26/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.26/1.68 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.26/1.68 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.26/1.68 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.26/1.68 X, T, 'tc_nat' ) ],
% 1.26/1.68 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.26/1.68 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.26/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.68 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.26/1.68 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.26/1.69 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.26/1.69 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' )
% 1.26/1.69 ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.26/1.69 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.26/1.69 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.26/1.69 T ), Z, X ) ) ],
% 1.26/1.69 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.26/1.69 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.26/1.69 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.26/1.69 ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.26/1.69 Y ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y ), X ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.26/1.69 'c_lessequals'( Y, hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), X ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), W, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), W, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.26/1.69 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.26/1.69 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.26/1.69 ) ) ), =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.26/1.69 ) ) ), =( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ) ],
% 1.26/1.69 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ),
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( Y, X, 'tc_nat' ) ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.26/1.69 X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ), hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.26/1.69 X ), Y ), Z ) ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.26/1.69 ) ), Z ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.26/1.69 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.26/1.69 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.26/1.69 , X ) ) ],
% 1.26/1.69 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.26/1.69 , Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.26/1.69 , Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.26/1.69 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.26/1.69 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.26/1.69 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.26/1.69 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), W ), T ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 X ), X ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.26/1.69 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.26/1.69 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.26/1.69 T, X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.26/1.69 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.26/1.69 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.26/1.69 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.26/1.69 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.26/1.69 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.26/1.69 , T ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.26/1.69 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.26/1.69 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.26/1.69 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y )
% 1.26/1.69 ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ), X ) ],
% 1.26/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.26/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.26/1.69 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.26/1.69 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.26/1.69 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.26/1.69 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.26/1.69 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.26/1.69 X ), Y ), Z ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) ) ) ],
% 1.26/1.69 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.26/1.69 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.26/1.69 , 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.26/1.69 , 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.26/1.69 , Z ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), X ) ],
% 1.26/1.69 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.69 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.26/1.69 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.26/1.69 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.26/1.69 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.26/1.69 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.26/1.69 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.26/1.69 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Y ), T ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Y ), Z ), T, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), 'c_lessequals'( U, T, X
% 1.26/1.69 ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), 'c_lessequals'( Z, Y, X
% 1.26/1.69 ), ~( 'c_lessequals'( U, T, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( T, U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.26/1.69 , X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U
% 1.26/1.69 , X ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.26/1.69 ), ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.26/1.69 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'( Y
% 1.26/1.69 , T, X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.26/1.69 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.26/1.69 'c_Int_OMin', X ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber__ring'( X ) ), =( hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.26/1.69 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ),
% 1.26/1.69 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.26/1.69 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y,
% 1.26/1.69 'tc_nat' ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.26/1.69 'tc_nat' ) ) ],
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.26/1.69 'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.26/1.69 'tc_nat' ) ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.26/1.69 ), Y ) ), Z ) ), Z ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.26/1.69 ~( 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X
% 1.26/1.69 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.26/1.69 ), Y ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.26/1.69 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.26/1.69 ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 1.26/1.69 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z,
% 1.26/1.69 'tc_nat' ) ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.26/1.69 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.26/1.69 'c_lessequals'( Y, T, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.26/1.69 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.26/1.69 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.26/1.69 'c_lessequals'( Z, T, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.26/1.69 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.26/1.69 'c_lessequals'( Y, T, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.26/1.69 'c_lessequals'( Z, T, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.26/1.69 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.26/1.69 hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Oabs__class_Oabs'(
% 1.26/1.69 X ), T ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y ), Y ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.26/1.69 ), =( Z, Y ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.26/1.69 ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.26/1.69 ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.26/1.69 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.26/1.69 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.26/1.69 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.26/1.69 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.26/1.69 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.26/1.69 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.26/1.69 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 1.26/1.69 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), T ) ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), Z, X ) ) ],
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.26/1.69 ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.26/1.69 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.26/1.69 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.26/1.69 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.26/1.69 , hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.26/1.69 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X
% 1.26/1.69 ), Y ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.26/1.69 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.26/1.69 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.26/1.69 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.26/1.69 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc',
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.26/1.69 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( X, Y
% 1.26/1.69 , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.69 X ), Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.69 X ), Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.26/1.69 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.69 X ), Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 X ), X ) ) ],
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.26/1.69 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( T, hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W
% 1.26/1.69 ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.26/1.69 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ), X ), ~(
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Z ), U ) ), W ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.69 X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ),
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.69 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.26/1.69 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.26/1.69 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.26/1.69 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.26/1.69 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.26/1.69 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.26/1.69 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.69 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.26/1.69 ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y )
% 1.26/1.69 ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.26/1.69 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ), 'tc_nat'
% 1.26/1.69 ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.26/1.69 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.26/1.69 ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.26/1.69 , Z ), Y ), 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.26/1.69 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.26/1.69 ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.26/1.69 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.26/1.69 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.26/1.69 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.26/1.69 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.26/1.69 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.26/1.69 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.26/1.69 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.26/1.69 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.26/1.69 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.26/1.69 , X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.26/1.69 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.26/1.69 , X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.26/1.69 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.26/1.69 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.26/1.69 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.26/1.69 ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.26/1.69 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.26/1.69 ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.26/1.69 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.26/1.69 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X, hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ) ) ],
% 1.26/1.69 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.26/1.69 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.26/1.69 'c_Int_OMin', X ) ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.26/1.69 ), Y ) ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.26/1.69 X ), Y ), Z ) ), T, X ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.26/1.69 'tc_nat' ), X ), Y ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.26/1.69 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Y ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.26/1.69 Y ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.26/1.69 Y ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.26/1.69 ), X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.26/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y ), X ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.26/1.69 ), Z ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.26/1.69 ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.26/1.69 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.26/1.69 'c_lessequals'( Z, Y, X ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.26/1.69 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.26/1.69 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.26/1.69 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.26/1.69 , 'tc_nat' ), 'tc_nat' ), 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.26/1.69 X ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.26/1.69 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.26/1.69 , 'tc_nat' ), 'tc_nat' ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.26/1.69 , 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.26/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.26/1.69 , 'tc_nat' ), 'tc_nat' ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.26/1.69 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.26/1.69 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.26/1.69 , 'tc_nat' ), 'tc_nat' ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), =( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.26/1.69 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.26/1.69 , hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), X ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.26/1.69 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( 'c_Suc',
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ), 'tc_nat' ) ],
% 1.26/1.69 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.26/1.69 , hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.26/1.69 ) ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ), X ),
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.26/1.69 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.26/1.69 Z, hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.26/1.69 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.26/1.69 , X ) ), hAPP( Y, T ) ) ), 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.26/1.69 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.26/1.69 Z, T, 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 X ), hAPP( Y, Z ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.26/1.69 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', Z ), T,
% 1.26/1.69 'tc_nat' ), 'tc_nat', X ) ) ), ~( 'c_HOL_Oord__class_Oless'( Z, T,
% 1.26/1.69 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.69 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.69 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.69 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.26/1.69 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.26/1.69 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.26/1.69 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.26/1.69 ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.26/1.69 ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.26/1.69 ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.26/1.69 ), W, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), W, X ), ~(
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Z ), T ) ), W ), X ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.26/1.69 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.26/1.69 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.26/1.69 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.26/1.69 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.26/1.69 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.26/1.69 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.26/1.69 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.26/1.69 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.26/1.69 ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), T ), Y ) ), Z ) ), U ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), T ), Z ) ), U ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~( 'c_lessequals'( Z, Y, X
% 1.26/1.69 ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 1.26/1.69 hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y
% 1.26/1.69 ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ), X ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.26/1.69 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber__ring'( X ) ), =( hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.26/1.69 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.26/1.69 Y, X ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.26/1.69 ), X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.26/1.69 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.26/1.69 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y
% 1.26/1.69 ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ), hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.26/1.69 X ), Y ), Z ) ), X ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ), U, X
% 1.26/1.69 ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ),
% 1.26/1.69 Y ), T, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.26/1.69 X ), Y ), Z ) ), Z ), Y ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.26/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.26/1.69 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.26/1.69 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.26/1.69 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.26/1.69 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 X ), Y ), Z ) ), T ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.26/1.69 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.26/1.69 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 X ), Y ), Z ) ), T ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.26/1.69 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y )
% 1.26/1.69 ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ), X ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.26/1.69 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.26/1.69 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.26/1.69 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.26/1.69 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.26/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.26/1.69 , X ) ), T, X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.26/1.69 ), Z ), T, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.26/1.69 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.26/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.26/1.69 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.26/1.69 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ) ), =( Z, T ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), T ), T ) ) ), =( Y, Z ) ],
% 1.26/1.69 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), U ) ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ) ) ],
% 1.26/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.26/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.26/1.69 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.26/1.69 , Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.26/1.69 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.26/1.69 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.26/1.69 ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.26/1.69 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.26/1.69 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.26/1.69 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ) ],
% 1.26/1.69 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.26/1.69 , Y ) ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) )
% 1.26/1.69 , ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.26/1.69 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.26/1.69 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.26/1.69 X ), T ), Y ) ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.26/1.69 , Y, 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y, hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), T ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber__ring'( X ) ), =( hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.26/1.69 , hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ), Y ) ),
% 1.26/1.69 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.26/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.69 X ), Y ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.26/1.69 ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.26/1.69 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.26/1.69 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.26/1.69 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 X ), Y ), Z ) ), Z ), Y ) ],
% 1.26/1.69 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), X ), Y ) ],
% 1.26/1.69 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Y ), X ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Z ), T ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.69 X ), Y ) ), Y ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.69 X ), Y ) ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.69 X ), Y ) ) ) ],
% 1.26/1.69 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.69 X ), Y ) ), Y ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.69 X ), Y ) ), Y ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.26/1.69 ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.26/1.69 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.26/1.69 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.26/1.69 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.26/1.69 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.26/1.69 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.26/1.69 Z ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.26/1.69 Z ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.26/1.69 ~( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X )
% 1.26/1.69 ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.26/1.69 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.26/1.69 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.26/1.69 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.26/1.69 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.26/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), Z ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Z ), Y ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), Z ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Z ), Y ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.26/1.69 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.26/1.69 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.69 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.26/1.69 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.69 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.26/1.69 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.26/1.69 ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.26/1.69 ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.69 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.69 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.26/1.69 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.26/1.69 , X ) ), T ) ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.26/1.69 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.26/1.69 , X ) ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ) ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.26/1.69 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.26/1.69 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.26/1.69 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.26/1.69 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.26/1.69 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.26/1.69 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.26/1.69 , X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.26/1.69 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.26/1.69 ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.26/1.69 ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.26/1.69 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.26/1.69 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~( 'c_lessequals'(
% 1.26/1.69 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~( 'c_lessequals'(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.26/1.69 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.26/1.69 ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.26/1.69 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.26/1.69 ), X ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.26/1.69 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.26/1.69 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.26/1.69 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.26/1.69 , X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.69 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.26/1.69 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.69 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.26/1.69 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.26/1.69 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.26/1.69 ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.69 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.69 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.69 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.69 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.26/1.69 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.26/1.69 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.26/1.69 X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Z,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.26/1.69 ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z
% 1.26/1.69 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) )
% 1.26/1.69 ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'(
% 1.26/1.69 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.69 ), T ), Z ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.69 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.26/1.69 X ), T ), Z ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.26/1.69 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.26/1.69 ~( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X )
% 1.26/1.69 ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.26/1.69 ~( 'c_lessequals'( Z, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.26/1.69 ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.26/1.69 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.26/1.69 ~( 'c_lessequals'( Z, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.26/1.69 ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.26/1.69 hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.26/1.69 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.26/1.69 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.26/1.69 ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.26/1.69 ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y ) ), =( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.26/1.69 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.26/1.69 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.26/1.69 ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.26/1.69 , Y ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.26/1.69 X ) ), =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.26/1.69 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.26/1.69 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.26/1.69 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.26/1.69 ), Y ) ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 X ) ) ), =( Y, Z ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 X ) ) ), =( Y, Z ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.26/1.69 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.26/1.69 Y ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.26/1.69 Y ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.26/1.69 Y ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.26/1.69 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.26/1.69 Y ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.26/1.69 Y ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.26/1.69 Y ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.26/1.69 Y ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.26/1.69 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.26/1.69 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.26/1.69 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.26/1.69 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y
% 1.26/1.69 ) ), Z ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.26/1.69 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.26/1.69 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.26/1.69 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.26/1.69 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.26/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.26/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.26/1.69 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.26/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.26/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.26/1.69 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.26/1.69 ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.26/1.69 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.26/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.26/1.69 T, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.26/1.69 , Z ) ) ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.26/1.69 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.26/1.69 , Z ) ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.26/1.69 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.26/1.69 , Z ) ) ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.26/1.69 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.26/1.69 , Z ) ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.26/1.69 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.26/1.69 ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.26/1.69 ), X ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.26/1.69 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.26/1.69 T, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.26/1.69 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.26/1.69 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.26/1.69 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.26/1.69 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.26/1.69 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.26/1.69 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.26/1.69 'class_Int_Onumber__ring'( X ) ), =( hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.26/1.69 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.26/1.69 ), X ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.69 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.26/1.69 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.69 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.26/1.69 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.69 X ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.26/1.69 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.69 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y
% 1.26/1.69 ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.26/1.69 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.26/1.69 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.26/1.69 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.26/1.69 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.69 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.26/1.69 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.26/1.69 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.26/1.69 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.69 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.69 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.26/1.69 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.26/1.69 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.26/1.69 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.69 X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.26/1.69 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.69 X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.26/1.69 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.26/1.69 ) ) ],
% 1.26/1.69 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.26/1.69 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.26/1.69 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.26/1.69 ) ) ],
% 1.26/1.69 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.26/1.69 ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.69 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.69 X ), Y ) ), Z ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.26/1.69 , Z ) ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y, hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), =( Y, Z ) ],
% 1.26/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.69 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.26/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.69 ), Y ), T ), Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.26/1.69 Y ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.26/1.69 Y ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.26/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), =( Z,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.69 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z )
% 1.26/1.69 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.26/1.69 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.69 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z )
% 1.26/1.69 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.26/1.69 X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.26/1.69 , Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ), =( Z,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z
% 1.26/1.69 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.69 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.69 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.69 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.69 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.26/1.69 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.26/1.69 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.26/1.69 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.26/1.69 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.26/1.69 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.26/1.69 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.26/1.69 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.26/1.69 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.26/1.69 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.26/1.69 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.26/1.69 'c_Finite__Set_Osetsum'( 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.26/1.69 Y, X, X, Z ), T, Z, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.26/1.69 'c_Finite__Set_Osetsum'( Y, T, Z, X ) ) ) ],
% 1.26/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), 'c_Finite__Set_Osetsum'( 'c_COMBB'(
% 1.26/1.69 'c_HOL_Oabs__class_Oabs'( X ), Y, X, X, Z ), T, Z, X ) ),
% 1.26/1.69 'c_Finite__Set_Osetsum'( 'c_COMBB'( 'c_HOL_Oabs__class_Oabs'( X ), Y, X,
% 1.26/1.69 X, Z ), T, Z, X ) ) ],
% 1.26/1.69 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.26/1.69 'c_Int_OPls', X ) ), Y ) ],
% 1.26/1.69 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.26/1.69 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.26/1.69 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.26/1.69 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.26/1.69 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.26/1.69 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.26/1.69 [ ~( =( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) )
% 1.26/1.69 , Y ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat'
% 1.26/1.69 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.26/1.69 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.26/1.69 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.26/1.69 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.26/1.69 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 X, hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.26/1.69 ), 'tc_nat' ) ) ],
% 1.26/1.69 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.26/1.69 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.26/1.69 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.26/1.69 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.26/1.69 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.26/1.69 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc',
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.26/1.69 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.26/1.69 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.26/1.69 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.26/1.69 ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.26/1.69 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.26/1.69 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.26/1.69 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc',
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.26/1.69 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 'tc_nat' ) ) ) ],
% 1.26/1.69 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.26/1.69 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.26/1.69 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.26/1.69 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.26/1.69 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.26/1.69 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', 'tc_nat' ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.26/1.69 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.26/1.69 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.26/1.69 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.26/1.69 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.26/1.69 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.26/1.69 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.26/1.69 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.26/1.69 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.26/1.69 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.26/1.69 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.26/1.69 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.26/1.69 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.26/1.69 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.26/1.69 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.26/1.69 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.26/1.69 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.26/1.69 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.26/1.69 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.26/1.69 'tc_nat' ) ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ), Y, 'tc_nat'
% 1.26/1.69 ) ) ],
% 1.26/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.26/1.69 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 1.26/1.69 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.26/1.69 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.26/1.69 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.26/1.69 ,
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ),
% 1.26/1.69 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.26/1.69 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.26/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.26/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.26/1.69 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.26/1.69 ) ), Z ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.26/1.69 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.26/1.69 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.26/1.69 , Y, 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.26/1.69 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.26/1.69 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.26/1.69 , X, 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.26/1.69 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.26/1.69 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.26/1.69 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.26/1.69 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.26/1.69 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.26/1.69 , X, 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.26/1.69 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.26/1.69 ), 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.26/1.69 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.26/1.69 ), 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.26/1.69 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.26/1.69 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.26/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.26/1.69 'tc_nat' ) ), =( Y, Z ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.26/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.26/1.69 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.26/1.69 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.69 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.26/1.69 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.26/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.26/1.69 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.26/1.69 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.26/1.69 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.26/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.26/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.26/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.69 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ),
% 1.26/1.70 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.26/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.26/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.70 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y ),
% 1.26/1.70 'tc_nat' ) ) ],
% 1.26/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.26/1.70 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 1.26/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.26/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.26/1.70 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.26/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.26/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.26/1.70 'v_m', 'tc_nat' ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( 'c_Finite__Set_Osetsum'(
% 1.26/1.70 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.26/1.70 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.70 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.26/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), 'c_HOL_Oone__class_Oone'(
% 1.26/1.70 X ) ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ),
% 1.26/1.70 'c_HOL_Oone__class_Oone'( X ) ) ) ), =( Y, 'c_HOL_Oone__class_Oone'( X )
% 1.26/1.70 ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.26/1.70 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.26/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.26/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.26/1.70 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.70 X ), T ), Z ), X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.26/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.26/1.70 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.26/1.70 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.26/1.70 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.70 ), Y ), T ), Z, X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.70 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), Z, X ) ) ]
% 1.26/1.70 ,
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.70 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.70 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ]
% 1.26/1.70 ,
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.26/1.70 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.70 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.26/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.26/1.70 ,
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.26/1.70 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.26/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.26/1.70 ,
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.26/1.70 ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.70 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.26/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.70 ), T ), Z ), X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.70 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.26/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.70 ), T ), Z ), X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.26/1.70 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.26/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.26/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.70 , Y ), T ), Z, X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.26/1.70 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.26/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.26/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.70 , Y ), T ), Z, X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), Z ) ), =( Z,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), T ) ), =( T,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.26/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.26/1.70 Y ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.26/1.70 Y ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.26/1.70 Y ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.26/1.70 Y ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.26/1.70 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.70 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.26/1.70 ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.26/1.70 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.70 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.26/1.70 ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.70 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.70 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.26/1.70 ) ],
% 1.26/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.26/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.26/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.26/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.26/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.70 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.70 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.26/1.70 T, X ) ), T, X ) ) ],
% 1.26/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.26/1.70 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.70 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.26/1.70 ) ), Z ), T, X ) ) ],
% 1.26/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.26/1.70 'c_Int_OMin', X ) ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.26/1.70 ) ],
% 1.26/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.26/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ), hAPP(
% 1.26/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.26/1.70 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.26/1.70 ,
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.26/1.70 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.26/1.70 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ),
% 1.26/1.70 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.26/1.70 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.70 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.70 'c_Power_Opower__class_Opower'( X ), Z ), Y ), X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.70 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.70 'c_Power_Opower__class_Opower'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.70 X ), X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.26/1.70 , Y ) ), Z ), X ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), =( Y,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.26/1.70 Z, 'tc_nat' ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.26/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.26/1.70 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.26/1.70 Z, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.70 X ), X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.26/1.70 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.26/1.70 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.70 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.26/1.70 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.26/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.26/1.70 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.26/1.70 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.26/1.70 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.26/1.70 'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.26/1.70 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.26/1.70 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.26/1.70 , X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.26/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.26/1.70 ), X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.26/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ), X ), ~( 'c_lessequals'( U
% 1.26/1.70 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.26/1.70 , U, X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.70 ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.26/1.70 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.26/1.70 X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.26/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.70 ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.26/1.70 , X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.26/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.26/1.70 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.26/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.26/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.70 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), U )
% 1.26/1.70 , X ), ~( 'c_lessequals'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 Y, T, X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.26/1.70 ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.26/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.26/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.26/1.70 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.26/1.70 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.26/1.70 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.26/1.70 , Y ) ), Z ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~(
% 1.26/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.26/1.70 ,
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.26/1.70 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.26/1.70 ,
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.26/1.70 ), X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.70 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), U )
% 1.26/1.70 , X ), ~( 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~(
% 1.26/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~(
% 1.26/1.70 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.26/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.26/1.70 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.26/1.70 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.26/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), Y, X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.26/1.70 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ),
% 1.26/1.70 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.26/1.70 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.26/1.70 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 1.26/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.26/1.70 X ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.26/1.70 hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP(
% 1.26/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Z
% 1.26/1.70 ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ]
% 1.26/1.70 ,
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.26/1.70 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.26/1.70 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.26/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.26/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.26/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.26/1.70 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.26/1.70 , Y ) ) ],
% 1.26/1.70 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.26/1.70 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.26/1.70 'tc_nat' ) ) ) ],
% 1.26/1.70 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.26/1.70 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.26/1.70 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.26/1.70 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.26/1.70 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.70 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.26/1.70 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.26/1.70 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.26/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.26/1.70 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.26/1.70 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.70 'tc_nat' ), 'tc_nat' ) ],
% 1.26/1.70 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.26/1.70 ), 'tc_nat' ) ) ],
% 1.26/1.70 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.26/1.70 ), 'tc_nat' ) ) ],
% 1.26/1.70 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.26/1.70 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.26/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ),
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.26/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.26/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.26/1.70 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), X ),
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.26/1.70 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.26/1.70 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.26/1.70 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.26/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.26/1.70 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.26/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.70 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.26/1.70 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.26/1.70 'tc_nat' ) ) ],
% 1.26/1.70 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.26/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.26/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.26/1.70 [ ~( 'class_RealVector_Oreal__field'( X ) ), =( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), W ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.26/1.70 X ), Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ), W ) ) ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), W ) ), U ) ) ) ],
% 1.26/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.26/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.26/1.70 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.26/1.70 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.26/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.26/1.70 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ),
% 1.26/1.70 'c_Finite__Set_Osetsum'( Y, Z, T, X ) ), 'c_Finite__Set_Osetsum'(
% 1.26/1.70 'c_COMBB'( 'c_HOL_Oabs__class_Oabs'( X ), Y, X, X, T ), Z, T, X ), X ) ]
% 1.26/1.70 ,
% 1.26/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.26/1.70 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.26/1.70 'c_Int_OMin', X ) ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.26/1.70 'c_Int_OMin', X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ]
% 1.26/1.70 ,
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.26/1.70 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.26/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.26/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ), hAPP(
% 1.26/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.26/1.70 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.26/1.70 'tc_nat' ), X ), hAPP( 'c_Suc', Y ) ), X, 'tc_nat' ), ~(
% 1.26/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.26/1.70 'tc_nat' ) ) ],
% 1.26/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.26/1.70 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.26/1.70 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 1.26/1.70 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.26/1.70 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.26/1.70 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.26/1.70 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.26/1.70 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.26/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.26/1.70 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.26/1.70 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP(
% 1.26/1.70 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 1.26/1.70 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.26/1.70 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.26/1.70 , X ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ),
% 1.26/1.70 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.26/1.70 'tc_nat' ) ) ],
% 1.26/1.70 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.26/1.70 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.26/1.70 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.26/1.70 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.26/1.70 [ =( 'c_Int_OBit1'( 'c_Int_OMin' ), 'c_Int_OMin' ) ],
% 1.26/1.70 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OMin' ) ), =( X, 'c_Int_OMin' ) ]
% 1.26/1.70 ,
% 1.26/1.70 [ ~( =( 'c_Int_OMin', 'c_Int_OBit1'( X ) ) ), =( 'c_Int_OMin', X ) ]
% 1.26/1.70 ,
% 1.26/1.70 [ =( 'c_Int_OMin', 'c_Int_OBit1'( 'c_Int_OMin' ) ) ],
% 1.26/1.70 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.26/1.70 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'(
% 1.26/1.70 X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.26/1.70 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.26/1.70 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.26/1.70 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ),
% 1.26/1.70 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.26/1.70 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 1.26/1.70 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.26/1.70 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), Y, X ) ) ]
% 1.26/1.70 ,
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.70 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.70 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.26/1.70 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.26/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.26/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.26/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.26/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.26/1.70 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.26/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.31/1.70 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.70 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.70 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.70 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.31/1.70 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.70 ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.31/1.70 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T )
% 1.31/1.70 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.31/1.70 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T )
% 1.31/1.70 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.31/1.70 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.31/1.70 ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.70 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.31/1.70 ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.31/1.70 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.31/1.70 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.31/1.70 ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.70 X ), T ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.31/1.70 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.31/1.70 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.31/1.70 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.31/1.70 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.31/1.70 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.31/1.70 ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.31/1.70 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.70 , X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.31/1.70 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ) )
% 1.31/1.70 , =( Y, T ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) )
% 1.31/1.70 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.31/1.70 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.31/1.70 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 hAPP( 'c_Suc', T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z
% 1.31/1.70 ), hAPP( 'c_Suc', T ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.31/1.70 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), X ) ), X ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.31/1.70 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.31/1.70 ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.31/1.70 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.31/1.70 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 X ), Y, X, 'tc_fun'( X, X ), Z ), T, Z, X, X ), U, Z, X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y, U, Z, X ) )
% 1.31/1.70 , 'c_Finite__Set_Osetsum'( T, U, Z, X ) ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.31/1.70 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), Z ), T, Z, X,
% 1.31/1.70 X ), U, Z, X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ),
% 1.31/1.70 'c_Finite__Set_Osetsum'( Y, U, Z, X ) ), 'c_Finite__Set_Osetsum'( T, U, Z
% 1.31/1.70 , X ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.31/1.70 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.31/1.70 ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.31/1.70 ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.31/1.70 ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.31/1.70 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ) ), 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), 'tc_nat' ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.31/1.70 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc',
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.31/1.70 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.31/1.70 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), ~(
% 1.31/1.70 'class_OrderedGroup_Omonoid__mult'( X ) ), =( 'c_Finite__Set_Osetsum'(
% 1.31/1.70 'c_COMBC'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), 'c_COMBS'(
% 1.31/1.70 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), 'c_COMBB'( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.31/1.70 , 'tc_fun'( X, X ), 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.31/1.70 , Y ), 'tc_nat', X, X ), X, 'tc_fun'( X, X ), 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), T ), 'tc_nat', X, X ),
% 1.31/1.70 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ), T, 'tc_nat' ), 'tc_nat', X ), 'c_Finite__Set_Osetsum'(
% 1.31/1.70 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' )
% 1.31/1.70 , 'c_COMBS'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), 'c_COMBB'(
% 1.31/1.70 hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.31/1.70 , 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ),
% 1.31/1.70 'tc_nat', X, X ), 'tc_nat', X, X ),
% 1.31/1.70 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ), T, 'tc_nat' ), 'tc_nat', X ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.31/1.70 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OMin', X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.31/1.70 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.31/1.70 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.70 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.70 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.70 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.70 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.70 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.70 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.70 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.70 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.31/1.70 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.31/1.70 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.70 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.70 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.70 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.31/1.70 ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), T ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.31/1.70 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.70 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.70 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.70 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.70 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.70 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.70 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.31/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~( 'c_lessequals'(
% 1.31/1.70 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 'c_lessequals'( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~( 'c_lessequals'(
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.31/1.70 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.70 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.31/1.70 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.31/1.70 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.31/1.70 , X, Z, U, W, V0 ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.31/1.70 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.31/1.70 Z, hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z,
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.31/1.70 , 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), X ), Y ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), X ), Z ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.31/1.70 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( Y ) ), Z ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), ~(
% 1.31/1.70 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ), hAPP(
% 1.31/1.70 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), 'c_Finite__Set_Osetsum'(
% 1.31/1.70 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' )
% 1.31/1.70 , 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), 'tc_nat', X, 'tc_nat' ),
% 1.31/1.70 'tc_nat', X, X ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', Z ), 'tc_nat' ),
% 1.31/1.70 'tc_nat', X ) ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.31/1.70 , Y ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.31/1.70 , X ) ), hAPP( 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.31/1.70 'tc_nat' ), X ), Y ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.31/1.70 'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 'tc_nat' ), X ), Y ) ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.31/1.70 X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 'tc_nat' ), X ), Y ) ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.31/1.70 X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.31/1.70 'c_Suc', Y ) ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ) ),
% 1.31/1.70 hAPP( 'c_Suc', Z ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.31/1.70 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z )
% 1.31/1.70 ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.31/1.70 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.31/1.70 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.31/1.70 V0, V1 ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.31/1.70 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.31/1.70 V0, V1 ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.31/1.70 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W
% 1.31/1.70 , V0, V1 ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.31/1.70 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W
% 1.31/1.70 , V0, V1 ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_Fun_Oinj__on'( 'c_Suc', X, 'tc_nat', 'tc_nat' ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.31/1.70 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =(
% 1.31/1.70 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), =( hAPP(
% 1.31/1.70 'c_Suc', X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ),
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.31/1.70 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.31/1.70 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( =( 'c_Int_OPls', 'c_Int_OMin' ) ) ],
% 1.31/1.70 [ ~( =( 'c_Int_OMin', 'c_Int_OPls' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.31/1.70 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP(
% 1.31/1.70 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.31/1.70 X ), Y ), Z ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP(
% 1.31/1.70 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), Z ) ) ],
% 1.31/1.70 [ ~( =( 'c_Int_OMin', 'c_Int_OBit0'( X ) ) ) ],
% 1.31/1.70 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OMin' ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ),
% 1.31/1.70 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 1.31/1.70 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.31/1.70 , Y ) ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ), ~(
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.70 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.31/1.70 ), Y ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.31/1.70 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.31/1.70 , Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 1.31/1.70 ), 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', Z ), Y, 'tc_nat' ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.31/1.70 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.31/1.70 , Z ) ],
% 1.31/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.31/1.70 , Z ) ],
% 1.31/1.70 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.31/1.70 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.31/1.70 ), Z ), Y ), 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.31/1.70 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.31/1.70 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.31/1.70 ), X ), Z ), 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.70 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.31/1.70 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.31/1.70 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.31/1.70 , X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.31/1.70 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y )
% 1.31/1.70 , T ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.31/1.70 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.31/1.70 X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.31/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z
% 1.31/1.70 ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.31/1.70 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.31/1.70 Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.31/1.70 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.31/1.70 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.31/1.70 , X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.31/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.70 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.31/1.70 ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.31/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.31/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.31/1.70 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.31/1.70 X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.31/1.70 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), Y ), T ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.31/1.70 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), T ), Z ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.31/1.70 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.31/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.31/1.70 Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 T, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.31/1.70 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.31/1.70 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.70 , Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.31/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.31/1.70 Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.70 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T )
% 1.31/1.70 , Z ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.70 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.31/1.70 ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.31/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T
% 1.31/1.70 ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( Y
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.31/1.70 ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.31/1.70 ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.31/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_Finite__Set_Osetsum'(
% 1.31/1.70 'c_COMBB'( 'c_HOL_Oabs__class_Oabs'( X ), Y, X, X, Z ), T, Z, X ), X ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.31/1.70 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.31/1.70 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.70 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.31/1.70 ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 'c_lessequals'( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.31/1.70 ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), T ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.31/1.70 ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.70 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.31/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z
% 1.31/1.70 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.31/1.70 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.70 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.31/1.70 ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.31/1.70 ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.70 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.31/1.70 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.31/1.70 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.31/1.70 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.31/1.70 ), Y ), hAPP( 'c_Suc', Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.31/1.70 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) )
% 1.31/1.70 ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.31/1.70 ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP(
% 1.31/1.70 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.31/1.70 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), Y ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.31/1.70 , Y ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 'tc_nat' ), X ), X ) ) ],
% 1.31/1.70 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ) ],
% 1.31/1.70 [ 'c_Fun_Oinj__on'( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X, 'tc_nat', 'tc_nat' ) ],
% 1.31/1.70 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.31/1.70 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.31/1.70 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.31/1.70 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.31/1.70 ) ), 'c_Complex_Oii' ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), X ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), X ) ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra__1'( X ) ), =(
% 1.31/1.70 'c_Series_Osuminf'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), Y, X, 'tc_fun'( X, X ), 'tc_nat' ), hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'tc_nat', X, X ), X ), hAPP( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.31/1.70 ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.31/1.70 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.31/1.70 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.31/1.70 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.31/1.70 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.31/1.70 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 X, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.31/1.70 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.31/1.70 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.31/1.70 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.31/1.70 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), X ) ],
% 1.31/1.70 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ) ), =( X,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_Fun_Oinj__on'( 'c_COMBB'( 'c_Suc', hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), X,
% 1.31/1.70 'tc_nat', 'tc_nat' ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.31/1.70 ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OMin', X ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~(
% 1.31/1.70 'class_OrderedGroup_Omonoid__mult'( X ) ), =( 'c_Finite__Set_Osetsum'(
% 1.31/1.70 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' )
% 1.31/1.70 , 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ), hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', T ) ), 'tc_nat'
% 1.31/1.70 , X, 'tc_nat' ), 'tc_nat', X, X ),
% 1.31/1.70 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ), hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), 'c_Finite__Set_Osetsum'(
% 1.31/1.70 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' )
% 1.31/1.70 , 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ), hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ),
% 1.31/1.70 'tc_nat', X, X ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', T ), 'tc_nat' ),
% 1.31/1.70 'tc_nat', X ) ) ) ],
% 1.31/1.70 [ ~( 'class_Power_Opower'( X ) ), ~(
% 1.31/1.70 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.31/1.70 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.31/1.70 X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ), hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ),
% 1.31/1.70 'tc_nat', X, X ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', T ), 'tc_nat' ),
% 1.31/1.70 'tc_nat', X ), 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_COMBB'( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.31/1.70 , 'tc_fun'( X, X ), 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.31/1.70 , Z ), 'tc_nat', X, X ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', T ), 'tc_nat' ),
% 1.31/1.70 'tc_nat', X ) ) ],
% 1.31/1.70 [ =( 'c_FFT__Mirabelle_ODFT'( X, Y, 'v_i' ), 'c_Finite__Set_Osetsum'(
% 1.31/1.70 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex'
% 1.31/1.70 ), 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'(
% 1.31/1.70 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( X ) ), hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'v_i' ), 'tc_nat',
% 1.31/1.70 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.31/1.70 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), Y, 'tc_nat',
% 1.31/1.70 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ),
% 1.31/1.70 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ), X, 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex' ) ) ],
% 1.31/1.70 [ =( 'c_FFT__Mirabelle_OIDFT'( X, Y, 'v_i' ), 'c_Finite__Set_Osetsum'(
% 1.31/1.70 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.70 'tc_Complex_Ocomplex' ), Y, 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.31/1.70 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'(
% 1.31/1.70 hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.31/1.70 'c_FFT__Mirabelle_Oroot'( X ) ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.31/1.70 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ),
% 1.31/1.70 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ), X, 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex' ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X
% 1.31/1.70 ) ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T,
% 1.31/1.70 X, X ), Z, T, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X
% 1.31/1.70 ) ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T,
% 1.31/1.70 X, X ), Z, T, X ) ) ],
% 1.31/1.70 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.31/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.31/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.31/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.31/1.70 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.31/1.70 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.70 , X ) ), Z ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.31/1.70 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.31/1.70 ), Y ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.31/1.70 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.31/1.70 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.70 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.70 , X ) ), Z ) ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.70 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.31/1.70 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 X ) ) ],
% 1.31/1.70 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.31/1.70 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.31/1.70 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ), =( Z,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.31/1.70 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) ), =( U,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.70 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.70 ), =( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), U ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.31/1.70 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.31/1.70 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.31/1.70 hAPP( 'c_Suc', Z ), hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.31/1.70 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ),
% 1.31/1.70 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.31/1.70 , X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.31/1.70 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.31/1.70 , 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.31/1.70 'c_FFT__Mirabelle_Oroot'( X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), Y ), Z ) ) ) ],
% 1.31/1.70 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.31/1.70 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.31/1.70 , Y ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.31/1.70 , Y ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Finite__Set_Osetsum'( Z, T, U
% 1.31/1.70 , X ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, U ), T, U, X ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Finite__Set_Osetsum'( Z, T, U
% 1.31/1.70 , X ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, U ), T, U, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.31/1.70 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.70 , X ) ), Z ) ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.31/1.70 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.70 , X ) ), Z ) ), Z ) ) ],
% 1.31/1.70 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.31/1.70 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), =(
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z ), =( T,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), Y ), Y ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.31/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.31/1.70 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.31/1.70 , hAPP( 'c_Suc', X ) ), Z ) ) ), =( Y, Z ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X )
% 1.31/1.70 ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T, X,
% 1.31/1.70 X ), Z, T, X ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X )
% 1.31/1.70 ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T, X,
% 1.31/1.70 X ), Z, T, X ) ) ],
% 1.31/1.70 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc'
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.31/1.70 [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 1.31/1.70 [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ), Y ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.31/1.70 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.31/1.70 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.31/1.70 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.31/1.70 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.31/1.70 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.31/1.70 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ), Z ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.31/1.70 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.31/1.70 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.31/1.70 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.31/1.70 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.31/1.70 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.31/1.70 , Y ) ],
% 1.31/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.31/1.70 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, hAPP(
% 1.31/1.70 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.31/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.31/1.70 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.31/1.70 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.31/1.70 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.31/1.70 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 hAPP( 'c_Suc', Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.31/1.70 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.31/1.70 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 1.31/1.70 , W ) ) ) ],
% 1.31/1.70 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.31/1.70 ) ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.70 ) ), =( 'c_Finite__Set_Osetsum'( Y,
% 1.31/1.70 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc',
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_nat' ), 'tc_nat', X ),
% 1.31/1.70 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.31/1.70 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), =( Z,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), =( Y,
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.71 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.31/1.71 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.31/1.71 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.31/1.71 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.71 ) ) ],
% 1.31/1.71 [ ~( =( 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.31/1.71 'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ), 'c_COMBB'(
% 1.31/1.71 'v_a', 'c_COMBB'( 'c_Suc', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.31/1.71 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat'
% 1.31/1.71 , 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.31/1.71 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'(
% 1.31/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.31/1.71 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.71 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.71 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ) ) ), 'v_i' ) ),
% 1.31/1.71 hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.31/1.71 'c_FFT__Mirabelle_Oroot'( 'v_m' ) ), 'v_i' ) ), 'tc_Complex_Ocomplex',
% 1.31/1.71 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex',
% 1.31/1.71 'tc_Complex_Ocomplex' ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'v_m', 'tc_nat' ), 'tc_nat',
% 1.31/1.71 'tc_Complex_Ocomplex' ), 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.31/1.71 'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ), 'c_COMBB'(
% 1.31/1.71 'v_a', 'c_COMBB'( 'c_Suc', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.31/1.71 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat'
% 1.31/1.71 , 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.31/1.71 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBC'(
% 1.31/1.71 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.31/1.71 'c_FFT__Mirabelle_Oroot'( 'v_m' ) ), 'v_i' ) ), 'tc_Complex_Ocomplex',
% 1.31/1.71 'tc_fun'( 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ),
% 1.31/1.71 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.31/1.71 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.71 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.71 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ) ) ), 'v_i' ),
% 1.31/1.71 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat',
% 1.31/1.71 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ),
% 1.31/1.71 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.71 'tc_nat' ), 'v_m', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex' ) ) ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ), ~(
% 1.31/1.71 'class_Lattices_Oboolean__algebra'( Y ) ) ],
% 1.31/1.71 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.31/1.71 'class_Orderings_Opreorder'( Y ) ) ],
% 1.31/1.71 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.31/1.71 'class_Orderings_Oorder'( Y ) ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.31/1.71 ],
% 1.31/1.71 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.31/1.71 ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.31/1.71 ],
% 1.31/1.71 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.31/1.71 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.31/1.71 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.31/1.71 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.31/1.71 ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.31/1.71 ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.31/1.71 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.31/1.71 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.31/1.71 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.31/1.71 ],
% 1.31/1.71 [ 'class_RealVector_Oreal__normed__algebra__1'( 'tc_Complex_Ocomplex' )
% 1.31/1.71 ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.31/1.71 ],
% 1.31/1.71 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.31/1.71 ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Complex_Ocomplex' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ 'class_RealVector_Oreal__field'( 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ],
% 1.31/1.71 [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 1.31/1.71 , W ) ) ) ],
% 1.31/1.71 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'c_fequal'( X, X, Y ) ],
% 1.31/1.71 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.31/1.71 ] .
% 1.31/1.71
% 1.31/1.71
% 1.31/1.71 percentage equality = 0.235294, percentage horn = 0.834158
% 1.31/1.71 This is a problem with some equality
% 1.31/1.71
% 1.31/1.71
% 1.31/1.71
% 1.31/1.71 Options Used:
% 1.31/1.71
% 1.31/1.71 useres = 1
% 1.31/1.71 useparamod = 1
% 1.31/1.71 useeqrefl = 1
% 1.31/1.71 useeqfact = 1
% 1.31/1.71 usefactor = 1
% 1.31/1.71 usesimpsplitting = 0
% 1.31/1.71 usesimpdemod = 5
% 1.31/1.71 usesimpres = 3
% 1.31/1.71
% 1.31/1.71 resimpinuse = 1000
% 1.31/1.71 resimpclauses = 20000
% 1.31/1.71 substype = eqrewr
% 1.31/1.71 backwardsubs = 1
% 1.31/1.71 selectoldest = 5
% 1.31/1.71
% 1.31/1.71 litorderings [0] = split
% 1.31/1.71 litorderings [1] = extend the termordering, first sorting on arguments
% 1.31/1.71
% 1.31/1.71 termordering = kbo
% 1.31/1.71
% 1.31/1.71 litapriori = 0
% 1.31/1.71 termapriori = 1
% 1.31/1.71 litaposteriori = 0
% 1.31/1.71 termaposteriori = 0
% 1.31/1.71 demodaposteriori = 0
% 1.31/1.71 ordereqreflfact = 0
% 1.31/1.71
% 1.31/1.71 litselect = negord
% 1.31/1.71
% 1.31/1.71 maxweight = 15
% 1.31/1.71 maxdepth = 30000
% 1.31/1.71 maxlength = 115
% 1.31/1.71 maxnrvars = 195
% 1.31/1.71 excuselevel = 1
% 1.31/1.71 increasemaxweight = 1
% 1.31/1.71
% 1.31/1.71 maxselected = 10000000
% 1.31/1.71 maxnrclauses = 10000000
% 1.31/1.71
% 1.31/1.71 showgenerated = 0
% 1.31/1.71 showkept = 0
% 1.31/1.71 showselected = 0
% 1.31/1.71 showdeleted = 0
% 1.31/1.71 showresimp = 1
% 1.31/1.71 showstatus = 2000
% 1.31/1.71
% 1.31/1.71 prologoutput = 1
% 1.31/1.71 nrgoals = 5000000
% 1.31/1.71 totalproof = 1
% 1.31/1.71
% 1.31/1.71 Symbols occurring in the translation:
% 1.31/1.71
% 1.31/1.71 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.31/1.71 . [1, 2] (w:1, o:157, a:1, s:1, b:0),
% 1.31/1.71 ! [4, 1] (w:0, o:72, a:1, s:1, b:0),
% 1.31/1.71 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.31/1.71 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.31/1.71 'class_OrderedGroup_Ocancel__semigroup__add' [40, 1] (w:1, o:77, a:1
% 1.31/1.71 , s:1, b:0),
% 1.31/1.71 'c_HOL_Oplus__class_Oplus' [41, 1] (w:1, o:79, a:1, s:1, b:0),
% 1.31/1.71 hAPP [43, 2] (w:1, o:182, a:1, s:1, b:0),
% 1.31/1.71 'class_OrderedGroup_Ocancel__ab__semigroup__add' [46, 1] (w:1, o:80
% 1.31/1.71 , a:1, s:1, b:0),
% 1.31/1.71 'class_Ring__and__Field_Oidom' [47, 1] (w:1, o:81, a:1, s:1, b:0),
% 1.31/1.71 'class_Int_Onumber__ring' [48, 1] (w:1, o:82, a:1, s:1, b:0),
% 1.31/1.71 'tc_nat' [52, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.31/1.71 'class_OrderedGroup_Opordered__ab__group__add__abs' [56, 1] (w:1, o:
% 1.31/1.71 84, a:1, s:1, b:0),
% 1.31/1.71 'c_HOL_Oabs__class_Oabs' [57, 1] (w:1, o:85, a:1, s:1, b:0),
% 1.31/1.71 'c_HOL_Ouminus__class_Ouminus' [58, 1] (w:1, o:87, a:1, s:1, b:0),
% 1.31/1.71 'c_lessequals' [59, 3] (w:1, o:187, a:1, s:1, b:0),
% 1.31/1.71 'class_Divides_Oring__div' [60, 1] (w:1, o:88, a:1, s:1, b:0),
% 1.31/1.71 'c_HOL_Ominus__class_Ominus' [61, 1] (w:1, o:89, a:1, s:1, b:0),
% 1.31/1.71 'c_Divides_Odiv__class_Omod' [62, 3] (w:1, o:188, a:1, s:1, b:0),
% 1.31/1.71 'c_Groebner__Basis_Ogb__semiring' [69, 6] (w:1, o:200, a:1, s:1, b:0)
% 1.31/1.71 ,
% 1.31/1.71 'class_OrderedGroup_Oab__group__add' [75, 1] (w:1, o:90, a:1, s:1, b:
% 1.83/2.18 0),
% 1.83/2.18 'class_OrderedGroup_Ogroup__add' [76, 1] (w:1, o:91, a:1, s:1, b:0),
% 1.83/2.18
% 1.83/2.18 'class_Ring__and__Field_Ocomm__semiring__1' [77, 1] (w:1, o:95, a:1
% 1.83/2.18 , s:1, b:0),
% 1.83/2.18 'class_Ring__and__Field_Oordered__field' [78, 1] (w:1, o:98, a:1, s:1
% 1.83/2.18 , b:0),
% 1.83/2.18 'c_HOL_Oinverse__class_Odivide' [79, 1] (w:1, o:99, a:1, s:1, b:0),
% 1.83/2.18 'c_HOL_Oone__class_Oone' [80, 1] (w:1, o:78, a:1, s:1, b:0),
% 1.83/2.18 'c_HOL_Oord__class_Oless' [81, 3] (w:1, o:189, a:1, s:1, b:0),
% 1.83/2.18 'c_HOL_Ozero__class_Ozero' [82, 1] (w:1, o:100, a:1, s:1, b:0),
% 1.83/2.18 'c_Parity_Oeven__odd__class_Oeven' [83, 2] (w:1, o:183, a:1, s:1, b:0
% 1.83/2.18 ),
% 1.83/2.18 'class_Ring__and__Field_Ocomm__ring__1' [84, 1] (w:1, o:92, a:1, s:1
% 1.83/2.18 , b:0),
% 1.83/2.18 'c_Power_Opower__class_Opower' [85, 1] (w:1, o:101, a:1, s:1, b:0),
% 1.83/2.18 'class_OrderedGroup_Opordered__comm__monoid__add' [86, 1] (w:1, o:102
% 1.83/2.18 , a:1, s:1, b:0),
% 1.83/2.18 'class_OrderedGroup_Opordered__ab__group__add' [87, 1] (w:1, o:103
% 1.83/2.18 , a:1, s:1, b:0),
% 1.83/2.18 'c_Suc' [89, 0] (w:1, o:47, a:1, s:1, b:0),
% 1.83/2.18 'class_OrderedGroup_Opordered__ab__semigroup__add' [90, 1] (w:1, o:
% 1.83/2.18 104, a:1, s:1, b:0),
% 1.83/2.18 hBOOL [92, 1] (w:1, o:105, a:1, s:1, b:0),
% 1.83/2.18 'c_Divides_Odiv__class_Odiv' [93, 3] (w:1, o:190, a:1, s:1, b:0),
% 1.83/2.18 'class_OrderedGroup_Olordered__ab__group__add' [94, 1] (w:1, o:106
% 1.83/2.18 , a:1, s:1, b:0),
% 1.83/2.18 'class_Divides_Osemiring__div' [95, 1] (w:1, o:107, a:1, s:1, b:0),
% 1.83/2.18 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [96, 1]
% 1.83/2.18 (w:1, o:108, a:1, s:1, b:0),
% 1.83/2.18 'class_OrderedGroup_Ocomm__monoid__add' [97, 1] (w:1, o:109, a:1, s:1
% 1.83/2.18 , b:0),
% 1.83/2.18 'class_OrderedGroup_Oordered__ab__group__add' [98, 1] (w:1, o:83, a:1
% 1.83/2.18 , s:1, b:0),
% 1.83/2.18 'class_Ring__and__Field_Oring' [99, 1] (w:1, o:110, a:1, s:1, b:0),
% 1.83/2.18 'c_HOL_Otimes__class_Otimes' [100, 1] (w:1, o:86, a:1, s:1, b:0),
% 1.83/2.18 'class_Ring__and__Field_Oordered__semidom' [102, 1] (w:1, o:112, a:1
% 1.83/2.18 , s:1, b:0),
% 1.83/2.18 'c_Int_OMin' [104, 0] (w:1, o:51, a:1, s:1, b:0),
% 1.83/2.18 'c_Int_Onumber__class_Onumber__of' [105, 2] (w:1, o:184, a:1, s:1, b:
% 1.83/2.18 0),
% 1.83/2.18 'class_Ring__and__Field_Opordered__ring' [109, 1] (w:1, o:117, a:1
% 1.83/2.18 , s:1, b:0),
% 1.83/2.18 'class_Ring__and__Field_Oordered__idom' [113, 1] (w:1, o:113, a:1, s:
% 1.83/2.18 1, b:0),
% 1.83/2.18 'class_Orderings_Oorder' [114, 1] (w:1, o:118, a:1, s:1, b:0),
% 1.83/2.18 'class_Orderings_Olinorder' [115, 1] (w:1, o:119, a:1, s:1, b:0),
% 1.83/2.18 'class_Orderings_Opreorder' [116, 1] (w:1, o:120, a:1, s:1, b:0),
% 1.83/2.18 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [117, 1]
% 1.83/2.18 (w:1, o:121, a:1, s:1, b:0),
% 1.83/2.18 'class_Int_Onumber' [120, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.83/2.18 'class_Lattices_Oboolean__algebra' [126, 1] (w:1, o:123, a:1, s:1, b:
% 1.83/2.18 0),
% 1.83/2.18 'class_OrderedGroup_Olordered__ab__group__add__abs' [127, 1] (w:1, o:
% 1.83/2.18 124, a:1, s:1, b:0),
% 1.83/2.18 'class_Ring__and__Field_Oabs__if' [128, 1] (w:1, o:125, a:1, s:1, b:0
% 1.83/2.18 ),
% 1.83/2.18 'class_Ring__and__Field_Ofield' [129, 1] (w:1, o:126, a:1, s:1, b:0)
% 1.83/2.18 ,
% 1.83/2.18 'class_Ring__and__Field_Odivision__by__zero' [130, 1] (w:1, o:128, a:
% 1.83/2.18 1, s:1, b:0),
% 1.83/2.18 'c_SetInterval_Oord__class_OatLeastLessThan' [132, 3] (w:1, o:191, a:
% 1.83/2.18 1, s:1, b:0),
% 1.83/2.18 'c_Finite__Set_Osetsum' [133, 4] (w:1, o:195, a:1, s:1, b:0),
% 1.83/2.18 'class_Ring__and__Field_Oordered__ring__strict' [134, 1] (w:1, o:111
% 1.83/2.18 , a:1, s:1, b:0),
% 1.83/2.18 'class_Ring__and__Field_Oordered__semiring__strict' [135, 1] (w:1, o:
% 1.83/2.18 114, a:1, s:1, b:0),
% 1.83/2.18 'class_Ring__and__Field_Oordered__comm__semiring__strict' [136, 1]
% 1.83/2.18 (w:1, o:115, a:1, s:1, b:0),
% 1.83/2.18 'class_Ring__and__Field_Omult__mono1' [137, 1] (w:1, o:130, a:1, s:1
% 1.83/2.18 , b:0),
% 1.83/2.18 'class_Ring__and__Field_Omult__mono' [138, 1] (w:1, o:131, a:1, s:1
% 1.83/2.18 , b:0),
% 1.83/2.18 'class_Ring__and__Field_Olordered__ring' [139, 1] (w:1, o:129, a:1
% 1.83/2.18 , s:1, b:0),
% 1.83/2.18 'class_OrderedGroup_Oab__semigroup__add' [140, 1] (w:1, o:132, a:1
% 1.83/2.18 , s:1, b:0),
% 1.83/2.18 'class_RealVector_Oreal__normed__algebra' [141, 1] (w:1, o:133, a:1
% 1.83/2.18 , s:1, b:0),
% 1.83/2.18 'class_Ring__and__Field_Opordered__cancel__semiring' [142, 1] (w:1
% 1.83/2.18 , o:134, a:1, s:1, b:0),
% 1.83/2.18 'class_Ring__and__Field_Opordered__semiring' [143, 1] (w:1, o:136, a:
% 8.58/9.01 1, s:1, b:0),
% 8.58/9.01 'class_Ring__and__Field_Osemiring' [144, 1] (w:1, o:140, a:1, s:1, b:
% 8.58/9.01 0),
% 8.58/9.01 'class_Ring__and__Field_Ozero__neq__one' [145, 1] (w:1, o:141, a:1
% 8.58/9.01 , s:1, b:0),
% 8.58/9.01 'class_OrderedGroup_Omonoid__add' [146, 1] (w:1, o:142, a:1, s:1, b:0
% 8.58/9.01 ),
% 8.58/9.01 'class_Ring__and__Field_Opordered__ring__abs' [147, 1] (w:1, o:135
% 8.58/9.01 , a:1, s:1, b:0),
% 8.58/9.01 'class_Ring__and__Field_Oordered__semiring' [148, 1] (w:1, o:116, a:1
% 8.58/9.01 , s:1, b:0),
% 8.58/9.01 'class_Ring__and__Field_Ocomm__semiring' [149, 1] (w:1, o:127, a:1
% 8.58/9.01 , s:1, b:0),
% 8.58/9.01 'class_OrderedGroup_Omonoid__mult' [151, 1] (w:1, o:143, a:1, s:1, b:
% 8.58/9.01 0),
% 8.58/9.01 'c_COMBB' [153, 5] (w:1, o:197, a:1, s:1, b:0),
% 8.58/9.01 'c_Int_OPls' [155, 0] (w:1, o:56, a:1, s:1, b:0),
% 8.58/9.01 'class_Power_Opower' [156, 1] (w:1, o:147, a:1, s:1, b:0),
% 8.58/9.01 'c_Int_OBit1' [157, 1] (w:1, o:149, a:1, s:1, b:0),
% 8.58/9.01 'c_Int_OBit0' [158, 1] (w:1, o:148, a:1, s:1, b:0),
% 8.58/9.01 'v_m' [159, 0] (w:1, o:57, a:1, s:1, b:0),
% 8.58/9.01 'class_OrderedGroup_Ocomm__monoid__mult' [160, 1] (w:1, o:144, a:1
% 8.58/9.01 , s:1, b:0),
% 8.58/9.01 'class_Ring__and__Field_Oring__1' [161, 1] (w:1, o:137, a:1, s:1, b:0
% 8.58/9.01 ),
% 8.58/9.01 'class_RealVector_Oreal__field' [162, 1] (w:1, o:150, a:1, s:1, b:0)
% 8.58/9.01 ,
% 8.58/9.01 'class_Ring__and__Field_Osemiring__0' [164, 1] (w:1, o:151, a:1, s:1
% 8.58/9.01 , b:0),
% 8.58/9.01 'tc_fun' [165, 2] (w:1, o:185, a:1, s:1, b:0),
% 8.58/9.01 'c_COMBS' [167, 5] (w:1, o:198, a:1, s:1, b:0),
% 8.58/9.01 'class_Ring__and__Field_Ocomm__ring' [168, 1] (w:1, o:93, a:1, s:1
% 8.58/9.01 , b:0),
% 8.58/9.01 'c_COMBC' [169, 5] (w:1, o:199, a:1, s:1, b:0),
% 8.58/9.01 'tc_Complex_Ocomplex' [170, 0] (w:1, o:58, a:1, s:1, b:0),
% 8.58/9.01 'c_FFT__Mirabelle_Oroot' [171, 1] (w:1, o:152, a:1, s:1, b:0),
% 8.58/9.01 'c_Fun_Oinj__on' [172, 4] (w:1, o:196, a:1, s:1, b:0),
% 8.58/9.01 'class_RealVector_Oreal__normed__field' [173, 1] (w:1, o:153, a:1, s:
% 8.58/9.01 1, b:0),
% 8.58/9.01 'class_Ring__and__Field_Osemiring__1' [174, 1] (w:1, o:154, a:1, s:1
% 8.58/9.01 , b:0),
% 8.58/9.01 'c_Complex_Oii' [175, 0] (w:1, o:59, a:1, s:1, b:0),
% 8.58/9.01 'class_RealVector_Oreal__normed__algebra__1' [176, 1] (w:1, o:155, a:
% 8.58/9.01 1, s:1, b:0),
% 8.58/9.01 'c_Series_Osuminf' [177, 2] (w:1, o:186, a:1, s:1, b:0),
% 8.58/9.01 'class_Ring__and__Field_Ocomm__semiring__0' [178, 1] (w:1, o:94, a:1
% 8.58/9.01 , s:1, b:0),
% 8.58/9.01 'v_i' [179, 0] (w:1, o:60, a:1, s:1, b:0),
% 8.58/9.01 'c_FFT__Mirabelle_ODFT' [180, 3] (w:1, o:192, a:1, s:1, b:0),
% 8.58/9.01 'c_FFT__Mirabelle_OIDFT' [181, 3] (w:1, o:193, a:1, s:1, b:0),
% 8.58/9.01 'class_Ring__and__Field_Ono__zero__divisors' [184, 1] (w:1, o:97, a:1
% 8.58/9.01 , s:1, b:0),
% 8.58/9.01 'class_Ring__and__Field_Omult__zero' [185, 1] (w:1, o:96, a:1, s:1
% 8.58/9.01 , b:0),
% 8.58/9.01 'class_Ring__and__Field_Oring__no__zero__divisors' [186, 1] (w:1, o:
% 8.58/9.01 138, a:1, s:1, b:0),
% 8.58/9.01 'class_OrderedGroup_Oab__semigroup__mult' [187, 1] (w:1, o:145, a:1
% 8.58/9.01 , s:1, b:0),
% 8.58/9.01 'class_OrderedGroup_Oab__semigroup__idem__mult' [188, 1] (w:1, o:146
% 8.58/9.01 , a:1, s:1, b:0),
% 8.58/9.01 'class_Ring__and__Field_Oring__1__no__zero__divisors' [189, 1] (w:1
% 8.58/9.01 , o:139, a:1, s:1, b:0),
% 8.58/9.01 'class_Int_Oring__char__0' [193, 1] (w:1, o:156, a:1, s:1, b:0),
% 8.58/9.01 'v_a' [194, 0] (w:1, o:66, a:1, s:1, b:0),
% 8.58/9.01 'tc_Int_Oint' [197, 0] (w:1, o:69, a:1, s:1, b:0),
% 8.58/9.01 'c_fequal' [198, 3] (w:1, o:194, a:1, s:1, b:0).
% 8.58/9.01
% 8.58/9.01
% 8.58/9.01 Starting Search:
% 8.58/9.01
% 8.58/9.01 Resimplifying inuse:
% 8.58/9.01 Done
% 8.58/9.01
% 8.58/9.01
% 8.58/9.01 Intermediate Status:
% 8.58/9.01 Generated: 4644
% 8.58/9.01 Kept: 2053
% 8.58/9.01 Inuse: 65
% 8.58/9.01 Deleted: 1
% 8.58/9.01 Deletedinuse: 0
% 8.58/9.01
% 8.58/9.01 Resimplifying inuse:
% 8.58/9.01 Done
% 8.58/9.01
% 8.58/9.01 Resimplifying inuse:
% 8.58/9.01 Done
% 8.58/9.01
% 8.58/9.01
% 8.58/9.01 Intermediate Status:
% 8.58/9.01 Generated: 12243
% 8.58/9.01 Kept: 4263
% 8.58/9.01 Inuse: 150
% 8.58/9.01 Deleted: 1
% 8.58/9.01 Deletedinuse: 0
% 8.58/9.01
% 8.58/9.01 Resimplifying inuse:
% 8.58/9.01 Done
% 8.58/9.01
% 8.58/9.01 Resimplifying inuse:
% 8.58/9.01 Done
% 8.58/9.01
% 8.58/9.01
% 8.58/9.01 Intermediate Status:
% 8.58/9.01 Generated: 21138
% 8.58/9.01 Kept: 6621
% 8.58/9.01 Inuse: 270
% 8.58/9.01 Deleted: 6
% 8.58/9.01 Deletedinuse: 0
% 8.58/9.01
% 8.58/9.01 Resimplifying inuse:
% 8.58/9.01 Done
% 8.58/9.01
% 8.58/9.01 Resimplifying inuse:
% 8.58/9.01 Done
% 8.58/9.01
% 8.58/9.01
% 8.58/9.01 Intermediate Status:
% 8.58/9.01 Generated: 27758
% 8.58/9.01 Kept: 8682
% 8.58/9.01 Inuse: 368
% 8.58/9.01 Deleted: 8
% 8.58/9.01 Deletedinuse: 0
% 8.58/9.01
% 8.58/9.01 Resimplifying inuse:
% 8.58/9.01 Done
% 8.58/9.01
% 8.58/9.01
% 8.58/9.01 Intermediate Status:
% 8.58/9.01 Generated: 33655
% 8.58/9.01 Kept: 11167
% 8.58/9.01 Inuse: 388
% 8.58/9.01 Deleted: 8
% 8.58/9.01 Deletedinuse: 0
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 41313
% 29.04/29.46 Kept: 13414
% 29.04/29.46 Inuse: 456
% 29.04/29.46 Deleted: 10
% 29.04/29.46 Deletedinuse: 0
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 46211
% 29.04/29.46 Kept: 15588
% 29.04/29.46 Inuse: 491
% 29.04/29.46 Deleted: 10
% 29.04/29.46 Deletedinuse: 0
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 52560
% 29.04/29.46 Kept: 18071
% 29.04/29.46 Inuse: 511
% 29.04/29.46 Deleted: 11
% 29.04/29.46 Deletedinuse: 1
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying clauses:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 57840
% 29.04/29.46 Kept: 20087
% 29.04/29.46 Inuse: 570
% 29.04/29.46 Deleted: 708
% 29.04/29.46 Deletedinuse: 1
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 64903
% 29.04/29.46 Kept: 22143
% 29.04/29.46 Inuse: 644
% 29.04/29.46 Deleted: 709
% 29.04/29.46 Deletedinuse: 1
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 74569
% 29.04/29.46 Kept: 24838
% 29.04/29.46 Inuse: 674
% 29.04/29.46 Deleted: 709
% 29.04/29.46 Deletedinuse: 1
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 81024
% 29.04/29.46 Kept: 26991
% 29.04/29.46 Inuse: 689
% 29.04/29.46 Deleted: 709
% 29.04/29.46 Deletedinuse: 1
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 87311
% 29.04/29.46 Kept: 29525
% 29.04/29.46 Inuse: 714
% 29.04/29.46 Deleted: 710
% 29.04/29.46 Deletedinuse: 2
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 92118
% 29.04/29.46 Kept: 31554
% 29.04/29.46 Inuse: 719
% 29.04/29.46 Deleted: 710
% 29.04/29.46 Deletedinuse: 2
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 100028
% 29.04/29.46 Kept: 33561
% 29.04/29.46 Inuse: 759
% 29.04/29.46 Deleted: 710
% 29.04/29.46 Deletedinuse: 2
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 104311
% 29.04/29.46 Kept: 35661
% 29.04/29.46 Inuse: 774
% 29.04/29.46 Deleted: 710
% 29.04/29.46 Deletedinuse: 2
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 111573
% 29.04/29.46 Kept: 37663
% 29.04/29.46 Inuse: 812
% 29.04/29.46 Deleted: 710
% 29.04/29.46 Deletedinuse: 2
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 118461
% 29.04/29.46 Kept: 39862
% 29.04/29.46 Inuse: 854
% 29.04/29.46 Deleted: 710
% 29.04/29.46 Deletedinuse: 2
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying clauses:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 124521
% 29.04/29.46 Kept: 41865
% 29.04/29.46 Inuse: 889
% 29.04/29.46 Deleted: 1436
% 29.04/29.46 Deletedinuse: 2
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 138175
% 29.04/29.46 Kept: 44418
% 29.04/29.46 Inuse: 899
% 29.04/29.46 Deleted: 1436
% 29.04/29.46 Deletedinuse: 2
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 153098
% 29.04/29.46 Kept: 47779
% 29.04/29.46 Inuse: 909
% 29.04/29.46 Deleted: 1436
% 29.04/29.46 Deletedinuse: 2
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 166885
% 29.04/29.46 Kept: 50167
% 29.04/29.46 Inuse: 919
% 29.04/29.46 Deleted: 1436
% 29.04/29.46 Deletedinuse: 2
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 173694
% 29.04/29.46 Kept: 52269
% 29.04/29.46 Inuse: 939
% 29.04/29.46 Deleted: 1436
% 29.04/29.46 Deletedinuse: 2
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 188502
% 29.04/29.46 Kept: 55378
% 29.04/29.46 Inuse: 984
% 29.04/29.46 Deleted: 1436
% 29.04/29.46 Deletedinuse: 2
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 198258
% 29.04/29.46 Kept: 57514
% 29.04/29.46 Inuse: 1004
% 29.04/29.46 Deleted: 1436
% 29.04/29.46 Deletedinuse: 2
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 205489
% 29.04/29.46 Kept: 59737
% 29.04/29.46 Inuse: 1024
% 29.04/29.46 Deleted: 1436
% 29.04/29.46 Deletedinuse: 2
% 29.04/29.46
% 29.04/29.46 Resimplifying clauses:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 214952
% 29.04/29.46 Kept: 61761
% 29.04/29.46 Inuse: 1059
% 29.04/29.46 Deleted: 1582
% 29.04/29.46 Deletedinuse: 3
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 223514
% 29.04/29.46 Kept: 63925
% 29.04/29.46 Inuse: 1092
% 29.04/29.46 Deleted: 1585
% 29.04/29.46 Deletedinuse: 4
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 232539
% 29.04/29.46 Kept: 65926
% 29.04/29.46 Inuse: 1124
% 29.04/29.46 Deleted: 1585
% 29.04/29.46 Deletedinuse: 4
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46 Resimplifying inuse:
% 29.04/29.46 Done
% 29.04/29.46
% 29.04/29.46
% 29.04/29.46 Intermediate Status:
% 29.04/29.46 Generated: 242390
% 29.04/29.46 Kept: 68012
% 66.60/67.00 Inuse: 1162
% 66.60/67.00 Deleted: 1585
% 66.60/67.00 Deletedinuse: 4
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 251217
% 66.60/67.00 Kept: 70040
% 66.60/67.00 Inuse: 1192
% 66.60/67.00 Deleted: 1585
% 66.60/67.00 Deletedinuse: 4
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 263819
% 66.60/67.00 Kept: 72078
% 66.60/67.00 Inuse: 1242
% 66.60/67.00 Deleted: 1585
% 66.60/67.00 Deletedinuse: 4
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 273678
% 66.60/67.00 Kept: 74289
% 66.60/67.00 Inuse: 1277
% 66.60/67.00 Deleted: 1585
% 66.60/67.00 Deletedinuse: 4
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 282759
% 66.60/67.00 Kept: 76370
% 66.60/67.00 Inuse: 1302
% 66.60/67.00 Deleted: 1585
% 66.60/67.00 Deletedinuse: 4
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 287627
% 66.60/67.00 Kept: 78389
% 66.60/67.00 Inuse: 1305
% 66.60/67.00 Deleted: 1585
% 66.60/67.00 Deletedinuse: 4
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 295463
% 66.60/67.00 Kept: 80451
% 66.60/67.00 Inuse: 1327
% 66.60/67.00 Deleted: 1585
% 66.60/67.00 Deletedinuse: 4
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00 Resimplifying clauses:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 304480
% 66.60/67.00 Kept: 82895
% 66.60/67.00 Inuse: 1342
% 66.60/67.00 Deleted: 2082
% 66.60/67.00 Deletedinuse: 4
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 312500
% 66.60/67.00 Kept: 84915
% 66.60/67.00 Inuse: 1355
% 66.60/67.00 Deleted: 2085
% 66.60/67.00 Deletedinuse: 7
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 321001
% 66.60/67.00 Kept: 86960
% 66.60/67.00 Inuse: 1382
% 66.60/67.00 Deleted: 2085
% 66.60/67.00 Deletedinuse: 7
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 328774
% 66.60/67.00 Kept: 89260
% 66.60/67.00 Inuse: 1402
% 66.60/67.00 Deleted: 2085
% 66.60/67.00 Deletedinuse: 7
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 335880
% 66.60/67.00 Kept: 91278
% 66.60/67.00 Inuse: 1426
% 66.60/67.00 Deleted: 2085
% 66.60/67.00 Deletedinuse: 7
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 343708
% 66.60/67.00 Kept: 93293
% 66.60/67.00 Inuse: 1456
% 66.60/67.00 Deleted: 2090
% 66.60/67.00 Deletedinuse: 12
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 351841
% 66.60/67.00 Kept: 95470
% 66.60/67.00 Inuse: 1487
% 66.60/67.00 Deleted: 2090
% 66.60/67.00 Deletedinuse: 12
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 361895
% 66.60/67.00 Kept: 97480
% 66.60/67.00 Inuse: 1520
% 66.60/67.00 Deleted: 2090
% 66.60/67.00 Deletedinuse: 12
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 378028
% 66.60/67.00 Kept: 99790
% 66.60/67.00 Inuse: 1557
% 66.60/67.00 Deleted: 2090
% 66.60/67.00 Deletedinuse: 12
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00 Resimplifying clauses:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 388127
% 66.60/67.00 Kept: 101791
% 66.60/67.00 Inuse: 1595
% 66.60/67.00 Deleted: 3146
% 66.60/67.00 Deletedinuse: 13
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 397125
% 66.60/67.00 Kept: 104140
% 66.60/67.00 Inuse: 1621
% 66.60/67.00 Deleted: 3148
% 66.60/67.00 Deletedinuse: 14
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 413569
% 66.60/67.00 Kept: 107988
% 66.60/67.00 Inuse: 1656
% 66.60/67.00 Deleted: 3149
% 66.60/67.00 Deletedinuse: 15
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 423781
% 66.60/67.00 Kept: 110161
% 66.60/67.00 Inuse: 1691
% 66.60/67.00 Deleted: 3149
% 66.60/67.00 Deletedinuse: 15
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 439414
% 66.60/67.00 Kept: 112177
% 66.60/67.00 Inuse: 1704
% 66.60/67.00 Deleted: 3153
% 66.60/67.00 Deletedinuse: 16
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 448005
% 66.60/67.00 Kept: 114442
% 66.60/67.00 Inuse: 1734
% 66.60/67.00 Deleted: 3158
% 66.60/67.00 Deletedinuse: 17
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 491915
% 66.60/67.00 Kept: 120043
% 66.60/67.00 Inuse: 1764
% 66.60/67.00 Deleted: 3158
% 66.60/67.00 Deletedinuse: 17
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 500398
% 66.60/67.00 Kept: 122308
% 66.60/67.00 Inuse: 1769
% 66.60/67.00 Deleted: 3158
% 66.60/67.00 Deletedinuse: 17
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00 Resimplifying clauses:
% 66.60/67.00 Done
% 66.60/67.00
% 66.60/67.00
% 66.60/67.00 Intermediate Status:
% 66.60/67.00 Generated: 509326
% 66.60/67.00 Kept: 124583
% 66.60/67.00 Inuse: 1774
% 66.60/67.00 Deleted: 4436
% 66.60/67.00 Deletedinuse: 17
% 66.60/67.00
% 66.60/67.00 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 520696
% 155.96/156.44 Kept: 126717
% 155.96/156.44 Inuse: 1804
% 155.96/156.44 Deleted: 4436
% 155.96/156.44 Deletedinuse: 17
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 538010
% 155.96/156.44 Kept: 129041
% 155.96/156.44 Inuse: 1833
% 155.96/156.44 Deleted: 4440
% 155.96/156.44 Deletedinuse: 20
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 547338
% 155.96/156.44 Kept: 131244
% 155.96/156.44 Inuse: 1838
% 155.96/156.44 Deleted: 4440
% 155.96/156.44 Deletedinuse: 20
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 556910
% 155.96/156.44 Kept: 133486
% 155.96/156.44 Inuse: 1843
% 155.96/156.44 Deleted: 4440
% 155.96/156.44 Deletedinuse: 20
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 567073
% 155.96/156.44 Kept: 135559
% 155.96/156.44 Inuse: 1868
% 155.96/156.44 Deleted: 4440
% 155.96/156.44 Deletedinuse: 20
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 577837
% 155.96/156.44 Kept: 137884
% 155.96/156.44 Inuse: 1898
% 155.96/156.44 Deleted: 4440
% 155.96/156.44 Deletedinuse: 20
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 587775
% 155.96/156.44 Kept: 140376
% 155.96/156.44 Inuse: 1918
% 155.96/156.44 Deleted: 4440
% 155.96/156.44 Deletedinuse: 20
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 603912
% 155.96/156.44 Kept: 144557
% 155.96/156.44 Inuse: 1938
% 155.96/156.44 Deleted: 4440
% 155.96/156.44 Deletedinuse: 20
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44 Resimplifying clauses:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 613221
% 155.96/156.44 Kept: 146815
% 155.96/156.44 Inuse: 1963
% 155.96/156.44 Deleted: 5067
% 155.96/156.44 Deletedinuse: 20
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 622609
% 155.96/156.44 Kept: 148827
% 155.96/156.44 Inuse: 1985
% 155.96/156.44 Deleted: 5067
% 155.96/156.44 Deletedinuse: 20
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 640804
% 155.96/156.44 Kept: 153101
% 155.96/156.44 Inuse: 2008
% 155.96/156.44 Deleted: 5067
% 155.96/156.44 Deletedinuse: 20
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 650632
% 155.96/156.44 Kept: 155107
% 155.96/156.44 Inuse: 2031
% 155.96/156.44 Deleted: 5067
% 155.96/156.44 Deletedinuse: 20
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 659648
% 155.96/156.44 Kept: 157296
% 155.96/156.44 Inuse: 2048
% 155.96/156.44 Deleted: 5067
% 155.96/156.44 Deletedinuse: 20
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 694561
% 155.96/156.44 Kept: 163649
% 155.96/156.44 Inuse: 2053
% 155.96/156.44 Deleted: 5067
% 155.96/156.44 Deletedinuse: 20
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44 Resimplifying clauses:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 706928
% 155.96/156.44 Kept: 165925
% 155.96/156.44 Inuse: 2073
% 155.96/156.44 Deleted: 5184
% 155.96/156.44 Deletedinuse: 20
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 718737
% 155.96/156.44 Kept: 168901
% 155.96/156.44 Inuse: 2083
% 155.96/156.44 Deleted: 5184
% 155.96/156.44 Deletedinuse: 20
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 734506
% 155.96/156.44 Kept: 172886
% 155.96/156.44 Inuse: 2108
% 155.96/156.44 Deleted: 5184
% 155.96/156.44 Deletedinuse: 20
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 744804
% 155.96/156.44 Kept: 175517
% 155.96/156.44 Inuse: 2113
% 155.96/156.44 Deleted: 5185
% 155.96/156.44 Deletedinuse: 21
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 758063
% 155.96/156.44 Kept: 178389
% 155.96/156.44 Inuse: 2128
% 155.96/156.44 Deleted: 5185
% 155.96/156.44 Deletedinuse: 21
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 773824
% 155.96/156.44 Kept: 181858
% 155.96/156.44 Inuse: 2148
% 155.96/156.44 Deleted: 5185
% 155.96/156.44 Deletedinuse: 21
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 797288
% 155.96/156.44 Kept: 187130
% 155.96/156.44 Inuse: 2168
% 155.96/156.44 Deleted: 5185
% 155.96/156.44 Deletedinuse: 21
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44 Resimplifying clauses:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 816097
% 155.96/156.44 Kept: 191566
% 155.96/156.44 Inuse: 2173
% 155.96/156.44 Deleted: 5508
% 155.96/156.44 Deletedinuse: 22
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 834783
% 155.96/156.44 Kept: 195914
% 155.96/156.44 Inuse: 2178
% 155.96/156.44 Deleted: 5508
% 155.96/156.44 Deletedinuse: 22
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 845730
% 155.96/156.44 Kept: 197923
% 155.96/156.44 Inuse: 2205
% 155.96/156.44 Deleted: 5508
% 155.96/156.44 Deletedinuse: 22
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44 Resimplifying inuse:
% 155.96/156.44 Done
% 155.96/156.44
% 155.96/156.44
% 155.96/156.44 Intermediate Status:
% 155.96/156.44 Generated: 856418
% 155.96/156.44 Kept: 200160
% 155.96/156.44 Inuse: 2218
% 296.48/296.90 Deleted: 5508
% 296.48/296.90 Deletedinuse: 22
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 870721
% 296.48/296.90 Kept: 203536
% 296.48/296.90 Inuse: 2228
% 296.48/296.90 Deleted: 5508
% 296.48/296.90 Deletedinuse: 22
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 883007
% 296.48/296.90 Kept: 206348
% 296.48/296.90 Inuse: 2233
% 296.48/296.90 Deleted: 5508
% 296.48/296.90 Deletedinuse: 22
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90 Resimplifying clauses:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 895233
% 296.48/296.90 Kept: 208572
% 296.48/296.90 Inuse: 2252
% 296.48/296.90 Deleted: 5754
% 296.48/296.90 Deletedinuse: 22
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 905243
% 296.48/296.90 Kept: 210745
% 296.48/296.90 Inuse: 2266
% 296.48/296.90 Deleted: 5756
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 915357
% 296.48/296.90 Kept: 213126
% 296.48/296.90 Inuse: 2286
% 296.48/296.90 Deleted: 5756
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 923384
% 296.48/296.90 Kept: 215187
% 296.48/296.90 Inuse: 2301
% 296.48/296.90 Deleted: 5756
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 932301
% 296.48/296.90 Kept: 217601
% 296.48/296.90 Inuse: 2316
% 296.48/296.90 Deleted: 5756
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 939459
% 296.48/296.90 Kept: 219604
% 296.48/296.90 Inuse: 2331
% 296.48/296.90 Deleted: 5756
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 959028
% 296.48/296.90 Kept: 224057
% 296.48/296.90 Inuse: 2346
% 296.48/296.90 Deleted: 5756
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 972972
% 296.48/296.90 Kept: 227178
% 296.48/296.90 Inuse: 2351
% 296.48/296.90 Deleted: 5756
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 987076
% 296.48/296.90 Kept: 230381
% 296.48/296.90 Inuse: 2356
% 296.48/296.90 Deleted: 5756
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90 Resimplifying clauses:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 1000503
% 296.48/296.90 Kept: 233598
% 296.48/296.90 Inuse: 2361
% 296.48/296.90 Deleted: 6492
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 1011963
% 296.48/296.90 Kept: 236045
% 296.48/296.90 Inuse: 2386
% 296.48/296.90 Deleted: 6492
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 1087876
% 296.48/296.90 Kept: 243521
% 296.48/296.90 Inuse: 2391
% 296.48/296.90 Deleted: 6492
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 1097483
% 296.48/296.90 Kept: 245642
% 296.48/296.90 Inuse: 2411
% 296.48/296.90 Deleted: 6492
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 1107107
% 296.48/296.90 Kept: 248125
% 296.48/296.90 Inuse: 2431
% 296.48/296.90 Deleted: 6492
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 1116034
% 296.48/296.90 Kept: 250370
% 296.48/296.90 Inuse: 2451
% 296.48/296.90 Deleted: 6492
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying clauses:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 1167291
% 296.48/296.90 Kept: 258024
% 296.48/296.90 Inuse: 2456
% 296.48/296.90 Deleted: 6628
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 1176516
% 296.48/296.90 Kept: 260038
% 296.48/296.90 Inuse: 2479
% 296.48/296.90 Deleted: 6628
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 1184804
% 296.48/296.90 Kept: 262402
% 296.48/296.90 Inuse: 2491
% 296.48/296.90 Deleted: 6628
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 1198746
% 296.48/296.90 Kept: 265564
% 296.48/296.90 Inuse: 2496
% 296.48/296.90 Deleted: 6628
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 1206683
% 296.48/296.90 Kept: 267583
% 296.48/296.90 Inuse: 2511
% 296.48/296.90 Deleted: 6628
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 1217506
% 296.48/296.90 Kept: 270063
% 296.48/296.90 Inuse: 2531
% 296.48/296.90 Deleted: 6628
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90 Resimplifying clauses:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 1224845
% 296.48/296.90 Kept: 272198
% 296.48/296.90 Inuse: 2546
% 296.48/296.90 Deleted: 6683
% 296.48/296.90 Deletedinuse: 23
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90 Resimplifying inuse:
% 296.48/296.90 Done
% 296.48/296.90
% 296.48/296.90
% 296.48/296.90 Intermediate Status:
% 296.48/296.90 Generated: 1234473
% 296.48/296.90 Kept: 274207
% 296.48/296.90 Inuse: 2569
% 296.48/296.90 DelCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------