TSTP Solution File: SWV662-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV662-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n006.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 16:27:35 EDT 2022
% Result : Timeout 300.06s 300.42s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV662-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.35 % Computer : n006.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 : Wed Jun 15 20:55:41 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.32/1.70 *** allocated 10000 integers for termspace/termends
% 1.32/1.70 *** allocated 10000 integers for clauses
% 1.32/1.70 *** allocated 10000 integers for justifications
% 1.32/1.70 *** allocated 15000 integers for termspace/termends
% 1.32/1.70 *** allocated 22500 integers for termspace/termends
% 1.32/1.70 *** allocated 33750 integers for termspace/termends
% 1.32/1.70 *** allocated 50625 integers for termspace/termends
% 1.32/1.70 Bliksem 1.12
% 1.32/1.70
% 1.32/1.70
% 1.32/1.70 Automatic Strategy Selection
% 1.32/1.70
% 1.32/1.70 Clauses:
% 1.32/1.70 [
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.32/1.70 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.70 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.32/1.70 ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.70 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.32/1.70 ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 1.32/1.70 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.32/1.70 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.32/1.70 V0, V1 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.32/1.70 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.32/1.70 V0, V1 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.32/1.70 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W
% 1.32/1.70 , V0, V1 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.32/1.70 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W
% 1.32/1.70 , V0, V1 ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =( hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.70 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.32/1.70 , Z ) ) ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.70 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =( hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.70 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.32/1.70 , Z ) ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.32/1.70 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =( hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.70 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.32/1.70 , Z ) ) ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.70 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =( hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.70 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.32/1.70 , Z ) ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.32/1.70 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.70 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.70 hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Oabs__class_Oabs'(
% 1.32/1.70 X ), T ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), Y ), Y ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.32/1.70 ), =( Z, Y ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.32/1.70 ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.32/1.70 ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.32/1.70 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.32/1.70 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.32/1.70 'class_RealVector_Oreal__normed__algebra__1'( Y ) ), =( Z, T ), ~(
% 1.32/1.70 'c_Lim_OLIM'( U, W, T, Y, X ) ), ~( 'c_Lim_OLIM'( U, W, Z, Y, X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.32/1.70 , Y, 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), =( Y, X ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ],
% 1.32/1.70 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.32/1.70 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.32/1.70 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.32/1.70 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.32/1.70 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.32/1.70 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =( hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.32/1.70 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 1.32/1.70 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), T ) ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), Z, X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.32/1.70 ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.70 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.70 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.70 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.70 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.32/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z
% 1.32/1.70 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.70 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.32/1.70 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.70 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.70 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.70 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.32/1.70 ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.70 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.70 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.70 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.32/1.70 ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), T ),
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.70 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.32/1.70 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.70 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.32/1.70 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.32/1.70 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 'tc_nat' ) ) ],
% 1.32/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.70 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.70 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.32/1.70 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X
% 1.32/1.70 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.32/1.70 ), Y ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.70 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.70 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.70 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.32/1.70 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.70 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.70 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.70 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.32/1.70 ~( 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.32/1.70 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.32/1.70 Z, hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z,
% 1.32/1.70 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.70 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.32/1.70 ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.32/1.70 ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.32/1.70 ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.70 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.70 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y, X,
% 1.32/1.70 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 1.32/1.70 [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.70 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.70 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.70 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.70 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.32/1.70 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.32/1.70 Z, hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.32/1.70 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.32/1.70 , X ) ), hAPP( Y, T ) ) ), 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.32/1.70 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.32/1.70 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.32/1.70 'c_SetInterval_Oord__class_OatLeastLessThan'( T, U, 'tc_nat' ), 'tc_nat'
% 1.32/1.70 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.32/1.70 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ), 'tc_nat'
% 1.32/1.70 , X ) ), ~( 'c_lessequals'( T, U, 'tc_nat' ) ), ~( 'c_lessequals'( Z, T,
% 1.32/1.70 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.32/1.70 Z, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.70 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.32/1.70 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.70 T, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.70 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'( Y
% 1.32/1.70 , T, X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.32/1.70 ), ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP(
% 1.32/1.70 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.32/1.70 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.32/1.70 , X ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ),
% 1.32/1.70 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.70 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.32/1.70 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.32/1.70 Z, T, 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.70 X ), hAPP( Y, Z ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.32/1.70 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', Z ), T,
% 1.32/1.70 'tc_nat' ), 'tc_nat', X ) ) ), ~( 'c_HOL_Oord__class_Oless'( Z, T,
% 1.32/1.70 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.70 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.70 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.32/1.70 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.32/1.70 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.32/1.70 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.32/1.70 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.32/1.70 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.70 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.32/1.70 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.32/1.70 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.32/1.70 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.32/1.70 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.32/1.70 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.32/1.70 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.70 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.32/1.70 ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.70 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z
% 1.32/1.70 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) )
% 1.32/1.70 ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.70 'v_m', 'tc_nat' ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.70 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.32/1.70 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.70 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.70 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.70 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.70 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.32/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.70 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.70 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.32/1.70 , Z ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), X ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.32/1.70 ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.70 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), U )
% 1.32/1.70 , X ), ~( 'c_lessequals'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 Y, T, X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.32/1.70 ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.32/1.70 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.32/1.70 , 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.32/1.70 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.32/1.70 , 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.32/1.70 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.32/1.70 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.32/1.70 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( Z
% 1.32/1.70 , T, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.32/1.70 X ), Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.70 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.70 X ), Y ), Z ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.70 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.70 X ), Z ), Y ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.70 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.70 X ), Y ), Z ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.70 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.70 X ), Z ), Y ), X ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.32/1.70 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.32/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc',
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y ) ), =( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 'tc_nat' ) ), X ) ],
% 1.32/1.70 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.70 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( 'c_Suc',
% 1.32/1.70 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ), 'tc_nat' ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.32/1.70 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.32/1.70 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.32/1.70 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.32/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.70 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.70 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.32/1.70 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.70 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.70 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.32/1.70 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.32/1.70 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.70 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.70 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.70 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.70 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.70 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.32/1.70 , hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.32/1.70 , Y ) ), Z ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.70 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.32/1.70 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.70 ), Y ), T ), Z, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.70 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.32/1.70 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.70 X ), T ), Z ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.32/1.70 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X
% 1.32/1.70 ), Y ), Z, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.32/1.70 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.32/1.70 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.70 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.70 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.70 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.70 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), 'tc_nat' ) ],
% 1.32/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.70 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.70 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.70 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.70 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( X, Y
% 1.32/1.70 , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Ominus__class_Ominus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.32/1.70 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.32/1.70 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.32/1.70 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ), 'tc_nat'
% 1.32/1.70 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.32/1.70 'c_SetInterval_Oord__class_OatLeastLessThan'( U, T, 'tc_nat' ), 'tc_nat'
% 1.32/1.70 , X ) ), ~( 'c_lessequals'( U, T, 'tc_nat' ) ), ~( 'c_lessequals'( Z, U,
% 1.32/1.70 'tc_nat' ) ) ],
% 1.32/1.70 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.32/1.70 ~( hBOOL( hAPP( X, T ) ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), hAPP( 'c_Suc', T ) ),
% 1.32/1.70 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.70 'tc_nat' ), Z ), T ), Y, 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.70 X ), Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =( hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.70 X ), Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.32/1.70 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.70 X ), Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.32/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.32/1.70 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.32/1.70 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.32/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.32/1.70 Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.70 T, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.32/1.70 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.32/1.70 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.70 , Z, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.32/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.32/1.70 Z, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.70 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T )
% 1.32/1.70 , Z ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.70 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.70 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.32/1.70 ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.32/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T
% 1.32/1.70 ), Z, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.32/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.32/1.70 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.70 , 'tc_nat' ), 'tc_nat' ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.32/1.70 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.70 , 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.70 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.32/1.70 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) )
% 1.32/1.70 ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.70 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_OPls'
% 1.32/1.70 , Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.32/1.70 ), X ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.70 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, hAPP(
% 1.32/1.70 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.70 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.32/1.70 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.32/1.70 , X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.70 'tc_nat' ), X ), Y ) ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.70 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.70 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.70 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 1.32/1.70 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 1.32/1.70 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.70 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.32/1.70 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.70 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.32/1.70 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), 'c_Finite__Set_Osetsum'( 'c_COMBB'(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), Y, X, X, Z ), T, Z, X ) ),
% 1.32/1.70 'c_Finite__Set_Osetsum'( 'c_COMBB'( 'c_HOL_Oabs__class_Oabs'( X ), Y, X,
% 1.32/1.70 X, Z ), T, Z, X ) ) ],
% 1.32/1.70 [ 'c_Fun_Oinj__on'( 'c_Suc', X, 'tc_nat', 'tc_nat' ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.32/1.70 ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.32/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.32/1.70 , hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.32/1.70 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), X ), ~(
% 1.32/1.70 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.70 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.70 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.32/1.70 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Z, X, X, Y ), T, hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), U ), Y, X ), ~( 'c_Lim_OLIM'( Z, T,
% 1.32/1.70 U, Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.70 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~( 'c_lessequals'( Z, Y, X
% 1.32/1.70 ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 1.32/1.70 hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y
% 1.32/1.70 ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ), X ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.32/1.70 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.70 hAPP( 'c_Suc', Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.70 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.70 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.32/1.70 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.70 T, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.70 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( Y
% 1.32/1.70 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.32/1.70 ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.32/1.70 ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.32/1.70 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.70 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), U )
% 1.32/1.70 , X ), ~( 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~(
% 1.32/1.70 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ),
% 1.32/1.70 'c_Finite__Set_Osetsum'( Y, Z, T, X ) ), 'c_Finite__Set_Osetsum'(
% 1.32/1.70 'c_COMBB'( 'c_HOL_Oabs__class_Oabs'( X ), Y, X, X, T ), Z, T, X ), X ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Z,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.70 'class_Int_Onumber__ring'( X ) ), =( hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.32/1.70 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.70 Y, X ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.70 ), X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.32/1.70 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.32/1.70 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), X,
% 1.32/1.70 'tc_nat' ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y
% 1.32/1.70 ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ), hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.70 X ), Y ), Z ) ), X ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.70 , hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), Z ) ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ), U, X
% 1.32/1.70 ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ),
% 1.32/1.70 Y ), T, X ) ) ],
% 1.32/1.70 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.70 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.32/1.70 , 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 'tc_nat' ), X, 'tc_nat' ) ],
% 1.32/1.70 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.70 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.32/1.70 , 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 'tc_nat' ), Y, 'tc_nat' ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.32/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.70 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.32/1.70 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.32/1.70 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.32/1.70 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.70 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.70 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.70 , 'tc_nat' ), 'tc_nat' ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ) ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), hAPP(
% 1.32/1.70 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Z ) ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.32/1.70 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ) )
% 1.32/1.70 , =( Y, T ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) )
% 1.32/1.70 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.70 ), T ), Z ), Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.70 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.70 X ), T ), Z ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.70 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.32/1.70 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.32/1.70 [ =( X, hAPP( 'c_Suc', Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.32/1.70 'c_lessequals'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.32/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.32/1.70 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.32/1.70 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP(
% 1.32/1.70 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 1.32/1.70 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.70 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.32/1.70 ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.70 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.32/1.70 ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Ominus__class_Ominus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.32/1.70 , hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.70 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_Int_Oint' ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.70 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.32/1.70 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.32/1.70 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.32/1.70 ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), =( Z,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.70 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.32/1.70 'c_Divides_Odiv__class_Odiv'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.32/1.70 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.70 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z )
% 1.32/1.70 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.32/1.70 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.70 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z )
% 1.32/1.70 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.70 X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.32/1.70 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.32/1.70 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.32/1.70 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.32/1.70 , V0, U, V1 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.32/1.70 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.32/1.70 , V0, U, V1 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.32/1.70 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.70 X, T, U, Y, W, V0 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.70 X, T, U, Z, W, V0 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.32/1.70 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.32/1.70 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.32/1.70 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.70 T, X, U, Y, W, V0 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.70 T, X, U, Z, W, V0 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.70 T, X, U, W, Y, V0 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.70 T, X, U, W, Z, V0 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.32/1.70 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.32/1.70 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.32/1.70 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.32/1.70 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.32/1.70 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.32/1.70 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.32/1.70 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.32/1.70 , V0, V1, V2 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.32/1.70 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.32/1.70 W, V0, V1, V2 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.32/1.70 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.32/1.70 , V0, V1, V2 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.32/1.70 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.32/1.70 W, V0, V1, V2 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.32/1.70 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.32/1.70 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.32/1.70 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.32/1.70 W, V0, V1, V2 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.32/1.70 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.32/1.70 W, V0, V1, V2 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.32/1.70 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.32/1.70 , V0, V1, V2 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.32/1.70 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.32/1.70 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.32/1.70 , V0, V1, V2 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.70 X, T, U, Y, W, V0 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.32/1.70 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.32/1.70 , V0, V1, V2 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.32/1.70 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.70 T, X, U, Y, W, V0 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.70 T, X, U, W, Y, V0 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.32/1.70 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.32/1.70 , V0, V1, V2 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.32/1.70 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.32/1.70 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.32/1.70 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.32/1.70 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.32/1.70 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.32/1.70 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.70 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ), ~(
% 1.32/1.70 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ) )
% 1.32/1.70 , ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ), ~(
% 1.32/1.70 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ) )
% 1.32/1.70 , ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.32/1.70 , Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.70 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), =( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.32/1.70 Z, 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.70 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.32/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.32/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.32/1.70 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.32/1.70 X ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.70 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.32/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.70 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.32/1.70 ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.32/1.70 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.70 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.32/1.70 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.32/1.70 , X ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.32/1.70 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.32/1.70 Z, X ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.70 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc',
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.32/1.70 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.32/1.70 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.32/1.70 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.70 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.32/1.70 ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.70 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =( hAPP(
% 1.32/1.70 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.32/1.70 , Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ), =( Z,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.32/1.70 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.70 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.32/1.70 ), X, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc',
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.32/1.70 ), X, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc',
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.32/1.70 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.32/1.70 , hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.32/1.70 ) ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ), X ),
% 1.32/1.70 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.70 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.32/1.70 ), 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.32/1.70 ), 'tc_nat' ) ) ],
% 1.32/1.70 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', 'tc_nat' ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.70 ), Y ), hAPP( 'c_Suc', Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.32/1.70 , Y ) ), Z ), X ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.32/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.70 'tc_nat' ), X ), Y ), hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 1.32/1.70 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.32/1.70 hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 1.32/1.70 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.70 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.32/1.70 ), Y ) ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.32/1.70 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.70 ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y )
% 1.32/1.70 ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ), X ) ],
% 1.32/1.70 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ) ), 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.32/1.70 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.32/1.70 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.32/1.70 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.32/1.70 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.32/1.70 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.32/1.70 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.32/1.70 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.32/1.70 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.70 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.70 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.32/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.32/1.70 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.32/1.70 ],
% 1.32/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.70 'tc_nat' ) ), =( Y, Z ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.70 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.70 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.70 ) ), =( 'c_Finite__Set_Osetsum'( Y,
% 1.32/1.70 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc',
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_nat' ), 'tc_nat', X ),
% 1.32/1.70 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.70 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.32/1.70 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.70 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.70 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.70 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.32/1.70 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.70 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.32/1.70 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.70 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.70 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.32/1.70 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.70 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.32/1.70 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.32/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z )
% 1.32/1.70 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ),
% 1.32/1.70 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.32/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X )
% 1.32/1.70 , Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ),
% 1.32/1.70 'tc_nat' ) ) ],
% 1.32/1.70 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.32/1.70 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 X, hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.32/1.70 ), 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.32/1.70 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.32/1.70 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.32/1.70 'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.32/1.70 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.70 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.70 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.32/1.70 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.70 , Y, X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.32/1.70 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.32/1.70 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.32/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.70 ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.32/1.70 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.70 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.32/1.70 ), 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.70 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.32/1.70 ), 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.70 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.70 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ),
% 1.32/1.70 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.32/1.70 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.32/1.70 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.70 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.70 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.70 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.70 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.32/1.70 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 1.32/1.70 ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.70 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.32/1.70 ), Z ), Y ), 'tc_nat' ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.70 'tc_nat' ) ), 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X,
% 1.32/1.70 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.32/1.70 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.70 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.70 'tc_nat' ) ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.70 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y ),
% 1.32/1.70 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.70 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP(
% 1.32/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ),
% 1.32/1.70 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), =( hAPP(
% 1.32/1.70 'c_Suc', X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 1.32/1.70 ,
% 1.32/1.70 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), 'c_lessequals'( Y,
% 1.32/1.70 X, 'tc_nat' ) ],
% 1.32/1.70 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP(
% 1.32/1.70 'c_Suc', Y ), X, 'tc_nat' ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.32/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.32/1.70 , Y ) ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) )
% 1.32/1.70 , ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.32/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.70 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.70 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.70 , 'tc_nat' ), 'tc_nat' ), 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.70 X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.32/1.70 X ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.32/1.70 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.71 X ), T ), Y ) ), Z, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), Y ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.71 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.71 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.71 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.71 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.32/1.71 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OMin',
% 1.32/1.71 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OMin',
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OMin', 'tc_Int_Oint' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OMin',
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.32/1.71 , Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y )
% 1.32/1.71 , 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.71 hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ), 'tc_nat' ), ~( 'c_lessequals'( Y,
% 1.32/1.71 Z, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.71 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.71 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.71 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.71 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.32/1.71 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.32/1.71 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.71 [ 'c_lessequals'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', X ), 'tc_nat' ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.71 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.71 X ), Y ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.32/1.71 ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.71 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.32/1.71 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.32/1.71 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.71 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.32/1.71 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.71 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.32/1.71 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.71 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.32/1.71 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.32/1.71 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.71 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.32/1.71 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.32/1.71 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.71 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.32/1.71 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.71 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.32/1.71 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.71 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.32/1.71 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.32/1.71 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.71 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.32/1.71 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.32/1.71 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.71 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.32/1.71 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.71 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.32/1.71 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.71 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.32/1.71 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.32/1.71 , X, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.71 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.71 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.71 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.32/1.71 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.71 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.32/1.71 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OPls', 'tc_Int_Oint' )
% 1.32/1.71 ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.71 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.71 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 1.32/1.71 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.32/1.71 'tc_nat' ) ) ],
% 1.32/1.71 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ),
% 1.32/1.71 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.71 'tc_nat' ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 1.32/1.71 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 1.32/1.71 'tc_nat' ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.71 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) )
% 1.32/1.71 ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.32/1.71 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.71 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ) )
% 1.32/1.71 ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.32/1.71 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.71 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) )
% 1.32/1.71 ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.32/1.71 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.71 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ) )
% 1.32/1.71 ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.32/1.71 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.71 X ), Y ) ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z
% 1.32/1.71 ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) )
% 1.32/1.71 , hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ) ],
% 1.32/1.71 [ =( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 'tc_nat' ), Z ), hAPP( 'c_Suc', X ) ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), Y,
% 1.32/1.71 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), Y ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 X ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 'tc_Int_Oint' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit0'( X ),
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit0'( X ),
% 1.32/1.71 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X,
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 'tc_Int_Oint' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit1'( X ),
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit1'( X ),
% 1.32/1.71 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X,
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.71 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.32/1.71 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.32/1.71 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.32/1.71 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.32/1.71 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.32/1.71 hAPP( 'c_Suc', Z ), hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.32/1.71 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ),
% 1.32/1.71 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.32/1.71 , X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.32/1.71 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y
% 1.32/1.71 , 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z,
% 1.32/1.71 'tc_nat' ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ),
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.32/1.71 'c_Divides_Odiv__class_Odiv'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.32/1.71 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.32/1.71 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.71 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), Y ), X ) ],
% 1.32/1.71 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.71 'c_lessequals'( Y, hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), X ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.71 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.32/1.71 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.32/1.71 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.32/1.71 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.32/1.71 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.32/1.71 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 'tc_nat' ), 'tc_nat' ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ) ) ), =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ) ) ), =( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_Finite__Set_Osetsum'(
% 1.32/1.71 'c_COMBB'( 'c_HOL_Oabs__class_Oabs'( X ), Y, X, X, Z ), T, Z, X ), X ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 1.32/1.71 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.32/1.71 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ),
% 1.32/1.71 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.32/1.71 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.32/1.71 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.32/1.71 X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ), hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.32/1.71 X ), Y ), Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.71 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) )
% 1.32/1.71 ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y
% 1.32/1.71 ) ), Z ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.32/1.71 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 'tc_nat' ) ) ) ],
% 1.32/1.71 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.32/1.71 , X ) ) ],
% 1.32/1.71 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.32/1.71 , Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.32/1.71 , Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.32/1.71 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber__ring'( X ) ), =( hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.32/1.71 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ), X ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.32/1.71 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 X ), X ) ) ],
% 1.32/1.71 [ =( X, hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.71 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.71 'tc_nat' ) ) ],
% 1.32/1.71 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.32/1.71 , X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.71 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.32/1.71 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.32/1.71 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.32/1.71 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.32/1.71 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z
% 1.32/1.71 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ), X ), ~( 'c_lessequals'( U
% 1.32/1.71 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.71 , U, X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.32/1.71 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.32/1.71 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.71 , X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.71 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.71 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.32/1.71 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.32/1.71 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.32/1.71 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 1.32/1.71 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.32/1.71 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.32/1.71 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.71 hAPP( 'c_Suc', T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z
% 1.32/1.71 ), hAPP( 'c_Suc', T ) ), X ) ) ],
% 1.32/1.71 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OMin',
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.71 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.32/1.71 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.71 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.32/1.71 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.32/1.71 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.32/1.71 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.71 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.32/1.71 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.32/1.71 , X, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.71 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.32/1.71 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.32/1.71 , Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.32/1.71 'c_Finite__Set_Osetsum'( 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.32/1.71 Y, X, X, Z ), T, Z, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.32/1.71 'c_Finite__Set_Osetsum'( Y, T, Z, X ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.71 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.32/1.71 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.32/1.71 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.71 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.32/1.71 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.32/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.71 X ), Y ) ), Y ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.71 X ), Y ) ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.71 X ), Y ) ) ) ],
% 1.32/1.71 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.71 X ), Y ) ), Y ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.71 X ), Y ) ), Y ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.71 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.32/1.71 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.71 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.32/1.71 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.32/1.71 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.32/1.71 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.32/1.71 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.32/1.71 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.32/1.71 Z ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.32/1.71 Z ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.32/1.71 ~( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X )
% 1.32/1.71 ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.32/1.71 ~( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X )
% 1.32/1.71 ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.32/1.71 ~( 'c_lessequals'( Z, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.32/1.71 ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.32/1.71 ~( 'c_lessequals'( Z, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.32/1.71 ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.32/1.71 'class_RealVector_Ometric__space'( Y ) ), ~(
% 1.32/1.71 'class_RealVector_Ometric__space'( Z ) ), 'c_Lim_OLIM'( 'c_COMBB'( T, U,
% 1.32/1.71 X, Y, Z ), W, hAPP( T, V0 ), Z, Y ), ~( 'c_Lim_OLIM'( U, W, V0, Z, X ) )
% 1.32/1.71 , ~( 'c_Lim_OLIM'( T, V0, hAPP( T, V0 ), X, Y ) ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.32/1.71 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), T, X, X, Y ), U,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_Lim_OLIM'( T, U,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.32/1.71 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), T, X, X, Y ), U,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_Lim_OLIM'( T, U,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.32/1.71 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'( Z,
% 1.32/1.71 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), X, Y, X ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( Z, T ), X, Y ), ~( 'c_Lim_OLIM'( Z
% 1.32/1.71 , T, hAPP( Z, T ), X, Y ) ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.32/1.71 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( Z, T, hAPP( Z, T
% 1.32/1.71 ), X, Y ), ~( 'c_Lim_OLIM'( 'c_COMBB'( Z, hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), T ), X, Y, X ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( Z, T ), X, Y ) ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.32/1.71 'class_RealVector_Oreal__normed__vector'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'(
% 1.32/1.71 Z, hAPP( 'c_HOL_Oplus__class_Oplus'( Y ), T ), Y, X, Y ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( Y ), U, Y, X ), ~( 'c_Lim_OLIM'( Z, T, U, Y,
% 1.32/1.71 X ) ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.32/1.71 'class_RealVector_Oreal__normed__vector'( Y ) ), 'c_Lim_OLIM'( Z, T, U, Y
% 1.32/1.71 , X ), ~( 'c_Lim_OLIM'( 'c_COMBB'( Z, hAPP( 'c_HOL_Oplus__class_Oplus'( Y
% 1.32/1.71 ), T ), Y, X, Y ), 'c_HOL_Ozero__class_Ozero'( Y ), U, Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.71 X ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.71 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.71 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.32/1.71 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.32/1.71 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.71 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.71 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.32/1.71 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.32/1.71 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.71 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.32/1.71 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y
% 1.32/1.71 ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.32/1.71 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.32/1.71 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.71 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.71 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.71 X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.71 X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.71 X ), Y ) ), Z ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.32/1.71 , Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Lim_OLIM'(
% 1.32/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X, X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y, hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), =( Y, Z ) ],
% 1.32/1.71 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.71 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.71 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.32/1.71 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.32/1.71 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.71 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.71 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.32/1.71 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.32/1.71 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.71 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.32/1.71 ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.32/1.71 ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.32/1.71 ), X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.32/1.71 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.32/1.71 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.32/1.71 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.32/1.71 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.32/1.71 ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.32/1.71 ), Z ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.32/1.71 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.71 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.71 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.71 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.32/1.71 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.71 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.71 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.71 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.71 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.32/1.71 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.71 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.32/1.71 ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y )
% 1.32/1.71 ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.32/1.71 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.32/1.71 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.71 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.71 T, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.32/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.32/1.71 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.32/1.71 ), Y ) ), Z ) ), Z ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.71 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.32/1.71 'c_lessequals'( Y, T, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.71 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.71 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.32/1.71 'c_lessequals'( Z, T, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.71 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.32/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.32/1.71 'c_lessequals'( Y, T, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.32/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.32/1.71 'c_lessequals'( Z, T, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.71 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.32/1.71 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.71 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y, hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), T ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.71 Y ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.32/1.71 Y ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.71 Y ) ],
% 1.32/1.71 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.32/1.71 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.32/1.71 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.32/1.71 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.71 , 'tc_nat' ), 'tc_nat' ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.71 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.71 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.32/1.71 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.32/1.71 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.32/1.71 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.32/1.71 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.32/1.71 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.71 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.71 X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.32/1.71 [ 'c_lessequals'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.32/1.71 X, Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', X
% 1.32/1.71 ), Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.71 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.71 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'c_lessequals'( hAPP( 'c_Suc', X ), X, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.71 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.32/1.71 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.32/1.71 ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X,
% 1.32/1.71 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.71 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.32/1.71 ), Y ), Z ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~(
% 1.32/1.71 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 1.32/1.71 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.32/1.71 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.32/1.71 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.32/1.71 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), Y ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), Y ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.71 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.32/1.71 ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.32/1.71 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.32/1.71 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.32/1.71 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.32/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z
% 1.32/1.71 ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.32/1.71 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.32/1.71 X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.32/1.71 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y )
% 1.32/1.71 , T ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.71 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.32/1.71 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.32/1.71 , X ) ],
% 1.32/1.71 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OMin',
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.32/1.71 hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.71 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.71 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.71 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.71 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.71 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_Int_Oint' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_Int_Oint' ), Z ), Y ), 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 X, Z, 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.32/1.71 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.71 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 'tc_nat' ) ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( 'c_Suc',
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.32/1.71 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.32/1.71 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 1.32/1.71 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.32/1.71 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.32/1.71 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.32/1.71 , X ) ) ],
% 1.32/1.71 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.32/1.71 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.32/1.71 , X ) ) ],
% 1.32/1.71 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.32/1.71 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.32/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.32/1.71 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.32/1.71 ) ) ],
% 1.32/1.71 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.32/1.71 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.32/1.71 ) ) ],
% 1.32/1.71 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.32/1.71 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.32/1.71 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X, hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.71 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 1.32/1.71 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), =( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.71 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.71 'tc_nat' ), X ), Y ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.32/1.71 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Z ), Y ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.71 'tc_nat' ), X ), hAPP( 'c_Suc', Y ) ), X, 'tc_nat' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.71 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.71 X, 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 'tc_nat' ), X ), 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ), Y,
% 1.32/1.71 'tc_nat' ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.32/1.71 Y ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.32/1.71 Y ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ), X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), Y ), X ) ],
% 1.32/1.71 [ 'c_lessequals'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.32/1.71 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', X
% 1.32/1.71 ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.32/1.71 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.32/1.71 'c_lessequals'( Z, Y, X ) ],
% 1.32/1.71 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.32/1.71 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.32/1.71 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.32/1.71 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber__ring'( X ) ), =( hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.32/1.71 , hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ), Y ) ),
% 1.32/1.71 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.71 'c_Int_OMin', X ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), ~(
% 1.32/1.71 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBC'(
% 1.32/1.71 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Z, X, 'tc_fun'( X, X ),
% 1.32/1.71 Y ), T, Y, X, X ), U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.71 'c_Lim_OLIM'( Z, U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.71 'c_Int_OMin', X ) ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.71 ), Y ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.32/1.71 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.71 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.71 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), T ) ),
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T ) ) ), Y ) ), ~(
% 1.32/1.71 'c_lessequals'( T, Z, 'tc_nat' ) ) ],
% 1.32/1.71 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc'
% 1.32/1.71 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.32/1.71 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.32/1.71 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ), 'tc_nat' ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), Z ) ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.32/1.71 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.32/1.71 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T,
% 1.32/1.71 Z, 'tc_nat' ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ), T ), U
% 1.32/1.71 , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ), 'tc_nat' ) ),
% 1.32/1.71 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.32/1.71 ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.32/1.71 ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ), U
% 1.32/1.71 , 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), T ) ), U ),
% 1.32/1.71 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ), 'tc_nat' ) ),
% 1.32/1.71 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.32/1.71 ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.32/1.71 ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ),
% 1.32/1.71 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.32/1.71 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.71 'tc_nat' ) ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.71 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.32/1.71 Y ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.32/1.71 Y ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.71 Y ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.32/1.71 Y ) ],
% 1.32/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.71 'c_Int_OMin', X ) ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.32/1.71 ) ],
% 1.32/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.71 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.71 X ), Y ), Z ) ), T, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.71 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y )
% 1.32/1.71 ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ), X ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.71 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.32/1.71 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.71 X ), Y ), T ) ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ), X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T, X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.71 , Z ), T ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.32/1.71 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.32/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.32/1.71 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.32/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.32/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.71 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.32/1.71 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.71 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.71 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.71 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.71 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.71 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.71 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.71 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.71 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.71 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.71 X ), Y ), Z ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), 'c_lessequals'( U, T, X
% 1.32/1.71 ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), 'c_lessequals'( Z, Y, X
% 1.32/1.71 ), ~( 'c_lessequals'( U, T, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( T, U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.32/1.71 , X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U
% 1.32/1.71 , X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.71 , Y ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.71 X ) ), =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 X ) ) ), =( Y, Z ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 X ) ) ), =( Y, Z ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.71 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) ) ],
% 1.32/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber__ring'( X ) ), =( hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.32/1.71 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ),
% 1.32/1.71 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.71 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.32/1.71 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.32/1.71 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.71 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.32/1.71 ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.32/1.71 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.71 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.32/1.71 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.71 , X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.71 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.71 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.71 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.32/1.71 ), X ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.32/1.71 ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.71 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.32/1.71 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~( 'c_lessequals'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~( 'c_lessequals'(
% 1.32/1.71 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.71 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.71 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.71 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.71 , X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.71 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.32/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.71 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.32/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.71 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.71 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T )
% 1.32/1.71 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.71 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T )
% 1.32/1.71 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.71 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.71 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.71 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.71 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.32/1.71 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.71 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.71 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.71 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.71 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), Y, X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.71 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.71 , Y ), T ), Z, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.71 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.71 , Y ), T ), Z, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.71 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.71 ), T ), Z ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.71 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.71 ), T ), Z ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.71 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.71 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.71 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.71 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.71 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.71 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), Z, X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.32/1.71 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.71 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.32/1.71 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.71 ), Y ), T ), Z, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.32/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.32/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.32/1.71 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 X ), T ), Z ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.71 'c_Int_OMin', X ) ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.71 'c_Int_OMin', X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.32/1.71 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.32/1.71 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.32/1.71 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.32/1.71 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.32/1.71 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.32/1.71 ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.71 X ), T ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.32/1.71 ), X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.71 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.32/1.71 ), X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.71 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.71 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.32/1.71 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.32/1.71 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), T ), 'tc_nat' ), 'tc_nat', X
% 1.32/1.71 ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.32/1.71 , 'tc_nat', X, 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.32/1.71 Z, U, 'tc_nat' ), 'tc_nat', X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.71 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.71 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.32/1.71 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.32/1.71 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.32/1.71 , 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 'tc_nat' ), X ), Y ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 'tc_nat' ), X ), Z ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.32/1.71 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( Y ) ), Z ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.71 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.32/1.71 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), T, X, X, Y ), U, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), W ), Y, X ), ~( 'c_Lim_OLIM'( T,
% 1.32/1.71 U, W, Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Finite__Set_Osetsum'( Z, T, U
% 1.32/1.71 , X ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, U ), T, U, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Finite__Set_Osetsum'( Z, T, U
% 1.32/1.71 , X ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, U ), T, U, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.71 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.32/1.71 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ],
% 1.32/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.32/1.71 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ) ), T ) )
% 1.32/1.71 ],
% 1.32/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.32/1.71 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), Y ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.71 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.71 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Lim_OLIM'(
% 1.32/1.71 'c_COMBC'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, X, X ), Z, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X, X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.32/1.71 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), =( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), =( Z,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ), Z ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.32/1.71 ), Y ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) ), =( U,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.71 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.71 ), =( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), U ), hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.32/1.71 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.32/1.71 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y,
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.71 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.71 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.71 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.32/1.71 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.32/1.71 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.32/1.71 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), =(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.32/1.71 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.32/1.71 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 X ) ) ],
% 1.32/1.71 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.32/1.71 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.32/1.71 X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.32/1.71 , T ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.71 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.71 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.71 X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.71 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Lim_OLIM'(
% 1.32/1.71 'c_COMBC'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, X, X ), Z, hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X, X ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.32/1.71 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.32/1.71 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.32/1.71 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.32/1.71 'c_Int_OBit0'( X ) ), 'c_Int_OBit1'( Y ) ), 'c_Int_OBit1'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.32/1.71 'c_Int_OBit1'( X ) ), 'c_Int_OBit0'( Y ) ), 'c_Int_OBit1'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.32/1.71 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.32/1.71 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X,
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.32/1.71 ) ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.32/1.71 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.71 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.71 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.32/1.71 ) ],
% 1.32/1.71 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ), =( Z,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.32/1.71 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.32/1.71 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat', X )
% 1.32/1.71 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 X ), hAPP( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( Y,
% 1.32/1.71 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), hAPP( Y,
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( Y,
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.32/1.71 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.71 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.32/1.71 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.71 ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.71 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.32/1.71 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.32/1.71 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.32/1.71 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.32/1.71 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.71 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.71 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.32/1.71 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.32/1.71 'tc_nat' ) ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ), Y, 'tc_nat'
% 1.32/1.71 ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.71 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.71 'tc_nat' ) ) ],
% 1.32/1.71 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.71 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.71 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.71 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.71 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.32/1.71 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.32/1.71 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.32/1.71 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.71 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.32/1.71 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.32/1.71 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), Z ),
% 1.32/1.71 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.32/1.71 ), Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~(
% 1.32/1.71 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.32/1.71 ), Y ), Z, 'tc_nat' ), ~( 'c_lessequals'( X, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~(
% 1.32/1.71 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~(
% 1.32/1.71 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.71 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.32/1.71 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.32/1.71 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.71 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.32/1.71 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.32/1.71 ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.32/1.71 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T,
% 1.32/1.71 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.71 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ), 'c_HOL_Oone__class_Oone'( X
% 1.32/1.71 ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.32/1.71 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.32/1.71 , X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.32/1.71 ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.71 ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.71 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.71 X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.71 ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.71 , X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.71 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.32/1.71 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.32/1.71 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.32/1.71 ), X ) ) ],
% 1.32/1.71 [ =( 'c_Int_OBit1'( 'c_Int_OMin' ), 'c_Int_OMin' ) ],
% 1.32/1.71 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OMin' ) ), =( X, 'c_Int_OMin' ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( =( 'c_Int_OMin', 'c_Int_OBit1'( X ) ) ), =( 'c_Int_OMin', X ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.32/1.71 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.32/1.71 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ =( 'c_Int_OMin', 'c_Int_OBit1'( 'c_Int_OMin' ) ) ],
% 1.32/1.71 [ ~( =( 'c_Int_OPls', 'c_Int_OMin' ) ) ],
% 1.32/1.71 [ ~( =( 'c_Int_OMin', 'c_Int_OPls' ) ) ],
% 1.32/1.71 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OPls',
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.32/1.71 'c_Int_OPls' ), X ), X ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ),
% 1.32/1.71 'c_Int_OPls' ), X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.32/1.71 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.32/1.71 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.32/1.71 X ), Y ), Z ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), Z ) ) ],
% 1.32/1.71 [ ~( =( 'c_Int_OMin', 'c_Int_OBit0'( X ) ) ) ],
% 1.32/1.71 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OMin' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.32/1.71 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.32/1.71 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.32/1.71 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.32/1.71 'c_Int_OBit0'( X ) ), 'c_Int_OBit0'( Y ) ), 'c_Int_OBit0'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.32/1.71 [ =( 'c_Int_OBit0'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_Int_Oint' ), X ), X ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.32/1.71 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.32/1.71 , ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.32/1.71 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' )
% 1.32/1.71 ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.32/1.71 , Y ) ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.71 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.32/1.71 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.71 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.32/1.71 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.71 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.32/1.71 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.71 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ), hAPP(
% 1.32/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.71 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.71 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.32/1.71 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.32/1.71 , Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.71 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.32/1.71 ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.71 , Z ), Y ), 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.71 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.32/1.71 ],
% 1.32/1.71 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.71 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.32/1.71 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.71 , X ), Y ), 'tc_nat' ) ],
% 1.32/1.71 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.71 , Y ), X ), 'tc_nat' ) ],
% 1.32/1.71 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.71 , X ), Y ), 'tc_nat' ) ],
% 1.32/1.71 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.71 , X ), Y ), 'tc_nat' ) ],
% 1.32/1.71 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.32/1.71 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.71 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.32/1.71 ) ) ],
% 1.32/1.71 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 X, T, 'tc_nat' ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.32/1.71 'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.71 X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.71 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.32/1.71 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ),
% 1.32/1.71 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.32/1.71 Z, 'tc_nat' ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.71 X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.32/1.71 'c_Suc', Y ) ) ) ],
% 1.32/1.71 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ],
% 1.32/1.71 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ],
% 1.32/1.71 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.71 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.71 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.32/1.71 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.71 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.32/1.71 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ),
% 1.32/1.71 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.32/1.71 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ),
% 1.32/1.71 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.32/1.71 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.32/1.71 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.32/1.71 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.32/1.71 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.32/1.71 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.32/1.71 'tc_nat' ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.71 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.71 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( 'c_lessequals'(
% 1.32/1.71 Z, Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.32/1.71 X ), Y ), Z, 'tc_nat' ), ~( 'c_lessequals'( X, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.71 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~(
% 1.32/1.71 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.32/1.71 ), Y ), X ), 'tc_nat' ) ), =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.71 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X )
% 1.32/1.71 ), X ), Y ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Y ), X ), ~(
% 1.32/1.71 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Y ), ~(
% 1.32/1.71 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y, hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), X ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~(
% 1.32/1.71 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ) ), ~(
% 1.32/1.71 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.71 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.71 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ), 'tc_nat'
% 1.32/1.71 ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Y ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.32/1.71 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.32/1.71 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.71 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.32/1.71 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.32/1.71 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.32/1.71 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.32/1.71 , X ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.32/1.71 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.32/1.71 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.32/1.71 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), Y ) ) ],
% 1.32/1.71 [ 'c_Fun_Oinj__on'( 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.32/1.71 , 'tc_nat', 'tc_nat', 'tc_nat' ), Y, 'tc_nat', 'tc_nat' ) ],
% 1.32/1.71 [ 'c_lessequals'( 'v_m', 'v_i', 'tc_nat' ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), X ) ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.71 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), X ) ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.71 ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.32/1.71 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.32/1.71 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.71 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.71 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.71 ,
% 1.32/1.71 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.32/1.71 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.32/1.71 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.32/1.71 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'tc_nat' ) ) ],
% 1.32/1.71 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.32/1.71 , 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), W, X ), ~(
% 1.32/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 X ), Z ), T ) ), W ), X ) ) ],
% 1.32/1.71 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.32/1.71 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.71 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.32/1.72 ), W, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.32/1.72 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ), X ), ~(
% 1.32/1.72 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), Z ), U ) ), W ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( T, hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W
% 1.32/1.72 ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), W, X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), W, X ) ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.72 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.72 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ), X ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.32/1.72 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBC'(
% 1.32/1.72 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Z, X, 'tc_fun'( X, X ), Y )
% 1.32/1.72 , T, Y, X, X ), U, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), W ), T
% 1.32/1.72 ), Y, X ), ~( 'c_Lim_OLIM'( Z, U, W, Y, X ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X )
% 1.32/1.72 ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T, X,
% 1.32/1.72 X ), Z, T, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X )
% 1.32/1.72 ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T, X,
% 1.32/1.72 X ), Z, T, X ) ) ],
% 1.32/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.32/1.72 ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ) )
% 1.32/1.72 , T ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), Z ) ), =( Z,
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), T ) ), =( T,
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.32/1.72 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.72 ) ],
% 1.32/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.72 ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.72 ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.32/1.72 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), =(
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z ), =( T,
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.32/1.72 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.72 , X ) ), Z ) ), Z ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.32/1.72 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.72 , X ) ), Z ) ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.32/1.72 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.72 , X ) ), Z ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.72 ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.72 ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.72 , X ) ), Z ) ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.72 X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.32/1.72 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.72 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.32/1.72 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.72 X ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.32/1.72 hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP(
% 1.32/1.72 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Z
% 1.32/1.72 ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.72 ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.72 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.72 'c_HOL_Oone__class_Oone'( X ) ) ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 Y, Z, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.72 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.72 'c_HOL_Oone__class_Oone'( X ) ) ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.72 Z, X ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), ~(
% 1.32/1.72 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBC'(
% 1.32/1.72 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Z, X, 'tc_fun'( X, X ),
% 1.32/1.72 Y ), T, Y, X, X ), U, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), W
% 1.32/1.72 ), T ), Y, X ), ~( 'c_Lim_OLIM'( Z, U, W, Y, X ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X
% 1.32/1.72 ) ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T,
% 1.32/1.72 X, X ), Z, T, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X
% 1.32/1.72 ) ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T,
% 1.32/1.72 X, X ), Z, T, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), X ) ), X ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.72 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.32/1.72 ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.72 X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.72 X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.32/1.72 ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.32/1.72 ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.32/1.72 ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), X ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.32/1.72 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.32/1.72 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.32/1.72 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ) ), =( X,
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.72 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.72 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.72 'tc_nat' ) ) ],
% 1.32/1.72 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.72 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.72 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.32/1.72 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.72 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.32/1.72 , ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.32/1.72 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Z ) ), T ) ) ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~(
% 1.32/1.72 'c_lessequals'( T, X, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ), U ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~(
% 1.32/1.72 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z, hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ) ), U ) )
% 1.32/1.72 , ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ), ~(
% 1.32/1.72 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.32/1.72 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Z ) ), T ) ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ) ) ],
% 1.32/1.72 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ), T ), U,
% 1.32/1.72 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z
% 1.32/1.72 ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ), 'tc_nat' ) ),
% 1.32/1.72 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.32/1.72 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.32/1.72 ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ), U,
% 1.32/1.72 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.32/1.72 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.72 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), T ) ), U ),
% 1.32/1.72 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T
% 1.32/1.72 ) ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ), 'tc_nat' ) ),
% 1.32/1.72 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.32/1.72 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.32/1.72 ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.72 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ),
% 1.32/1.72 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.32/1.72 'class_Power_Opower'( X ) ), ~( 'class_RealVector_Ometric__space'( Y ) )
% 1.32/1.72 , 'c_Lim_OLIM'( 'c_COMBC'( 'c_COMBB'( 'c_Power_Opower__class_Opower'( X )
% 1.32/1.72 , Z, X, 'tc_fun'( 'tc_nat', X ), Y ), T, Y, 'tc_nat', X ), U, hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), W ), T ), Y, X ), ~( 'c_Lim_OLIM'( Z
% 1.32/1.72 , U, W, Y, X ) ) ],
% 1.32/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.72 'c_Int_OMin', X ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.72 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ), hAPP(
% 1.32/1.72 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.32/1.72 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.32/1.72 ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.72 'tc_nat' ) ) ],
% 1.32/1.72 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.72 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.32/1.72 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.32/1.72 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), Y, 'tc_nat' ) ) ],
% 1.32/1.72 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.72 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.32/1.72 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.72 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.32/1.72 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.32/1.72 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.32/1.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.32/1.72 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.32/1.72 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.32/1.72 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.32/1.72 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.72 'tc_nat' ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.72 'tc_nat' ) ) ],
% 1.32/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.32/1.72 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.32/1.72 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.32/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.32/1.72 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.32/1.72 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.32/1.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.72 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.32/1.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.32/1.72 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.32/1.72 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.72 ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) )
% 1.32/1.72 , 'tc_nat' ) ],
% 1.32/1.72 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T )
% 1.32/1.72 , 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.32/1.72 , Z, 'tc_nat' ) ) ],
% 1.32/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.32/1.72 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.32/1.72 , hAPP( 'c_Suc', X ) ), Z ) ) ), =( Y, Z ) ],
% 1.32/1.72 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.32/1.72 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.32/1.72 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.32/1.72 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.32/1.72 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.32/1.72 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.32/1.72 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.32/1.72 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.72 'tc_nat' ) ), Y ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.72 'tc_nat' ) ) ) ],
% 1.32/1.72 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.72 ), Z ), Y ), 'tc_nat' ) ) ],
% 1.32/1.72 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.72 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.32/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.72 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.72 ), X ), X ), 'tc_nat' ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.32/1.72 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) )
% 1.32/1.72 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), hAPP( 'c_Suc', Y ) )
% 1.32/1.72 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.32/1.72 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ) ), Z )
% 1.32/1.72 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', X
% 1.32/1.72 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ),
% 1.32/1.72 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.32/1.72 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.32/1.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.72 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.72 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.32/1.72 'tc_nat' ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.32/1.72 , X ) ), hAPP( 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.72 'tc_nat' ), X ), Y ) ) ],
% 1.32/1.72 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.72 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.32/1.72 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' )
% 1.32/1.72 ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ) ),
% 1.32/1.72 hAPP( 'c_Suc', Z ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.32/1.72 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z )
% 1.32/1.72 ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Y ), ~(
% 1.32/1.72 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.32/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), X ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.32/1.72 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ), ~(
% 1.32/1.72 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.32/1.72 ],
% 1.32/1.72 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.32/1.72 X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y )
% 1.32/1.72 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y
% 1.32/1.72 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.32/1.72 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.32/1.72 X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y )
% 1.32/1.72 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.32/1.72 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.32/1.72 X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z )
% 1.32/1.72 , 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.32/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~(
% 1.32/1.72 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) )
% 1.32/1.72 , =( X, Z ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.72 'tc_nat' ) ) ],
% 1.32/1.72 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.32/1.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.32/1.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.72 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.32/1.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.32/1.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.72 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.32/1.72 X ), Y ), X, 'tc_nat' ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), ~( 'c_lessequals'(
% 1.32/1.72 Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.32/1.72 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.32/1.72 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 1.32/1.72 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.72 [ ~( =( 'c_Complex_Oii', 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex'
% 1.32/1.72 ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( 'c_Finite__Set_Osetsum'(
% 1.32/1.72 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.72 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.72 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.72 X ) ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ),
% 1.32/1.72 'c_HOL_Oone__class_Oone'( X ) ) ) ), =( Y, 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.72 ) ],
% 1.32/1.72 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.32/1.72 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 X, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.32/1.72 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), 'tc_nat' ), 'tc_nat', X
% 1.32/1.72 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'(
% 1.32/1.72 'c_COMBB'( Y, 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T,
% 1.32/1.72 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat', X, 'tc_nat' ),
% 1.32/1.72 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.72 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.32/1.72 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.72 'tc_nat' ), T, 'tc_nat' ), 'tc_nat', X ) ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.32/1.72 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.32/1.72 , 'tc_nat', X, 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), T, 'tc_nat' ), 'tc_nat', X ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), 'c_Finite__Set_Osetsum'( Y
% 1.32/1.72 , 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), Z ), 'tc_nat' ), 'tc_nat', X
% 1.32/1.72 ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.32/1.72 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.72 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.32/1.72 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBC'(
% 1.32/1.72 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Z, X, 'tc_fun'( X, X ), Y )
% 1.32/1.72 , T, Y, X, X ), U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.72 'c_Lim_OLIM'( Z, U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.32/1.72 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBC'(
% 1.32/1.72 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Z, X, 'tc_fun'( X, X ), Y )
% 1.32/1.72 , T, Y, X, X ), U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.72 'c_Lim_OLIM'( Z, U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.32/1.72 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBC'(
% 1.32/1.72 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Z, X, 'tc_fun'( X, X ), Y )
% 1.32/1.72 , T, Y, X, X ), U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.72 'c_Lim_OLIM'( Z, U, T, Y, X ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.32/1.72 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( Z, T, U, Y, X ),
% 1.32/1.72 ~( 'c_Lim_OLIM'( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X )
% 1.32/1.72 , Z, X, 'tc_fun'( X, X ), Y ), U, Y, X, X ), T,
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~( 'c_lessequals'(
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 'c_lessequals'(
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~( 'c_lessequals'(
% 1.32/1.72 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.72 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.32/1.72 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.72 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.72 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.72 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.72 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.72 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.72 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.72 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.72 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.72 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.72 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.72 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.32/1.72 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.32/1.72 ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), T ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.72 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.72 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.72 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.72 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.32/1.72 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.72 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.32/1.72 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.72 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.72 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.72 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.72 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.72 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.72 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.72 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.72 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.72 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.72 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.72 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.72 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.72 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.32/1.72 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.72 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.32/1.72 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.32/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.32/1.72 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ), 'tc_nat' ), 'tc_nat', X ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( 'c_COMBB'(
% 1.32/1.72 Y, hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', X, 'tc_nat' ),
% 1.32/1.72 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.72 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ), 'c_Finite__Set_Osetsum'(
% 1.32/1.72 'c_COMBB'( Y, 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.32/1.72 ), hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 1.32/1.72 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.32/1.72 'tc_nat' ), 'tc_nat', X, 'tc_nat' ),
% 1.32/1.72 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.72 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.32/1.72 'class_RealVector_Oreal__normed__vector'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'(
% 1.32/1.72 Z, 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( Y ), T, Y, Y, Y ), Y, X, Y ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( Y ), U ), T ), W, Y, X ), ~(
% 1.32/1.72 'c_Lim_OLIM'( Z, U, W, Y, X ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.32/1.72 , X, Z, U, W, V0 ) ) ],
% 1.32/1.72 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.32/1.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.32/1.72 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.32/1.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.72 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.32/1.72 'tc_Int_Oint' ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.72 'tc_nat' ) ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ =( 'c_FFT__Mirabelle_ODFT'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.72 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_Complex_Ocomplex' ),
% 1.32/1.72 'c_FFT__Mirabelle_ODFT'( X, 'c_COMBB'( Y, hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat'
% 1.32/1.72 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), X ) ) ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), hAPP(
% 1.32/1.72 hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.32/1.72 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.72 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), X ) ) ),
% 1.32/1.72 'c_FFT__Mirabelle_ODFT'( X, 'c_COMBB'( Y, 'c_COMBC'( 'c_COMBB'(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 1.32/1.72 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.32/1.72 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), X ) ) ) ) ), ~(
% 1.32/1.72 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.32/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), 'c_Int_OBit1'( 'c_Int_OPls'
% 1.32/1.72 ) ), Y ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.32/1.72 ) ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ),
% 1.32/1.72 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP(
% 1.32/1.72 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.32/1.72 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.72 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.72 X ), Y ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.72 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.32/1.72 , Y ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.32/1.72 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) )
% 1.32/1.72 ) ],
% 1.32/1.72 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.32/1.72 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ) ],
% 1.32/1.72 [ 'c_Fun_Oinj__on'( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), X, 'tc_nat', 'tc_nat' ) ],
% 1.32/1.72 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.72 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.32/1.72 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.32/1.72 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.32/1.72 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.72 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.32/1.72 ) ), 'c_Complex_Oii' ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.32/1.72 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.32/1.72 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.72 X ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.72 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ =( 'c_FFT__Mirabelle_ODFT'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.72 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_Complex_Ocomplex' ),
% 1.32/1.72 'c_FFT__Mirabelle_ODFT'( X, 'c_COMBB'( Y, hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat'
% 1.32/1.72 ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.32/1.72 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ), Z ) ), 'c_FFT__Mirabelle_ODFT'(
% 1.32/1.72 X, 'c_COMBB'( Y, 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 'tc_nat' ), hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 1.32/1.72 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.32/1.72 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), Z ) ) ) ) ],
% 1.32/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.72 'c_Int_OMin', X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.32/1.72 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ =( 'c_FFT__Mirabelle_OIDFT'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.72 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_Complex_Ocomplex' ),
% 1.32/1.72 'c_FFT__Mirabelle_OIDFT'( X, 'c_COMBB'( Y, hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat'
% 1.32/1.72 ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.32/1.72 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.72 'tc_Complex_Ocomplex' ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex'
% 1.32/1.72 ) ), 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.72 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ) ), Z ) ),
% 1.32/1.72 'c_FFT__Mirabelle_OIDFT'( X, 'c_COMBB'( Y, 'c_COMBC'( 'c_COMBB'(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 1.32/1.72 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.32/1.72 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), Z ) ) ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.32/1.72 ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.32/1.72 ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.32/1.72 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.72 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.32/1.72 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.32/1.72 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.32/1.72 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ],
% 1.32/1.72 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.72 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.72 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.32/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.72 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.72 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.32/1.72 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.32/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.72 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.32/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.32/1.72 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.72 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.32/1.72 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.32/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.72 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.72 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.32/1.72 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.72 ), Y ) ],
% 1.32/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.32/1.72 ) ],
% 1.32/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.32/1.72 ) ],
% 1.32/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.32/1.72 ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.72 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.32/1.72 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.32/1.72 , Y ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.32/1.72 , Y ) ],
% 1.32/1.72 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.32/1.72 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.32/1.72 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.32/1.72 ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.32/1.72 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.32/1.72 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.32/1.72 ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.32/1.72 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__field'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), W ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ), W ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), W ) ), U ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.32/1.72 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.32/1.72 , 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.72 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.32/1.72 'c_FFT__Mirabelle_Oroot'( X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 'tc_nat' ), Y ), Z ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.32/1.72 ) ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.32/1.72 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), W ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.32/1.72 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.32/1.72 Y ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.72 'tc_nat' ) ), Y ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.72 'tc_nat' ) ), Y ) ],
% 1.32/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.32/1.72 , Z ) ],
% 1.32/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.32/1.72 , Z ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.72 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.32/1.72 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.72 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.32/1.72 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.72 ) ), Z ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.32/1.72 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.32/1.72 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.32/1.72 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.32/1.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.32/1.72 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.32/1.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.32/1.72 ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.72 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.32/1.72 ) ],
% 1.32/1.72 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.32/1.72 'tc_nat' ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), Y ), Y ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.72 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.32/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.72 'c_Int_OPls', X ) ), Y ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.32/1.72 , 'c_FFT__Mirabelle_Oroot'( X ) ), X ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.72 'tc_Complex_Ocomplex' ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.72 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.32/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.32/1.72 , Y ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.32/1.72 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.72 , X ) ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ) ) ) ],
% 1.32/1.72 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.72 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.32/1.72 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), T ), Y ) ), Z ) ), U ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), T ), Z ) ), U ) ) ],
% 1.32/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.72 Y ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.32/1.72 Y ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.32/1.72 Y ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.32/1.72 Y ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.72 Y ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.32/1.72 Y ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.72 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.32/1.72 ) ), Z ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.72 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.32/1.72 ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.72 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.32/1.72 ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.72 X ), Y ), Z ) ), Z ), Y ) ],
% 1.32/1.72 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 X ), Y ), Z ) ), T ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 X ), Y ), Z ) ), T ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.32/1.72 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.32/1.72 'tc_nat' ) ) ],
% 1.32/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.32/1.72 'tc_nat' ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ) ), =( Z, T ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), T ), T ) ) ), =( Y, Z ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.32/1.72 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.72 , X ) ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.32/1.72 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), U ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.32/1.72 ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.32/1.72 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.32/1.72 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 'tc_nat' ), X ), X ) ) ],
% 1.32/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.72 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.32/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.32/1.72 , Y ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.32/1.72 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.72 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.32/1.72 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.72 X ), Y ), Z ) ), Z ), Y ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), X ), Y ) ],
% 1.32/1.72 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Y ), X ) ],
% 1.32/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.32/1.72 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.32/1.72 [ ~( =( 'c_FFT__Mirabelle_OIDFT'( hAPP( hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ), 'v_a', 'v_i' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_Complex_Ocomplex' ),
% 1.32/1.72 'c_FFT__Mirabelle_OIDFT'( 'v_m', 'c_COMBB'( 'v_a', hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat'
% 1.32/1.72 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'v_i' ), 'v_m'
% 1.32/1.72 ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' )
% 1.32/1.72 , hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.32/1.72 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ),
% 1.32/1.72 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ),
% 1.32/1.72 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.72 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.72 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ) ) ) ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'v_i' ), 'v_m' ) ) ),
% 1.32/1.72 'c_FFT__Mirabelle_OIDFT'( 'v_m', 'c_COMBB'( 'v_a', 'c_COMBC'( 'c_COMBB'(
% 1.32/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP(
% 1.32/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.72 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 1.32/1.72 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.32/1.72 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), hAPP( hAPP(
% 1.32/1.72 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'v_i' ), 'v_m' ) ) ) ) ) ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ), ~(
% 1.32/1.72 'class_Lattices_Oboolean__algebra'( Y ) ) ],
% 1.32/1.72 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.32/1.72 'class_Orderings_Opreorder'( Y ) ) ],
% 1.32/1.72 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.32/1.72 'class_Orderings_Oorder'( Y ) ) ],
% 1.32/1.72 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.32/1.72 ],
% 1.32/1.72 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.32/1.72 ) ],
% 1.32/1.72 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.32/1.72 ],
% 1.32/1.72 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.32/1.72 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.32/1.72 'tc_Int_Oint' ) ],
% 1.32/1.72 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.32/1.72 'tc_Int_Oint' ) ],
% 1.32/1.72 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.32/1.72 'tc_Int_Oint' ) ],
% 1.32/1.72 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.32/1.72 ],
% 1.32/1.72 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.32/1.72 ],
% 1.32/1.72 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.32/1.72 ,
% 1.32/1.72 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.32/1.72 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.32/1.72 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.32/1.72 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.32/1.72 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.32/1.73 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.32/1.73 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.32/1.73 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.32/1.73 ],
% 1.32/1.73 [ 'class_RealVector_Oreal__normed__algebra__1'( 'tc_Complex_Ocomplex' )
% 1.32/1.73 ],
% 1.32/1.73 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.32/1.73 ],
% 1.32/1.73 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.32/1.73 ],
% 1.32/1.73 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.73 ,
% 1.32/1.73 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.73 ,
% 1.32/1.73 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.73 ,
% 1.32/1.73 [ 'class_RealVector_Oreal__normed__vector'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.73 ,
% 1.32/1.73 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.73 ,
% 1.32/1.73 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.73 ,
% 1.32/1.73 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.73 ,
% 1.32/1.73 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.73 ,
% 1.32/1.73 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.73 ,
% 1.32/1.73 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.73 ,
% 1.32/1.73 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.73 ,
% 1.32/1.73 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ 'class_RealVector_Ometric__space'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ 'class_RealVector_Oreal__field'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.73 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.32/1.73 ,
% 1.32/1.73 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.32/1.73 ,
% 1.32/1.73 [ 'c_fequal'( X, X, Y ) ],
% 1.32/1.73 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.32/1.73 ] .
% 1.32/1.73
% 1.32/1.73
% 1.32/1.73 percentage equality = 0.227338, percentage horn = 0.856278
% 1.32/1.73 This is a problem with some equality
% 1.32/1.73
% 1.32/1.73
% 1.32/1.73
% 1.32/1.73 Options Used:
% 1.32/1.73
% 1.32/1.73 useres = 1
% 1.32/1.73 useparamod = 1
% 1.32/1.73 useeqrefl = 1
% 1.32/1.73 useeqfact = 1
% 1.32/1.73 usefactor = 1
% 1.32/1.73 usesimpsplitting = 0
% 1.32/1.73 usesimpdemod = 5
% 1.32/1.73 usesimpres = 3
% 1.32/1.73
% 1.32/1.73 resimpinuse = 1000
% 1.32/1.73 resimpclauses = 20000
% 1.32/1.73 substype = eqrewr
% 1.32/1.73 backwardsubs = 1
% 1.32/1.73 selectoldest = 5
% 1.32/1.73
% 1.32/1.73 litorderings [0] = split
% 1.32/1.73 litorderings [1] = extend the termordering, first sorting on arguments
% 1.32/1.73
% 1.32/1.73 termordering = kbo
% 1.32/1.73
% 1.32/1.73 litapriori = 0
% 1.32/1.73 termapriori = 1
% 1.32/1.73 litaposteriori = 0
% 1.32/1.73 termaposteriori = 0
% 1.32/1.73 demodaposteriori = 0
% 1.32/1.73 ordereqreflfact = 0
% 1.32/1.73
% 1.32/1.73 litselect = negord
% 1.32/1.73
% 1.32/1.73 maxweight = 15
% 1.32/1.73 maxdepth = 30000
% 1.32/1.73 maxlength = 115
% 1.32/1.73 maxnrvars = 195
% 1.32/1.73 excuselevel = 1
% 1.32/1.73 increasemaxweight = 1
% 1.32/1.73
% 1.32/1.73 maxselected = 10000000
% 1.32/1.73 maxnrclauses = 10000000
% 1.32/1.73
% 1.32/1.73 showgenerated = 0
% 1.32/1.73 showkept = 0
% 1.32/1.73 showselected = 0
% 1.32/1.73 showdeleted = 0
% 1.32/1.73 showresimp = 1
% 1.32/1.73 showstatus = 2000
% 1.32/1.73
% 1.32/1.73 prologoutput = 1
% 1.32/1.73 nrgoals = 5000000
% 1.32/1.73 totalproof = 1
% 1.32/1.73
% 1.32/1.73 Symbols occurring in the translation:
% 1.32/1.73
% 1.32/1.73 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.32/1.73 . [1, 2] (w:1, o:163, a:1, s:1, b:0),
% 1.32/1.73 ! [4, 1] (w:0, o:79, a:1, s:1, b:0),
% 1.32/1.73 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.32/1.73 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.32/1.73 'class_Ring__and__Field_Oordered__field' [40, 1] (w:1, o:89, a:1, s:1
% 1.32/1.73 , b:0),
% 1.32/1.73 'class_Ring__and__Field_Odivision__by__zero' [41, 1] (w:1, o:93, a:1
% 1.32/1.73 , s:1, b:0),
% 1.32/1.73 'class_Int_Onumber' [42, 1] (w:1, o:94, a:1, s:1, b:0),
% 1.32/1.73 'c_HOL_Oinverse__class_Odivide' [43, 1] (w:1, o:95, a:1, s:1, b:0),
% 1.32/1.73 hAPP [45, 2] (w:1, o:188, a:1, s:1, b:0),
% 1.32/1.73 'c_Int_Onumber__class_Onumber__of' [48, 2] (w:1, o:189, a:1, s:1, b:0
% 1.32/1.73 ),
% 1.32/1.73 'c_lessequals' [49, 3] (w:1, o:192, a:1, s:1, b:0),
% 1.32/1.73 'c_HOL_Ozero__class_Ozero' [50, 1] (w:1, o:96, a:1, s:1, b:0),
% 1.32/1.73 'c_HOL_Oord__class_Oless' [51, 3] (w:1, o:193, a:1, s:1, b:0),
% 1.32/1.73 'class_OrderedGroup_Olordered__ab__group__add' [52, 1] (w:1, o:97, a:
% 1.32/1.73 1, s:1, b:0),
% 1.32/1.73 'c_HOL_Ouminus__class_Ouminus' [54, 1] (w:1, o:99, a:1, s:1, b:0),
% 1.32/1.73 'c_HOL_Oplus__class_Oplus' [55, 1] (w:1, o:101, a:1, s:1, b:0),
% 1.32/1.73 'c_Suc' [58, 0] (w:1, o:22, a:1, s:1, b:0),
% 1.32/1.73 'c_Groebner__Basis_Ogb__semiring' [64, 6] (w:1, o:204, a:1, s:1, b:0)
% 1.32/1.73 ,
% 1.32/1.73 'class_Ring__and__Field_Opordered__ring__abs' [66, 1] (w:1, o:108, a:
% 1.32/1.73 1, s:1, b:0),
% 1.32/1.73 'c_HOL_Oabs__class_Oabs' [67, 1] (w:1, o:109, a:1, s:1, b:0),
% 1.32/1.73 'c_HOL_Otimes__class_Otimes' [68, 1] (w:1, o:98, a:1, s:1, b:0),
% 1.32/1.73 'tc_nat' [69, 0] (w:1, o:35, a:1, s:1, b:0),
% 1.32/1.73 'class_Ring__and__Field_Oordered__idom' [73, 1] (w:1, o:102, a:1, s:1
% 1.32/1.73 , b:0),
% 1.32/1.73 'c_Power_Opower__class_Opower' [74, 1] (w:1, o:110, a:1, s:1, b:0),
% 1.32/1.73 'c_Parity_Oeven__odd__class_Oeven' [76, 2] (w:1, o:190, a:1, s:1, b:0
% 1.32/1.73 ),
% 1.32/1.73 'class_OrderedGroup_Opordered__ab__group__add__abs' [77, 1] (w:1, o:
% 1.32/1.73 112, a:1, s:1, b:0),
% 1.32/1.73 'class_Orderings_Olinorder' [78, 1] (w:1, o:113, a:1, s:1, b:0),
% 2.56/2.89 'class_Orderings_Oorder' [79, 1] (w:1, o:114, a:1, s:1, b:0),
% 2.56/2.89 'class_RealVector_Ometric__space' [81, 1] (w:1, o:115, a:1, s:1, b:0)
% 2.56/2.89 ,
% 2.56/2.89 'class_RealVector_Oreal__normed__algebra__1' [82, 1] (w:1, o:116, a:1
% 2.56/2.89 , s:1, b:0),
% 2.56/2.89 'c_Lim_OLIM' [86, 5] (w:1, o:201, a:1, s:1, b:0),
% 2.56/2.89 'tc_Int_Oint' [88, 0] (w:1, o:48, a:1, s:1, b:0),
% 2.56/2.89 hBOOL [90, 1] (w:1, o:117, a:1, s:1, b:0),
% 2.56/2.89 'class_Lattices_Oboolean__algebra' [91, 1] (w:1, o:118, a:1, s:1, b:0
% 2.56/2.89 ),
% 2.56/2.89 'class_OrderedGroup_Ogroup__add' [92, 1] (w:1, o:119, a:1, s:1, b:0)
% 2.56/2.89 ,
% 2.56/2.89 'class_OrderedGroup_Olordered__ab__group__add__abs' [93, 1] (w:1, o:
% 2.56/2.89 120, a:1, s:1, b:0),
% 2.56/2.89 'class_Divides_Osemiring__div' [94, 1] (w:1, o:121, a:1, s:1, b:0),
% 2.56/2.89 'c_Divides_Odiv__class_Odiv' [95, 3] (w:1, o:194, a:1, s:1, b:0),
% 2.56/2.89 'class_OrderedGroup_Opordered__ab__group__add' [96, 1] (w:1, o:122
% 2.56/2.89 , a:1, s:1, b:0),
% 2.56/2.89 'class_Ring__and__Field_Ozero__neq__one' [97, 1] (w:1, o:123, a:1, s:
% 2.56/2.89 1, b:0),
% 2.56/2.89 'class_Ring__and__Field_Ono__zero__divisors' [98, 1] (w:1, o:88, a:1
% 2.56/2.89 , s:1, b:0),
% 2.56/2.89 'class_Ring__and__Field_Omult__zero' [99, 1] (w:1, o:85, a:1, s:1, b:
% 2.56/2.89 0),
% 2.56/2.89 'class_Power_Opower' [100, 1] (w:1, o:139, a:1, s:1, b:0),
% 2.56/2.89 'class_Ring__and__Field_Osemiring__0' [101, 1] (w:1, o:144, a:1, s:1
% 2.56/2.89 , b:0),
% 2.56/2.89 'class_Ring__and__Field_Oordered__ring__strict' [102, 1] (w:1, o:103
% 2.56/2.89 , a:1, s:1, b:0),
% 2.56/2.89 'class_Ring__and__Field_Oordered__semiring__strict' [103, 1] (w:1, o:
% 2.56/2.89 104, a:1, s:1, b:0),
% 2.56/2.89 'class_OrderedGroup_Ocomm__monoid__add' [104, 1] (w:1, o:124, a:1, s:
% 2.56/2.89 1, b:0),
% 2.56/2.89 'c_SetInterval_Oord__class_OatLeastLessThan' [105, 3] (w:1, o:195, a:
% 2.56/2.89 1, s:1, b:0),
% 2.56/2.89 'c_Finite__Set_Osetsum' [106, 4] (w:1, o:199, a:1, s:1, b:0),
% 2.56/2.89 'class_Ring__and__Field_Oordered__semidom' [107, 1] (w:1, o:105, a:1
% 2.56/2.89 , s:1, b:0),
% 2.56/2.89 'class_Ring__and__Field_Omult__mono1' [108, 1] (w:1, o:86, a:1, s:1
% 2.56/2.89 , b:0),
% 2.56/2.89 'class_Ring__and__Field_Omult__mono' [109, 1] (w:1, o:87, a:1, s:1
% 2.56/2.89 , b:0),
% 2.56/2.89 'class_Ring__and__Field_Opordered__ring' [110, 1] (w:1, o:145, a:1
% 2.56/2.89 , s:1, b:0),
% 2.56/2.89 'c_HOL_Ominus__class_Ominus' [111, 1] (w:1, o:146, a:1, s:1, b:0),
% 2.56/2.89 'v_m' [114, 0] (w:1, o:51, a:1, s:1, b:0),
% 2.56/2.89 'class_Ring__and__Field_Opordered__cancel__semiring' [115, 1] (w:1
% 2.56/2.89 , o:147, a:1, s:1, b:0),
% 2.56/2.89 'c_HOL_Oone__class_Oone' [117, 1] (w:1, o:100, a:1, s:1, b:0),
% 2.56/2.89 'class_OrderedGroup_Oordered__ab__group__add' [118, 1] (w:1, o:111
% 2.56/2.89 , a:1, s:1, b:0),
% 2.56/2.89 'class_Ring__and__Field_Opordered__semiring' [119, 1] (w:1, o:148, a:
% 2.56/2.89 1, s:1, b:0),
% 2.56/2.89 'class_OrderedGroup_Opordered__comm__monoid__add' [120, 1] (w:1, o:
% 2.56/2.89 125, a:1, s:1, b:0),
% 2.56/2.89 'class_OrderedGroup_Oab__group__add' [122, 1] (w:1, o:126, a:1, s:1
% 2.56/2.89 , b:0),
% 2.56/2.89 'class_Ring__and__Field_Oabs__if' [123, 1] (w:1, o:149, a:1, s:1, b:0
% 2.56/2.89 ),
% 2.56/2.89 'class_Ring__and__Field_Oordered__semiring' [124, 1] (w:1, o:106, a:1
% 2.56/2.89 , s:1, b:0),
% 2.56/2.89 'class_Int_Onumber__ring' [125, 1] (w:1, o:150, a:1, s:1, b:0),
% 2.56/2.89 'c_Int_OPls' [126, 0] (w:1, o:55, a:1, s:1, b:0),
% 2.56/2.89 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [128, 1]
% 2.56/2.89 (w:1, o:127, a:1, s:1, b:0),
% 2.56/2.89 'c_COMBB' [129, 5] (w:1, o:202, a:1, s:1, b:0),
% 2.56/2.89 'c_Fun_Oinj__on' [132, 4] (w:1, o:200, a:1, s:1, b:0),
% 2.56/2.89 'class_RealVector_Oreal__normed__vector' [134, 1] (w:1, o:151, a:1
% 2.56/2.89 , s:1, b:0),
% 2.56/2.89 'class_Ring__and__Field_Olordered__ring' [135, 1] (w:1, o:84, a:1, s:
% 2.56/2.89 1, b:0),
% 2.56/2.89 'class_Ring__and__Field_Ofield' [136, 1] (w:1, o:152, a:1, s:1, b:0)
% 2.56/2.89 ,
% 2.56/2.89 'class_Orderings_Opreorder' [137, 1] (w:1, o:128, a:1, s:1, b:0),
% 2.56/2.89 'c_Int_OMin' [146, 0] (w:1, o:64, a:1, s:1, b:0),
% 2.56/2.89 'class_OrderedGroup_Omonoid__mult' [147, 1] (w:1, o:129, a:1, s:1, b:
% 2.56/2.89 0),
% 2.56/2.89 'c_Int_OBit1' [149, 1] (w:1, o:154, a:1, s:1, b:0),
% 2.56/2.89 'class_Ring__and__Field_Oordered__comm__semiring__strict' [150, 1]
% 2.56/2.89 (w:1, o:107, a:1, s:1, b:0),
% 2.56/2.89 'class_Ring__and__Field_Ocomm__ring__1' [151, 1] (w:1, o:90, a:1, s:1
% 2.56/2.89 , b:0),
% 2.56/2.89 'c_Int_OBit0' [152, 1] (w:1, o:153, a:1, s:1, b:0),
% 10.47/10.81 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [154, 1]
% 10.47/10.81 (w:1, o:130, a:1, s:1, b:0),
% 10.47/10.81 'class_RealVector_Oreal__normed__algebra' [158, 1] (w:1, o:155, a:1
% 10.47/10.81 , s:1, b:0),
% 10.47/10.81 'class_Ring__and__Field_Oring' [159, 1] (w:1, o:140, a:1, s:1, b:0),
% 10.47/10.81
% 10.47/10.81 'class_Ring__and__Field_Oring__no__zero__divisors' [160, 1] (w:1, o:
% 10.47/10.81 141, a:1, s:1, b:0),
% 10.47/10.81 'class_Ring__and__Field_Ocomm__semiring__1' [161, 1] (w:1, o:91, a:1
% 10.47/10.81 , s:1, b:0),
% 10.47/10.81 'class_Ring__and__Field_Oidom' [162, 1] (w:1, o:156, a:1, s:1, b:0),
% 10.47/10.81
% 10.47/10.81 'class_OrderedGroup_Opordered__ab__semigroup__add' [163, 1] (w:1, o:
% 10.47/10.81 131, a:1, s:1, b:0),
% 10.47/10.81 'class_OrderedGroup_Omonoid__add' [164, 1] (w:1, o:132, a:1, s:1, b:0
% 10.47/10.81 ),
% 10.47/10.81 'class_RealVector_Oreal__normed__field' [165, 1] (w:1, o:157, a:1, s:
% 10.47/10.81 1, b:0),
% 10.47/10.81 'tc_fun' [166, 2] (w:1, o:191, a:1, s:1, b:0),
% 10.47/10.81 'c_COMBC' [167, 5] (w:1, o:203, a:1, s:1, b:0),
% 10.47/10.81 'tc_Complex_Ocomplex' [171, 0] (w:1, o:69, a:1, s:1, b:0),
% 10.47/10.81 'c_FFT__Mirabelle_Oroot' [172, 1] (w:1, o:158, a:1, s:1, b:0),
% 10.47/10.81 'class_Ring__and__Field_Oring__1__no__zero__divisors' [175, 1] (w:1
% 10.47/10.81 , o:142, a:1, s:1, b:0),
% 10.47/10.81 'v_i' [176, 0] (w:1, o:70, a:1, s:1, b:0),
% 10.47/10.81 'class_Ring__and__Field_Oring__1' [178, 1] (w:1, o:143, a:1, s:1, b:0
% 10.47/10.81 ),
% 10.47/10.81 'c_Complex_Oii' [179, 0] (w:1, o:71, a:1, s:1, b:0),
% 10.47/10.81 'c_FFT__Mirabelle_ODFT' [180, 3] (w:1, o:196, a:1, s:1, b:0),
% 10.47/10.81 'class_Ring__and__Field_Osemiring__1' [181, 1] (w:1, o:159, a:1, s:1
% 10.47/10.81 , b:0),
% 10.47/10.81 'c_FFT__Mirabelle_OIDFT' [182, 3] (w:1, o:197, a:1, s:1, b:0),
% 10.47/10.81 'class_Ring__and__Field_Ocomm__semiring' [186, 1] (w:1, o:92, a:1, s:
% 10.47/10.81 1, b:0),
% 10.47/10.81 'class_OrderedGroup_Ocancel__ab__semigroup__add' [187, 1] (w:1, o:133
% 10.47/10.81 , a:1, s:1, b:0),
% 10.47/10.81 'class_OrderedGroup_Ocancel__semigroup__add' [188, 1] (w:1, o:134, a:
% 10.47/10.81 1, s:1, b:0),
% 10.47/10.81 'class_RealVector_Oreal__field' [189, 1] (w:1, o:160, a:1, s:1, b:0)
% 10.47/10.81 ,
% 10.47/10.81 'class_Ring__and__Field_Osemiring' [191, 1] (w:1, o:161, a:1, s:1, b:
% 10.47/10.81 0),
% 10.47/10.81 'class_OrderedGroup_Oab__semigroup__mult' [192, 1] (w:1, o:135, a:1
% 10.47/10.81 , s:1, b:0),
% 10.47/10.81 'class_OrderedGroup_Ocomm__monoid__mult' [193, 1] (w:1, o:136, a:1
% 10.47/10.81 , s:1, b:0),
% 10.47/10.81 'class_OrderedGroup_Oab__semigroup__idem__mult' [194, 1] (w:1, o:137
% 10.47/10.81 , a:1, s:1, b:0),
% 10.47/10.81 'class_OrderedGroup_Oab__semigroup__add' [195, 1] (w:1, o:138, a:1
% 10.47/10.81 , s:1, b:0),
% 10.47/10.81 'class_Int_Oring__char__0' [198, 1] (w:1, o:162, a:1, s:1, b:0),
% 10.47/10.81 'v_a' [199, 0] (w:1, o:74, a:1, s:1, b:0),
% 10.47/10.81 'c_fequal' [202, 3] (w:1, o:198, a:1, s:1, b:0).
% 10.47/10.81
% 10.47/10.81
% 10.47/10.81 Starting Search:
% 10.47/10.81
% 10.47/10.81 Resimplifying inuse:
% 10.47/10.81 Done
% 10.47/10.81
% 10.47/10.81
% 10.47/10.81 Intermediate Status:
% 10.47/10.81 Generated: 4208
% 10.47/10.81 Kept: 2012
% 10.47/10.81 Inuse: 85
% 10.47/10.81 Deleted: 1
% 10.47/10.81 Deletedinuse: 0
% 10.47/10.81
% 10.47/10.81 Resimplifying inuse:
% 10.47/10.81 Done
% 10.47/10.81
% 10.47/10.81 Resimplifying inuse:
% 10.47/10.81 Done
% 10.47/10.81
% 10.47/10.81
% 10.47/10.81 Intermediate Status:
% 10.47/10.81 Generated: 10226
% 10.47/10.81 Kept: 4138
% 10.47/10.81 Inuse: 135
% 10.47/10.81 Deleted: 1
% 10.47/10.81 Deletedinuse: 0
% 10.47/10.81
% 10.47/10.81 Resimplifying inuse:
% 10.47/10.81 Done
% 10.47/10.81
% 10.47/10.81 Resimplifying inuse:
% 10.47/10.81 Done
% 10.47/10.81
% 10.47/10.81
% 10.47/10.81 Intermediate Status:
% 10.47/10.81 Generated: 16351
% 10.47/10.81 Kept: 6159
% 10.47/10.81 Inuse: 193
% 10.47/10.81 Deleted: 8
% 10.47/10.81 Deletedinuse: 0
% 10.47/10.81
% 10.47/10.81 Resimplifying inuse:
% 10.47/10.81 Done
% 10.47/10.81
% 10.47/10.81 Resimplifying inuse:
% 10.47/10.81 Done
% 10.47/10.81
% 10.47/10.81
% 10.47/10.81 Intermediate Status:
% 10.47/10.81 Generated: 25082
% 10.47/10.81 Kept: 8236
% 10.47/10.81 Inuse: 268
% 10.47/10.81 Deleted: 8
% 10.47/10.81 Deletedinuse: 0
% 10.47/10.81
% 10.47/10.81 Resimplifying inuse:
% 10.47/10.81 Done
% 10.47/10.81
% 10.47/10.81 Resimplifying inuse:
% 10.47/10.81 Done
% 10.47/10.81
% 10.47/10.81
% 10.47/10.81 Intermediate Status:
% 10.47/10.81 Generated: 33039
% 10.47/10.81 Kept: 10330
% 10.47/10.81 Inuse: 327
% 10.47/10.81 Deleted: 9
% 10.47/10.81 Deletedinuse: 0
% 10.47/10.81
% 10.47/10.81 Resimplifying inuse:
% 10.47/10.81 Done
% 10.47/10.81
% 10.47/10.81
% 10.47/10.81 Intermediate Status:
% 10.47/10.81 Generated: 40467
% 10.47/10.81 Kept: 12967
% 10.47/10.81 Inuse: 375
% 10.47/10.81 Deleted: 13
% 10.47/10.81 Deletedinuse: 1
% 10.47/10.81
% 10.47/10.81 Resimplifying inuse:
% 10.47/10.81 Done
% 10.47/10.81
% 10.47/10.81 Resimplifying inuse:
% 10.47/10.81 Done
% 10.47/10.81
% 10.47/10.81
% 10.47/10.81 Intermediate Status:
% 10.47/10.81 Generated: 46188
% 10.47/10.81 Kept: 15611
% 10.47/10.81 Inuse: 384
% 10.47/10.81 Deleted: 13
% 10.47/10.81 Deletedinuse: 1
% 10.47/10.81
% 10.47/10.81 Resimplifying inuse:
% 10.47/10.81 Done
% 10.47/10.81
% 10.47/10.81 Resimplifying inuse:
% 10.47/10.81 Done
% 10.47/10.81
% 10.47/10.81
% 10.47/10.81 Intermediate Status:
% 10.47/10.81 Generated: 51571
% 10.47/10.81 Kept: 17640
% 10.47/10.81 Inuse: 404
% 10.47/10.81 Deleted: 13
% 10.47/10.81 Deletedinuse: 1
% 10.47/10.81
% 10.47/10.81 Resimplifying inuse:
% 10.47/10.81 Done
% 10.47/10.81
% 10.47/10.81 Resimplifying inuse:
% 10.47/10.81 Done
% 10.47/10.81
% 10.47/10.81
% 10.47/10.81 Intermediate Status:
% 10.47/10.81 Generated: 59124
% 10.47/10.81 Kept: 19857
% 10.47/10.81 Inuse: 448
% 10.47/10.81 Deleted: 15
% 10.47/10.81 Deletedinuse: 2
% 10.47/10.81
% 10.47/10.81 Resimplifying clauses:
% 10.47/10.81 Done
% 10.47/10.81
% 10.47/10.81 Resimplifying inuse:
% 10.47/10.81 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 66336
% 32.98/33.35 Kept: 22186
% 32.98/33.35 Inuse: 500
% 32.98/33.35 Deleted: 322
% 32.98/33.35 Deletedinuse: 2
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 72643
% 32.98/33.35 Kept: 24231
% 32.98/33.35 Inuse: 525
% 32.98/33.35 Deleted: 325
% 32.98/33.35 Deletedinuse: 5
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 80340
% 32.98/33.35 Kept: 26231
% 32.98/33.35 Inuse: 540
% 32.98/33.35 Deleted: 325
% 32.98/33.35 Deletedinuse: 5
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 86805
% 32.98/33.35 Kept: 28414
% 32.98/33.35 Inuse: 575
% 32.98/33.35 Deleted: 325
% 32.98/33.35 Deletedinuse: 5
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 93540
% 32.98/33.35 Kept: 30468
% 32.98/33.35 Inuse: 615
% 32.98/33.35 Deleted: 325
% 32.98/33.35 Deletedinuse: 5
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 104692
% 32.98/33.35 Kept: 33358
% 32.98/33.35 Inuse: 655
% 32.98/33.35 Deleted: 325
% 32.98/33.35 Deletedinuse: 5
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 111290
% 32.98/33.35 Kept: 35511
% 32.98/33.35 Inuse: 695
% 32.98/33.35 Deleted: 325
% 32.98/33.35 Deletedinuse: 5
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 117351
% 32.98/33.35 Kept: 37721
% 32.98/33.35 Inuse: 725
% 32.98/33.35 Deleted: 325
% 32.98/33.35 Deletedinuse: 5
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 125545
% 32.98/33.35 Kept: 39819
% 32.98/33.35 Inuse: 758
% 32.98/33.35 Deleted: 325
% 32.98/33.35 Deletedinuse: 5
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying clauses:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 136522
% 32.98/33.35 Kept: 43198
% 32.98/33.35 Inuse: 793
% 32.98/33.35 Deleted: 859
% 32.98/33.35 Deletedinuse: 6
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 142346
% 32.98/33.35 Kept: 45198
% 32.98/33.35 Inuse: 822
% 32.98/33.35 Deleted: 859
% 32.98/33.35 Deletedinuse: 6
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 150162
% 32.98/33.35 Kept: 47384
% 32.98/33.35 Inuse: 845
% 32.98/33.35 Deleted: 859
% 32.98/33.35 Deletedinuse: 6
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 158047
% 32.98/33.35 Kept: 49485
% 32.98/33.35 Inuse: 870
% 32.98/33.35 Deleted: 859
% 32.98/33.35 Deletedinuse: 6
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 164503
% 32.98/33.35 Kept: 51564
% 32.98/33.35 Inuse: 895
% 32.98/33.35 Deleted: 859
% 32.98/33.35 Deletedinuse: 6
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 171498
% 32.98/33.35 Kept: 53583
% 32.98/33.35 Inuse: 910
% 32.98/33.35 Deleted: 860
% 32.98/33.35 Deletedinuse: 7
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 185898
% 32.98/33.35 Kept: 55988
% 32.98/33.35 Inuse: 935
% 32.98/33.35 Deleted: 860
% 32.98/33.35 Deletedinuse: 7
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 195125
% 32.98/33.35 Kept: 58121
% 32.98/33.35 Inuse: 960
% 32.98/33.35 Deleted: 860
% 32.98/33.35 Deletedinuse: 7
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 202489
% 32.98/33.35 Kept: 60231
% 32.98/33.35 Inuse: 975
% 32.98/33.35 Deleted: 860
% 32.98/33.35 Deletedinuse: 7
% 32.98/33.35
% 32.98/33.35 Resimplifying clauses:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 211533
% 32.98/33.35 Kept: 62234
% 32.98/33.35 Inuse: 1004
% 32.98/33.35 Deleted: 1291
% 32.98/33.35 Deletedinuse: 7
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 219857
% 32.98/33.35 Kept: 64508
% 32.98/33.35 Inuse: 1030
% 32.98/33.35 Deleted: 1291
% 32.98/33.35 Deletedinuse: 7
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 225886
% 32.98/33.35 Kept: 66914
% 32.98/33.35 Inuse: 1045
% 32.98/33.35 Deleted: 1291
% 32.98/33.35 Deletedinuse: 7
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 234478
% 32.98/33.35 Kept: 69113
% 32.98/33.35 Inuse: 1075
% 32.98/33.35 Deleted: 1291
% 32.98/33.35 Deletedinuse: 7
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 242026
% 32.98/33.35 Kept: 71221
% 32.98/33.35 Inuse: 1095
% 32.98/33.35 Deleted: 1291
% 32.98/33.35 Deletedinuse: 7
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 32.98/33.35 Generated: 250727
% 32.98/33.35 Kept: 73347
% 32.98/33.35 Inuse: 1115
% 32.98/33.35 Deleted: 1291
% 32.98/33.35 Deletedinuse: 7
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35 Resimplifying inuse:
% 32.98/33.35 Done
% 32.98/33.35
% 32.98/33.35
% 32.98/33.35 Intermediate Status:
% 80.55/80.90 Generated: 258908
% 80.55/80.90 Kept: 75652
% 80.55/80.90 Inuse: 1135
% 80.55/80.90 Deleted: 1291
% 80.55/80.90 Deletedinuse: 7
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 267642
% 80.55/80.90 Kept: 77673
% 80.55/80.90 Inuse: 1166
% 80.55/80.90 Deleted: 1291
% 80.55/80.90 Deletedinuse: 7
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 277489
% 80.55/80.90 Kept: 79687
% 80.55/80.90 Inuse: 1198
% 80.55/80.90 Deleted: 1291
% 80.55/80.90 Deletedinuse: 7
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying clauses:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 284936
% 80.55/80.90 Kept: 81882
% 80.55/80.90 Inuse: 1205
% 80.55/80.90 Deleted: 1660
% 80.55/80.90 Deletedinuse: 7
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 292735
% 80.55/80.90 Kept: 84054
% 80.55/80.90 Inuse: 1225
% 80.55/80.90 Deleted: 1660
% 80.55/80.90 Deletedinuse: 7
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 300543
% 80.55/80.90 Kept: 86113
% 80.55/80.90 Inuse: 1235
% 80.55/80.90 Deleted: 1660
% 80.55/80.90 Deletedinuse: 7
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 309479
% 80.55/80.90 Kept: 88273
% 80.55/80.90 Inuse: 1265
% 80.55/80.90 Deleted: 1660
% 80.55/80.90 Deletedinuse: 7
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 318943
% 80.55/80.90 Kept: 90485
% 80.55/80.90 Inuse: 1295
% 80.55/80.90 Deleted: 1661
% 80.55/80.90 Deletedinuse: 8
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 328587
% 80.55/80.90 Kept: 92898
% 80.55/80.90 Inuse: 1320
% 80.55/80.90 Deleted: 1661
% 80.55/80.90 Deletedinuse: 8
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 345668
% 80.55/80.90 Kept: 96546
% 80.55/80.90 Inuse: 1326
% 80.55/80.90 Deleted: 1661
% 80.55/80.90 Deletedinuse: 8
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 356979
% 80.55/80.90 Kept: 99861
% 80.55/80.90 Inuse: 1345
% 80.55/80.90 Deleted: 1661
% 80.55/80.90 Deletedinuse: 8
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying clauses:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 362559
% 80.55/80.90 Kept: 101861
% 80.55/80.90 Inuse: 1360
% 80.55/80.90 Deleted: 2067
% 80.55/80.90 Deletedinuse: 8
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 369871
% 80.55/80.90 Kept: 104217
% 80.55/80.90 Inuse: 1380
% 80.55/80.90 Deleted: 2067
% 80.55/80.90 Deletedinuse: 8
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 376167
% 80.55/80.90 Kept: 106233
% 80.55/80.90 Inuse: 1400
% 80.55/80.90 Deleted: 2067
% 80.55/80.90 Deletedinuse: 8
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 383741
% 80.55/80.90 Kept: 108334
% 80.55/80.90 Inuse: 1425
% 80.55/80.90 Deleted: 2073
% 80.55/80.90 Deletedinuse: 14
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 391840
% 80.55/80.90 Kept: 110656
% 80.55/80.90 Inuse: 1445
% 80.55/80.90 Deleted: 2073
% 80.55/80.90 Deletedinuse: 14
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 400023
% 80.55/80.90 Kept: 112736
% 80.55/80.90 Inuse: 1455
% 80.55/80.90 Deleted: 2073
% 80.55/80.90 Deletedinuse: 14
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 406744
% 80.55/80.90 Kept: 114819
% 80.55/80.90 Inuse: 1480
% 80.55/80.90 Deleted: 2073
% 80.55/80.90 Deletedinuse: 14
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 414569
% 80.55/80.90 Kept: 116820
% 80.55/80.90 Inuse: 1505
% 80.55/80.90 Deleted: 2073
% 80.55/80.90 Deletedinuse: 14
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 438532
% 80.55/80.90 Kept: 120173
% 80.55/80.90 Inuse: 1525
% 80.55/80.90 Deleted: 2073
% 80.55/80.90 Deletedinuse: 14
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying clauses:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 450109
% 80.55/80.90 Kept: 122653
% 80.55/80.90 Inuse: 1555
% 80.55/80.90 Deleted: 3311
% 80.55/80.90 Deletedinuse: 14
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 459739
% 80.55/80.90 Kept: 125010
% 80.55/80.90 Inuse: 1575
% 80.55/80.90 Deleted: 3311
% 80.55/80.90 Deletedinuse: 14
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 468853
% 80.55/80.90 Kept: 127159
% 80.55/80.90 Inuse: 1595
% 80.55/80.90 Deleted: 3311
% 80.55/80.90 Deletedinuse: 14
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 482600
% 80.55/80.90 Kept: 130538
% 80.55/80.90 Inuse: 1615
% 80.55/80.90 Deleted: 3311
% 80.55/80.90 Deletedinuse: 14
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90 Resimplifying inuse:
% 80.55/80.90 Done
% 80.55/80.90
% 80.55/80.90
% 80.55/80.90 Intermediate Status:
% 80.55/80.90 Generated: 490332
% 195.40/195.78 Kept: 132813
% 195.40/195.78 Inuse: 1639
% 195.40/195.78 Deleted: 3312
% 195.40/195.78 Deletedinuse: 14
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 498416
% 195.40/195.78 Kept: 134983
% 195.40/195.78 Inuse: 1668
% 195.40/195.78 Deleted: 3313
% 195.40/195.78 Deletedinuse: 14
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 514032
% 195.40/195.78 Kept: 138415
% 195.40/195.78 Inuse: 1693
% 195.40/195.78 Deleted: 3313
% 195.40/195.78 Deletedinuse: 14
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 522210
% 195.40/195.78 Kept: 140511
% 195.40/195.78 Inuse: 1698
% 195.40/195.78 Deleted: 3313
% 195.40/195.78 Deletedinuse: 14
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying clauses:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 532626
% 195.40/195.78 Kept: 142625
% 195.40/195.78 Inuse: 1723
% 195.40/195.78 Deleted: 3793
% 195.40/195.78 Deletedinuse: 14
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 543237
% 195.40/195.78 Kept: 144949
% 195.40/195.78 Inuse: 1746
% 195.40/195.78 Deleted: 3796
% 195.40/195.78 Deletedinuse: 15
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 568852
% 195.40/195.78 Kept: 151514
% 195.40/195.78 Inuse: 1766
% 195.40/195.78 Deleted: 3796
% 195.40/195.78 Deletedinuse: 15
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 612152
% 195.40/195.78 Kept: 155609
% 195.40/195.78 Inuse: 1801
% 195.40/195.78 Deleted: 3796
% 195.40/195.78 Deletedinuse: 15
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 620667
% 195.40/195.78 Kept: 157684
% 195.40/195.78 Inuse: 1806
% 195.40/195.78 Deleted: 3797
% 195.40/195.78 Deletedinuse: 16
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 628910
% 195.40/195.78 Kept: 159797
% 195.40/195.78 Inuse: 1811
% 195.40/195.78 Deleted: 3797
% 195.40/195.78 Deletedinuse: 16
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 650459
% 195.40/195.78 Kept: 164934
% 195.40/195.78 Inuse: 1831
% 195.40/195.78 Deleted: 3797
% 195.40/195.78 Deletedinuse: 16
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying clauses:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 659745
% 195.40/195.78 Kept: 167111
% 195.40/195.78 Inuse: 1856
% 195.40/195.78 Deleted: 5637
% 195.40/195.78 Deletedinuse: 16
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 669728
% 195.40/195.78 Kept: 169375
% 195.40/195.78 Inuse: 1881
% 195.40/195.78 Deleted: 5637
% 195.40/195.78 Deletedinuse: 16
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 680160
% 195.40/195.78 Kept: 171499
% 195.40/195.78 Inuse: 1906
% 195.40/195.78 Deleted: 5638
% 195.40/195.78 Deletedinuse: 17
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 690505
% 195.40/195.78 Kept: 173522
% 195.40/195.78 Inuse: 1922
% 195.40/195.78 Deleted: 5638
% 195.40/195.78 Deletedinuse: 17
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 696940
% 195.40/195.78 Kept: 175577
% 195.40/195.78 Inuse: 1941
% 195.40/195.78 Deleted: 5638
% 195.40/195.78 Deletedinuse: 17
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 706764
% 195.40/195.78 Kept: 177607
% 195.40/195.78 Inuse: 1965
% 195.40/195.78 Deleted: 5638
% 195.40/195.78 Deletedinuse: 17
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 717133
% 195.40/195.78 Kept: 179617
% 195.40/195.78 Inuse: 1974
% 195.40/195.78 Deleted: 5638
% 195.40/195.78 Deletedinuse: 17
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 727521
% 195.40/195.78 Kept: 182114
% 195.40/195.78 Inuse: 1991
% 195.40/195.78 Deleted: 5638
% 195.40/195.78 Deletedinuse: 17
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 736642
% 195.40/195.78 Kept: 184399
% 195.40/195.78 Inuse: 2011
% 195.40/195.78 Deleted: 5638
% 195.40/195.78 Deletedinuse: 17
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying clauses:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 745571
% 195.40/195.78 Kept: 186636
% 195.40/195.78 Inuse: 2031
% 195.40/195.78 Deleted: 6324
% 195.40/195.78 Deletedinuse: 17
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 755242
% 195.40/195.78 Kept: 188816
% 195.40/195.78 Inuse: 2056
% 195.40/195.78 Deleted: 6324
% 195.40/195.78 Deletedinuse: 17
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 763723
% 195.40/195.78 Kept: 190825
% 195.40/195.78 Inuse: 2080
% 195.40/195.78 Deleted: 6324
% 195.40/195.78 Deletedinuse: 17
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78
% 195.40/195.78 Intermediate Status:
% 195.40/195.78 Generated: 772128
% 195.40/195.78 Kept: 192834
% 195.40/195.78 Inuse: 2101
% 195.40/195.78 Deleted: 6324
% 195.40/195.78 Deletedinuse: 17
% 195.40/195.78
% 195.40/195.78 Resimplifying inuse:
% 195.40/195.78 Done
% 195.40/195.78
% 195.40/195.78 Resimplifying inusCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------