TSTP Solution File: SWV588-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV588-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:26:56 EDT 2022
% Result : Timeout 300.07s 300.45s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV588-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13 % Command : bliksem %s
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % DateTime : Wed Jun 15 09:07:39 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.31/1.68 *** allocated 10000 integers for termspace/termends
% 1.31/1.68 *** allocated 10000 integers for clauses
% 1.31/1.68 *** allocated 10000 integers for justifications
% 1.31/1.68 *** allocated 15000 integers for termspace/termends
% 1.31/1.68 *** allocated 22500 integers for termspace/termends
% 1.31/1.68 *** allocated 33750 integers for termspace/termends
% 1.31/1.68 *** allocated 50625 integers for termspace/termends
% 1.31/1.68 Bliksem 1.12
% 1.31/1.68
% 1.31/1.68
% 1.31/1.68 Automatic Strategy Selection
% 1.31/1.68
% 1.31/1.68 Clauses:
% 1.31/1.68 [
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.31/1.68 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.68 X ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.31/1.68 ,
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.31/1.68 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.68 X ), Y ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.68 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ), Z ) ]
% 1.31/1.68 ,
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.68 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ) ) ],
% 1.31/1.68 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.31/1.68 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.31/1.68 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.31/1.68 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =( hAPP(
% 1.31/1.68 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.31/1.68 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.68 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.31/1.68 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.31/1.68 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.31/1.68 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.68 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.31/1.68 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.31/1.68 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.31/1.68 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.31/1.68 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.31/1.68 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.31/1.68 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.31/1.68 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.68 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.31/1.68 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.31/1.68 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.31/1.68 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.31/1.68 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.31/1.68 [ ~( 'class_RealVector_Ometric__space'( X ) ), =( Y, Z ), ~(
% 1.31/1.68 'c_SEQ_OLIMSEQ'( T, Z, X ) ), ~( 'c_SEQ_OLIMSEQ'( T, Y, X ) ) ],
% 1.31/1.68 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.68 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.31/1.68 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.31/1.68 , Y, 'tc_nat' ) ) ],
% 1.31/1.68 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.31/1.68 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.31/1.68 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.31/1.68 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.31/1.68 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.31/1.68 ) ],
% 1.31/1.68 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.31/1.68 ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.31/1.68 ), =( Z, Y ) ],
% 1.31/1.68 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.31/1.68 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.31/1.68 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( 'c_Suc',
% 1.31/1.68 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 1.31/1.68 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.68 'tc_nat' ), X ), Z ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 1.31/1.68 Z, Y, 'tc_nat' ) ) ],
% 1.31/1.68 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.31/1.68 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ),
% 1.31/1.68 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.31/1.68 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.31/1.68 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.31/1.68 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ),
% 1.31/1.68 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.31/1.68 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.31/1.68 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.31/1.68 'c_lessequals'( Z, T, X ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.31/1.68 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.31/1.68 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.31/1.68 'c_lessequals'( Y, T, X ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.31/1.68 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.68 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.31/1.68 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.31/1.68 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.31/1.68 'c_lessequals'( Z, T, X ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.31/1.68 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.68 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.31/1.68 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.31/1.68 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.31/1.68 'c_lessequals'( Y, T, X ) ) ],
% 1.31/1.68 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), X ), T ), X ), ~(
% 1.31/1.68 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.31/1.68 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.31/1.68 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.31/1.68 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.31/1.68 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.68 'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z,
% 1.31/1.68 'tc_nat' ) ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.68 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ominus__class_Ominus'(
% 1.31/1.68 hAPP( 'c_Suc', Z ), T, 'tc_nat' ) ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.68 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.31/1.68 , T, 'tc_nat' ) ) ), Y ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.31/1.68 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.31/1.68 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.31/1.68 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.31/1.68 ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 1.31/1.68 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.68 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.68 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.68 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.68 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.31/1.68 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.68 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.31/1.68 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.68 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.68 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.68 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.68 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.31/1.68 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.68 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.31/1.68 ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.68 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.68 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.31/1.68 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.31/1.68 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP(
% 1.31/1.68 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X ) ) ],
% 1.31/1.68 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.68 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ), hAPP(
% 1.31/1.68 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.31/1.68 'tc_nat' ) ) ), 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.31/1.68 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.68 ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.31/1.68 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.68 ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.31/1.68 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.68 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.68 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.31/1.68 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.68 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.68 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.68 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.31/1.68 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.31/1.68 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.68 'tc_nat' ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.68 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.68 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.68 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.31/1.68 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.31/1.68 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.31/1.68 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.68 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.31/1.68 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.68 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.68 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.68 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.31/1.68 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.31/1.68 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.31/1.68 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.31/1.68 ), 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.31/1.68 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.68 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.68 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.31/1.68 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.31/1.68 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ), ~( 'c_lessequals'( Z
% 1.31/1.68 , Y, 'tc_nat' ) ) ],
% 1.31/1.68 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.31/1.68 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.68 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), Y ) ), ~(
% 1.31/1.68 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 1.31/1.68 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( 'c_Suc',
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.68 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.31/1.68 ],
% 1.31/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.68 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.68 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.68 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.68 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.31/1.68 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.68 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.31/1.68 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.31/1.68 , hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.31/1.68 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), hAPP(
% 1.31/1.68 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.68 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.68 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.31/1.68 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.68 ), Y ), T ), Z, X ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.68 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.68 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.31/1.68 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.68 X ), T ), Z ), X ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.31/1.68 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.68 X ), X ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.31/1.68 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.31/1.68 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.31/1.68 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.68 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.31/1.68 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP( X, Z ), Y ) ),
% 1.31/1.68 =( Z, Y ), ~( 'c_Ring__and__Field_Oordered__idom'( T, U, W, V0, V1, X, V2
% 1.31/1.68 , V3, V4, V5, V6 ) ) ],
% 1.31/1.68 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( Y, Z ) ), hAPP( hAPP( X, Z ),
% 1.31/1.68 Z ) ), ~( 'c_Ring__and__Field_Oordered__idom'( T, U, W, V0, V1, V2, Y, V3
% 1.31/1.68 , X, V4, V5 ) ) ],
% 1.31/1.68 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( T, Z ) ), Z ), ~(
% 1.31/1.68 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1, V2, V3, T, V4, X, Y,
% 1.31/1.68 V5 ) ) ],
% 1.31/1.68 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.31/1.68 hAPP( X, T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1,
% 1.31/1.68 V2, V3, V4, V5, Y, X, V6 ) ) ],
% 1.31/1.68 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.31/1.68 hAPP( X, T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1,
% 1.31/1.68 V2, V3, X, V4, Y, V5, V6 ) ) ],
% 1.31/1.68 [ =( hAPP( X, hAPP( X, Y ) ), hAPP( X, Y ) ), ~(
% 1.31/1.68 'c_Ring__and__Field_Oordered__idom'( Z, T, U, W, V0, V1, V2, V3, V4, X,
% 1.31/1.68 V5 ) ) ],
% 1.31/1.68 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.31/1.68 V3, V4 ) ), =( hAPP( V3, Z ), Z ) ],
% 1.31/1.68 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( Z, T ), U, W, V0,
% 1.31/1.68 V1, V2, V3, Z, V4 ) ), =( T, hAPP( Z, T ) ) ],
% 1.31/1.68 [ =( hAPP( X, Y ), hAPP( hAPP( Z, Y ), hAPP( T, Y ) ) ), ~(
% 1.31/1.68 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1, V2, V3, X, V4, Z, T,
% 1.31/1.68 V5 ) ) ],
% 1.31/1.68 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.68 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.68 'c_Int_OMin', X ) ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.68 'c_Int_OMin', X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ]
% 1.31/1.68 ,
% 1.31/1.68 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z,
% 1.31/1.68 T, U ), hAPP( W, Y ) ), V0 ) ) ) ), ~(
% 1.31/1.68 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, V4, X, W, Z, T, V5, U
% 1.31/1.68 ) ), =( V0, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.68 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.31/1.68 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.31/1.68 ,
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.31/1.68 ,
% 1.31/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.68 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.31/1.68 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.31/1.68 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.31/1.68 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.31/1.68 ,
% 1.31/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.31/1.68 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.31/1.68 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.31/1.68 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.31/1.68 ,
% 1.31/1.68 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~(
% 1.31/1.68 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z, hAPP( hAPP(
% 1.31/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( T
% 1.31/1.68 , X, 'tc_nat' ) ), Y ) ), U ) ) ],
% 1.31/1.68 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~(
% 1.31/1.68 'c_lessequals'( T, X, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.31/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X
% 1.31/1.68 , T, 'tc_nat' ) ), Y ) ), Z ), U ) ],
% 1.31/1.68 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.31/1.68 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.31/1.68 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.31/1.68 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.31/1.68 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.68 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.31/1.68 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.31/1.68 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.31/1.68 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.68 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.31/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.68 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.68 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.31/1.68 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.31/1.68 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.68 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.68 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.31/1.68 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.68 ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.68 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.31/1.68 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.68 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.68 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.31/1.68 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.31/1.68 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.68 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.31/1.68 ) ],
% 1.31/1.68 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc',
% 1.31/1.68 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.31/1.68 'tc_nat' ), Y, 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 1.31/1.68 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.31/1.68 , Y, 'tc_nat' ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.68 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.31/1.68 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.68 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.31/1.68 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.31/1.68 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.31/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y
% 1.31/1.68 , X, 'tc_nat' ) ), Z ) ), T ) ) ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.68 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.68 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.68 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.31/1.68 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.31/1.68 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.31/1.68 ~( hBOOL( hAPP( X, T ) ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.68 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), hAPP( 'c_Suc', T ) ),
% 1.31/1.68 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.68 'tc_nat' ), Z ), T ), Y, 'tc_nat' ) ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.31/1.68 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.68 ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.31/1.68 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.68 ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.31/1.68 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.31/1.68 ) ],
% 1.31/1.68 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.31/1.68 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.68 ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.31/1.68 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.68 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 1.31/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.68 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.68 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.31/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.31/1.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.31/1.69 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.31/1.69 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.31/1.69 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.31/1.69 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.31/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.31/1.69 Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.69 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.69 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.31/1.69 ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.31/1.69 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.31/1.69 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.31/1.69 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.31/1.69 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.31/1.69 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.69 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.31/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 1.31/1.69 , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.31/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.69 , 'tc_nat' ), 'tc_nat' ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.69 , 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.31/1.69 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y,
% 1.31/1.69 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.31/1.69 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.31/1.69 ), X ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.69 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.69 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.31/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.31/1.69 hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~(
% 1.31/1.69 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( T, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.31/1.69 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X
% 1.31/1.69 ) ), U ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), T ), U ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ), W, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.31/1.69 ) ), T ) ), U ), W, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), Y ), T ) ), U ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.69 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.31/1.69 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.69 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.31/1.69 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ),
% 1.31/1.69 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.69 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.31/1.69 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.69 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.31/1.69 ), X ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.69 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.31/1.69 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.31/1.69 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.31/1.69 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.31/1.69 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.31/1.69 ), X ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.31/1.69 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.31/1.69 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.31/1.69 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.31/1.69 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.31/1.69 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.31/1.69 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.69 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.69 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.31/1.69 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), U ), W ) ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.31/1.69 X, Y, Z ), T ), U ) ), W ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z
% 1.31/1.69 ) ) ],
% 1.31/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.69 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.69 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.31/1.69 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.31/1.69 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.31/1.69 ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.31/1.69 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.31/1.69 ), Y ) ), Z ) ), Z ) ],
% 1.31/1.69 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ), W ) )
% 1.31/1.69 , hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), hAPP( X, U ) ), W ) ),
% 1.31/1.69 ~( 'c_Ring__and__Field_Oordered__idom'( V0, V1, V2, V3, V4, V5, X, Y, Z,
% 1.31/1.69 V6, T ) ) ],
% 1.31/1.69 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), hAPP( U, W
% 1.31/1.69 ) ), V0 ) ), hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), W
% 1.31/1.69 ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( V1, U, V2, V3, V4,
% 1.31/1.69 V5, X, Y, Z, V6, T ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.69 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.31/1.69 'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.31/1.69 'tc_nat' ) ) ) ],
% 1.31/1.69 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.31/1.69 V3, V4 ) ), hBOOL( hAPP( hAPP( W, Z ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower_Opower'( V1, V2, V4 ), hAPP( V0, V5 ) ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.31/1.69 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Z ), X ), T, X ), hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.31/1.69 X ), Y ) ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.31/1.69 Y, Z, X ), T, X ) ) ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) )
% 1.31/1.69 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 1.31/1.69 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.69 ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.31/1.69 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.31/1.69 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), 'c_HOL_Oinverse__class_Odivide'( Y
% 1.31/1.69 , Z, X ) ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.31/1.69 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.31/1.69 ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.31/1.69 ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.31/1.69 ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.31/1.69 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 1.31/1.69 ],
% 1.31/1.69 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.31/1.69 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.31/1.69 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc',
% 1.31/1.69 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.31/1.69 'tc_nat' ), Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.31/1.69 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.69 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 'tc_nat' ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'( X
% 1.31/1.69 ) ) ), =( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), Z ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.69 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.31/1.69 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.31/1.69 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.69 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.31/1.69 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.69 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.31/1.69 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.31/1.69 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.31/1.69 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.31/1.69 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.31/1.69 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.31/1.69 , X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), W ) ), hAPP( hAPP( Y, hAPP(
% 1.31/1.69 hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), U ) ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower_Opower'( X, Y, Z ), T ), W ) ) ), ~(
% 1.31/1.69 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.69 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.69 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.69 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.31/1.69 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.69 'c_Int_OMin', X ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.31/1.69 Z, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.31/1.69 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.69 T, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.69 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'( Y
% 1.31/1.69 , T, X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =( hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), =( Y, Z ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), =( Y, Z ), =( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.69 ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.31/1.69 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.31/1.69 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.69 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.31/1.69 [ =( hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X, hAPP( 'c_Suc',
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.69 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.31/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.69 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.69 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.69 , X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.69 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.31/1.69 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.31/1.69 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.31/1.69 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.31/1.69 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.69 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.69 , Y ), Z ), T, X ) ) ],
% 1.31/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.69 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.69 , Y ), T ), Z, X ) ) ],
% 1.31/1.69 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.31/1.69 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.31/1.69 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.31/1.69 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.31/1.69 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.31/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.31/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.31/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.31/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.31/1.69 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.31/1.69 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.31/1.69 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.31/1.69 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.31/1.69 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.31/1.69 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.31/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.31/1.69 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.31/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.31/1.69 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.31/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.31/1.69 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.31/1.69 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.31/1.69 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.31/1.69 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.31/1.69 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 1.31/1.69 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 1.31/1.69 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.31/1.69 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.31/1.69 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.31/1.69 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.31/1.69 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.31/1.69 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.31/1.69 ), Y ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.31/1.69 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 1.31/1.69 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 1.31/1.69 ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.31/1.69 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.31/1.69 , hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.31/1.69 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), X ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.31/1.69 ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.31/1.69 ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ) ), Y ) ), U ), 'tc_nat' )
% 1.31/1.69 ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), T ) ), U ), 'tc_nat' )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T
% 1.31/1.69 ) ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ), 'tc_nat' ) ),
% 1.31/1.69 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.31/1.69 ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.31/1.69 ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ) ), Y ) ), Z ), U, 'tc_nat'
% 1.31/1.69 ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ) ), T ), U, 'tc_nat'
% 1.31/1.69 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z
% 1.31/1.69 ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ), 'tc_nat' ) ),
% 1.31/1.69 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.31/1.69 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( T, Y, X
% 1.31/1.69 ) ), Z ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.69 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.69 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~( 'c_lessequals'( Z, Y, X
% 1.31/1.69 ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.31/1.69 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.69 hAPP( 'c_Suc', Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'tc_nat' ),
% 1.31/1.69 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.31/1.69 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.69 T, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) )
% 1.31/1.69 ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber__ring'( X ) ), =( hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) )
% 1.31/1.69 ],
% 1.31/1.69 [ 'c_lessequals'( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ),
% 1.31/1.69 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.31/1.69 X, Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.69 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.31/1.69 'tc_nat' ) ), Y ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.31/1.69 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.69 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.69 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.69 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( Y
% 1.31/1.69 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.31/1.69 ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.31/1.69 ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, X, Z ), T )
% 1.31/1.69 , U ) ), T ), hAPP( hAPP( X, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y
% 1.31/1.69 , X, Z ), T ), U ) ) ), ~( 'c_OrderedGroup_Omonoid__mult'( Y, X, Z ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc',
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z, 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ), ~(
% 1.31/1.69 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.31/1.69 ],
% 1.31/1.69 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), hAPP(
% 1.31/1.69 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.69 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), Z ) ) ],
% 1.31/1.69 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.31/1.69 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.31/1.69 Z, X ) ), 'c_HOL_Oinverse__class_Odivide'( Y, hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ), =( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.31/1.69 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.31/1.69 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), X,
% 1.31/1.69 'tc_nat' ) ],
% 1.31/1.69 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.31/1.69 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), T ), ~(
% 1.31/1.69 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.31/1.69 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.69 ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.69 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.69 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.31/1.69 ), Z ), Y ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ), Y ) ],
% 1.31/1.69 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.69 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.31/1.69 , 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 'tc_nat' ), X, 'tc_nat' ) ],
% 1.31/1.69 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.69 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.31/1.69 , 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 'tc_nat' ), Y, 'tc_nat' ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.31/1.69 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.69 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.69 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.69 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.69 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ), Y ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.31/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.31/1.69 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.31/1.69 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.69 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.31/1.69 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.69 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.31/1.69 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.31/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.31/1.69 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.31/1.69 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.31/1.69 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.69 , 'tc_nat' ), 'tc_nat' ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 X ), Y ), Z ) ), T ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 X ), Y ), Z ) ), T ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.69 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.31/1.69 ), Y ) ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.31/1.69 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.69 ) ) ],
% 1.31/1.69 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.31/1.69 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.31/1.69 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.31/1.69 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.31/1.69 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.31/1.69 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.31/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.31/1.69 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.31/1.69 ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ), Z ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.31/1.69 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.69 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.69 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.31/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.31/1.69 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.31/1.69 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.69 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.69 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.31/1.69 ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.69 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.31/1.69 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.69 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.31/1.69 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.31/1.69 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.31/1.69 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.31/1.69 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.31/1.69 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.31/1.69 , 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.31/1.69 , 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.31/1.69 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.31/1.69 Z, X ) ), 'c_HOL_Oinverse__class_Odivide'( Y, hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.31/1.69 Z, X ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.31/1.69 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.31/1.69 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.31/1.69 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( Z
% 1.31/1.69 , T, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.31/1.69 X ), Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.69 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.69 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oone__class_Oone'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X
% 1.31/1.69 ), Y ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.31/1.69 ],
% 1.31/1.69 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 1.31/1.69 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), Y ), Z ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), Z ), Y ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), Y ), Z ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), Z ), Y ), X ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.31/1.69 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.31/1.69 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc',
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y ) ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 'tc_nat' ) ), X ) ],
% 1.31/1.69 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.31/1.69 , U ) ), hAPP( hAPP( Y, hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T
% 1.31/1.69 ), U ) ), T ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.31/1.69 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.31/1.69 ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) )
% 1.31/1.69 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.69 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.69 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.31/1.69 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.31/1.69 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.69 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.69 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.31/1.69 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.31/1.69 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.69 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( 'c_Suc',
% 1.31/1.69 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ), 'tc_nat' ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.31/1.69 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.69 ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.31/1.69 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.31/1.69 X ), Y ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.31/1.69 X ), Y ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ), 'c_HOL_Oone__class_Oone'( X
% 1.31/1.69 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.31/1.69 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.31/1.69 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.31/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.69 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.69 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.31/1.69 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.69 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.69 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.31/1.69 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.31/1.69 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.31/1.69 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ) )
% 1.31/1.69 , =( Y, T ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) )
% 1.31/1.69 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.69 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.31/1.69 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.31/1.69 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.31/1.69 , X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.31/1.69 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.31/1.69 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.31/1.69 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.31/1.69 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.69 ), T ), Z ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.31/1.69 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.31/1.69 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.69 ), T ), Z ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.31/1.69 , X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.31/1.69 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.31/1.69 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.31/1.69 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), T ), Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.31/1.69 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), T ), Z, X ) ) ],
% 1.31/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.31/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.31/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.31/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ],
% 1.31/1.69 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ],
% 1.31/1.69 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.31/1.69 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.31/1.69 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP(
% 1.31/1.69 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.31/1.69 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.31/1.69 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.31/1.69 ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.31/1.69 ) ],
% 1.31/1.69 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.31/1.69 hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.31/1.69 X ), Y ) ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ), hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 X ), Y ), Z ) ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ),
% 1.31/1.69 hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), =( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.69 ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.31/1.69 X ), Y ) ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ), hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.31/1.69 X ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ),
% 1.31/1.69 hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), =( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.69 ) ],
% 1.31/1.69 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.31/1.69 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.31/1.69 hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.31/1.69 'c_HOL_Oone__class_Oone'( X ) ), X ), Z, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.31/1.69 'c_HOL_Oone__class_Oone'( X ) ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 Y, Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.31/1.69 ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Z, X ) ), =( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.31/1.69 , T, X ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), T, X ) ), =( T,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.31/1.69 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.31/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.31/1.69 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.31/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.31/1.69 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.31/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.31/1.69 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.31/1.69 'c_Suc', X ), Y, 'tc_nat' ), 'tc_nat' ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.31/1.69 hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ), 'c_Fact_Ofact__class_Ofact'(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.31/1.69 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.31/1.69 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.31/1.69 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.69 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.31/1.69 , X ) ), T, X ) ) ],
% 1.31/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.69 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.31/1.69 ), Z ), T, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.31/1.69 ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.31/1.69 ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.31/1.69 ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.31/1.69 ), X ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.31/1.69 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.69 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.31/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.31/1.69 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.31/1.69 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.31/1.69 ],
% 1.31/1.69 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.31/1.69 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 1.31/1.69 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.31/1.69 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.31/1.69 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.31/1.69 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.31/1.69 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.31/1.69 ],
% 1.31/1.69 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.31/1.69 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.31/1.69 , T, X ) ) ), =( Z, T ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.31/1.69 , T, X ) ) ), =( Y, Z ) ],
% 1.31/1.69 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.69 'tc_nat' ) ), =( Y, Z ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.69 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.69 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.31/1.69 , X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.31/1.69 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.31/1.69 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.31/1.69 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.31/1.69 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.31/1.69 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.31/1.69 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.69 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.31/1.69 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.69 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.31/1.69 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.31/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z )
% 1.31/1.69 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ),
% 1.31/1.69 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.31/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X )
% 1.31/1.69 , Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ),
% 1.31/1.69 'tc_nat' ) ) ],
% 1.31/1.69 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.31/1.69 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 X, hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.31/1.69 ), 'tc_nat' ) ) ],
% 1.31/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.31/1.69 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.31/1.69 ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.31/1.69 ), Y ), Z, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ) ],
% 1.31/1.69 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.69 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X
% 1.31/1.69 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), 'c_HOL_Ominus__class_Ominus'( Y, T, X ) ),
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, T, X
% 1.31/1.69 ) ), U ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ) ) ],
% 1.31/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.31/1.69 , 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat'
% 1.31/1.69 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.31/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.31/1.69 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.31/1.69 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.31/1.69 'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.69 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.69 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.31/1.69 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.31/1.69 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.31/1.69 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.31/1.69 , Y, X ) ) ],
% 1.31/1.69 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 1.31/1.69 'tc_nat' ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.31/1.69 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.31/1.69 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.69 ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.31/1.69 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.69 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.31/1.69 ), 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.69 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.31/1.69 ), 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.31/1.69 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.31/1.69 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ),
% 1.31/1.69 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.31/1.69 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.31/1.69 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.69 ) ), =( Y, Z ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.69 ) ), =( Y, Z ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.31/1.69 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.31/1.69 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.31/1.69 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.31/1.69 , T, 'tc_nat' ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ) ), ~( 'c_lessequals'(
% 1.31/1.69 T, Z, 'tc_nat' ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ),
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'(
% 1.31/1.69 Y, T, X ) ), 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.31/1.69 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.31/1.69 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.31/1.69 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.31/1.69 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.31/1.69 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.31/1.69 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.31/1.69 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.69 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.69 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.31/1.69 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.69 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.69 ), X ) ) ],
% 1.31/1.69 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 1.31/1.69 ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.31/1.69 ), Z ) ), T ) ) ],
% 1.31/1.69 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.31/1.69 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.31/1.69 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.31/1.69 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 1.31/1.69 , 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X
% 1.31/1.69 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.69 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.31/1.69 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.69 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.69 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_OrderedGroup_Omonoid__mult'( Z
% 1.31/1.69 , X, T ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_OrderedGroup_Omonoid__mult'( Y
% 1.31/1.69 , X, T ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.69 , 'tc_nat' ), 'tc_nat' ), 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.31/1.69 X ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.31/1.69 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =( hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.31/1.69 ) ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.31/1.69 [ ~( 'class_RealVector_Oreal__normed__div__algebra'( X ) ),
% 1.31/1.69 'c_SEQ_OLIMSEQ'( 'c_COMBB'( 'c_HOL_Oinverse__class_Oinverse'( X ), Y, X,
% 1.31/1.69 X, 'tc_nat' ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ), X ), =(
% 1.31/1.69 Z, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_SEQ_OLIMSEQ'( Y, Z, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.31/1.69 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.31/1.69 ), 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.31/1.69 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X,
% 1.31/1.69 'tc_nat' ) ],
% 1.31/1.69 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), Z, 'tc_nat' ), 'tc_nat'
% 1.31/1.69 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( =( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) )
% 1.31/1.69 , Y ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat'
% 1.31/1.69 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.31/1.69 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X )
% 1.31/1.69 , Y ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ), X ), hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.31/1.69 X ), Y ) ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ) ), hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ) ), =( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.69 ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.31/1.69 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 1.31/1.69 Y, Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.31/1.69 ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.31/1.69 'c_Divides_Odiv__class_Odiv'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.31/1.69 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.31/1.69 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.31/1.69 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.31/1.69 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.31/1.69 , V0, U, V1 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.31/1.69 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.31/1.69 , V0, U, V1 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.31/1.69 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.31/1.69 X, T, U, Y, W, V0 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.31/1.69 X, T, U, Z, W, V0 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.31/1.69 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.31/1.69 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.31/1.69 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.31/1.69 T, X, U, Y, W, V0 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.31/1.69 T, X, U, Z, W, V0 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.31/1.69 T, X, U, W, Y, V0 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.31/1.69 T, X, U, W, Z, V0 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.31/1.69 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.31/1.69 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.31/1.69 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.31/1.69 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.31/1.69 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.31/1.69 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.31/1.69 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.31/1.69 , V0, V1, V2 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.31/1.69 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.31/1.69 W, V0, V1, V2 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.31/1.69 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.31/1.69 , V0, V1, V2 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.31/1.69 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.31/1.69 W, V0, V1, V2 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.31/1.69 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.31/1.69 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.31/1.69 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.31/1.69 W, V0, V1, V2 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.31/1.69 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.31/1.69 W, V0, V1, V2 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.31/1.69 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.31/1.69 , V0, V1, V2 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.31/1.69 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.31/1.69 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.31/1.69 , V0, V1, V2 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.31/1.69 X, T, U, Y, W, V0 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.31/1.69 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.31/1.69 , V0, V1, V2 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.31/1.69 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.31/1.69 T, X, U, Y, W, V0 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.31/1.69 T, X, U, W, Y, V0 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.31/1.69 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.31/1.69 , V0, V1, V2 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.31/1.69 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.31/1.69 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.31/1.69 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.31/1.69 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.31/1.69 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.31/1.69 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.31/1.69 , T, X ), X ), T, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.31/1.69 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.31/1.69 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.31/1.69 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.69 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.31/1.69 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.31/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.31/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.31/1.69 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.31/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.31/1.69 ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.31/1.69 ) ],
% 1.31/1.69 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.31/1.69 ) ],
% 1.31/1.69 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.31/1.69 ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.31/1.69 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.69 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ), 'c_HOL_Oone__class_Oone'( X
% 1.31/1.69 ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =(
% 1.31/1.69 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), X ), Y ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) )
% 1.31/1.69 ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.31/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.31/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.31/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.31/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.31/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.31/1.69 X ), Z ) ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ), =( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.69 ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.31/1.69 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ), Y ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.31/1.69 Z, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.69 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.69 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.31/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 1.31/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.31/1.69 U ), hAPP( W, V0 ) ), V1 ) ) ), =( V0, Y ), ~(
% 1.31/1.69 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, V4, V5, X, W, Z, T, V6, U
% 1.31/1.69 ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.69 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.69 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.69 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.31/1.69 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.31/1.69 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.69 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.31/1.69 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.31/1.69 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.31/1.69 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.31/1.69 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T,
% 1.31/1.69 'tc_nat' ) ) ],
% 1.31/1.69 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.31/1.69 ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.69 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), ~( 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.31/1.69 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.31/1.69 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T
% 1.31/1.69 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.69 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.69 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.31/1.69 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.69 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.31/1.69 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.69 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.31/1.69 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.31/1.69 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.69 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.31/1.69 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.31/1.69 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X ) ) ],
% 1.31/1.69 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.31/1.69 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.31/1.69 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.31/1.69 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.31/1.69 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.31/1.69 ), 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 'tc_nat' ) ],
% 1.31/1.69 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ),
% 1.31/1.69 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'(
% 1.31/1.69 'tc_nat' ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ), =( X,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.69 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.31/1.69 , Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.31/1.69 hAPP( U, T ), W ) ), ~( hBOOL( hAPP( hAPP( X, Z ), V0 ) ) ), ~(
% 1.31/1.69 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Y, V5,
% 1.31/1.69 V6 ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.31/1.69 hAPP( X, U ), Z ) ) ), hBOOL( hAPP( hAPP( W, V0 ), T ) ), ~(
% 1.31/1.69 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Y, V5,
% 1.31/1.69 V6 ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.31/1.69 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.31/1.69 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Z, V5,
% 1.31/1.69 V6 ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.31/1.69 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.31/1.69 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Z, V5,
% 1.31/1.69 V6 ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.31/1.69 hAPP( U, Z ), W ) ), ~( hBOOL( hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.31/1.69 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Y, V5,
% 1.31/1.69 V6 ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.31/1.69 hAPP( X, U ), T ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Z ) ), ~(
% 1.31/1.69 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Y, V5,
% 1.31/1.69 V6 ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.31/1.69 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.31/1.69 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Z, V5,
% 1.31/1.69 V6 ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.31/1.69 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.31/1.69 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Z, V5,
% 1.31/1.69 V6 ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.31/1.69 hAPP( U, T ), W ) ), ~( hBOOL( hAPP( hAPP( X, Z ), V0 ) ) ), ~(
% 1.31/1.69 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Y, V5,
% 1.31/1.69 V6 ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.31/1.69 hAPP( X, U ), Z ) ) ), hBOOL( hAPP( hAPP( W, V0 ), T ) ), ~(
% 1.31/1.69 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Y, V5,
% 1.31/1.69 V6 ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.31/1.69 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.31/1.69 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Z, V5,
% 1.31/1.69 V6 ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.31/1.69 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.31/1.69 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Z, V5,
% 1.31/1.69 V6 ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.31/1.69 hAPP( U, Z ), W ) ), ~( hBOOL( hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.31/1.69 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Y, V5,
% 1.31/1.69 V6 ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.31/1.69 hAPP( X, U ), T ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Z ) ), ~(
% 1.31/1.69 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Y, V5,
% 1.31/1.69 V6 ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.31/1.69 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.31/1.69 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Z, V5,
% 1.31/1.69 V6 ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.31/1.69 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.31/1.69 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Z, V5,
% 1.31/1.69 V6 ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.31/1.69 Y ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Y, V0, V1, X
% 1.31/1.69 , V2, V3, V4, Z, V5 ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.31/1.69 T, Z ) ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Y, V0, V1, X
% 1.31/1.69 , V2, V3, V4, T, V5 ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.31/1.69 Z ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, T, V0, V1, X
% 1.31/1.69 , V2, V3, V4, Y, V5 ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, hAPP( T, Y
% 1.31/1.69 ) ), Z ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Z, V0, V1, X
% 1.31/1.69 , V2, V3, V4, T, V5 ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.31/1.69 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.31/1.69 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.31/1.69 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.31/1.69 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.69 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.31/1.69 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.31/1.69 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y, hAPP(
% 1.31/1.69 'c_HOL_Ouminus__class_Ouminus'( X ), T ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.31/1.69 ), 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.31/1.69 ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.31/1.69 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.69 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.69 , X ), X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.69 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.31/1.69 ), X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.69 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.31/1.69 , X ), X ), Z, X ) ) ],
% 1.31/1.69 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.31/1.69 , 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.31/1.69 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 1.31/1.69 ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.31/1.69 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.69 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.31/1.69 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.31/1.69 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.31/1.69 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.31/1.69 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.31/1.69 , X, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.31/1.69 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.31/1.69 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.31/1.69 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.31/1.69 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.31/1.69 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.31/1.69 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.31/1.69 , X, 'tc_nat' ) ) ],
% 1.31/1.69 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.69 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.31/1.69 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.31/1.69 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.31/1.69 , Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.31/1.69 U ), hAPP( W, V0 ) ), V1 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'(
% 1.31/1.69 V2, V3, Y, V4, X, V5, W, Z, T, V6, U ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.31/1.69 ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.69 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.31/1.69 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.69 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.69 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.31/1.69 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.31/1.69 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.31/1.69 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.31/1.69 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.69 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.31/1.69 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.31/1.69 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.69 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.69 Y ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.31/1.69 Y ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.69 Y ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.31/1.69 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.31/1.69 Y ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.31/1.69 Y ) ],
% 1.31/1.69 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.31/1.69 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.31/1.69 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.69 Y ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.31/1.69 Y ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 'c_lessequals'(
% 1.31/1.69 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 'c_lessequals'(
% 1.31/1.69 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.31/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.31/1.69 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.69 , Y ), Z ), Z, X ), Y ) ],
% 1.31/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.69 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ) ]
% 1.31/1.69 ,
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.31/1.69 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.31/1.69 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.69 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.31/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.69 ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.31/1.69 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.69 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.31/1.69 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.31/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), Y ) ), Y ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.31/1.70 X ), Y ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.31/1.70 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.70 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.31/1.70 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.70 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.31/1.70 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.31/1.70 , hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.31/1.70 ) ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ), X ),
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.31/1.70 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.31/1.70 ), 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.31/1.70 ), 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X
% 1.31/1.70 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), Y ) ) ), =( X,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.31/1.70 ), Y ), hAPP( 'c_Suc', Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ), hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.31/1.70 ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ), hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.31/1.70 ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.31/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.31/1.70 'tc_nat' ), hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.31/1.70 ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.31/1.70 ), T ) ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.31/1.70 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 1.31/1.70 ), T ) ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 1.31/1.70 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.31/1.70 hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 1.31/1.70 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.31/1.70 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.31/1.70 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ),
% 1.31/1.70 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.31/1.70 Z, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.31/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.31/1.70 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.31/1.70 X ), Y ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.31/1.70 X ), Y ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.31/1.70 ) ],
% 1.31/1.70 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 1.31/1.70 hBOOL( hAPP( X, Z ) ) ],
% 1.31/1.70 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 1.31/1.70 hBOOL( hAPP( X, Z ) ) ],
% 1.31/1.70 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ) ), Y ) ), Z ), U, 'tc_nat'
% 1.31/1.70 ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ) ), Y ) ), U ), 'tc_nat' )
% 1.31/1.70 ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.31/1.70 Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc',
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ),
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.31/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.31/1.70 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.31/1.70 ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.31/1.70 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.70 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.70 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.31/1.70 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.31/1.70 ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__field'( X ) ), =(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), W, X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), Y ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.31/1.70 Z, U, X ), W, X ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, T, X )
% 1.31/1.70 , W, X ) ), U ) ) ) ],
% 1.31/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.31/1.70 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.31/1.70 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.31/1.70 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.70 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ =( hAPP( X, Y ), hAPP( Z, T ) ), ~( hBOOL( hAPP( hAPP( U, Y ), W ) ) )
% 1.31/1.70 , ~( 'c_Ring__and__Field_Oordered__idom'( V0, Z, W, V1, V2, U, V3, T, V4
% 1.31/1.70 , X, V5 ) ) ],
% 1.31/1.70 [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( T, U ), Y ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( W, V0, U, V1, V2, T, V3, Z, V4, X,
% 1.31/1.70 V5 ) ) ],
% 1.31/1.70 [ ~( =( hAPP( X, Y ), hAPP( Z, T ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( U, Z, W, V0, V1, V2, V3, T, V4, X,
% 1.31/1.70 V5 ) ), hBOOL( hAPP( hAPP( V2, Y ), W ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 1.31/1.70 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ),
% 1.31/1.70 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 1.31/1.70 'tc_nat' ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.70 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) )
% 1.31/1.70 ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.31/1.70 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.31/1.70 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ) )
% 1.31/1.70 ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.31/1.70 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.70 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) )
% 1.31/1.70 ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.31/1.70 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.31/1.70 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ) )
% 1.31/1.70 ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.31/1.70 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), Y ) ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z
% 1.31/1.70 ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.31/1.70 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.31/1.70 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.31/1.70 X ) ) ],
% 1.31/1.70 [ =( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), Z ), hAPP( 'c_Suc', X ) ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), Y,
% 1.31/1.70 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X
% 1.31/1.70 ) ), Z ) ), T ), W ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X
% 1.31/1.70 ) ), Z ) ), W ) ) ],
% 1.31/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.31/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.31/1.70 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.31/1.70 ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.31/1.70 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.70 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.31/1.70 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.31/1.70 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.31/1.70 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.31/1.70 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.31/1.70 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.31/1.70 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ),
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.31/1.70 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y
% 1.31/1.70 , 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z,
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.70 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.70 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.31/1.70 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), X, 'tc_nat' ),
% 1.31/1.70 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.31/1.70 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.31/1.70 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.31/1.70 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.31/1.70 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.70 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.31/1.70 ) ],
% 1.31/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.70 ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.31/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 X, T, 'tc_nat' ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.31/1.70 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.31/1.70 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.31/1.70 hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Z
% 1.31/1.70 ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), Y ) ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), Y ) ) ) ],
% 1.31/1.70 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), Y ) ), Y ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), Y ) ), Y ) ],
% 1.31/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.31/1.70 ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.31/1.70 X ) ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.31/1.70 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.31/1.70 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.31/1.70 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.31/1.70 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.31/1.70 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.31/1.70 Z ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.31/1.70 Z ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.31/1.70 ~( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X )
% 1.31/1.70 ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.31/1.70 ~( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X )
% 1.31/1.70 ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.31/1.70 ~( 'c_lessequals'( Z, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.31/1.70 ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.31/1.70 ~( 'c_lessequals'( Z, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.31/1.70 ) ],
% 1.31/1.70 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.31/1.70 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.31/1.70 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Odiv'(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.31/1.70 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.31/1.70 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.31/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.31/1.70 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.70 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.31/1.70 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.31/1.70 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.31/1.70 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.31/1.70 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.31/1.70 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.31/1.70 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Oinverse'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.31/1.70 X ), Y ) ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.31/1.70 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.31/1.70 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.31/1.70 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), Y ) ), Z ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.31/1.70 , X ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), Y ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y, hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), =( Y, Z ) ],
% 1.31/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), Y ), T ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.31/1.70 Y ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.31/1.70 Y ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.31/1.70 Y ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.31/1.70 Y ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.31/1.70 Y ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.31/1.70 Y ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.31/1.70 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.31/1.70 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.31/1.70 ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.31/1.70 T, X ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.31/1.70 T, X ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.31/1.70 ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.31/1.70 ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.31/1.70 T, X ) ), T, X ) ) ],
% 1.31/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.31/1.70 ) ), Z ), T, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.31/1.70 , X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.31/1.70 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.31/1.70 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.70 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.31/1.70 , 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.70 , X ) ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.31/1.70 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.31/1.70 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.31/1.70 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.70 , X ) ), T ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OMin', X ) ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.31/1.70 ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.70 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), X ), X ) ],
% 1.31/1.70 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', X
% 1.31/1.70 ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.31/1.70 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 Z, X ) ), ~( 'c_lessequals'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X )
% 1.31/1.70 , Z ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.31/1.70 hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Oinverse'( X ), Z ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.70 'c_lessequals'( Z, Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.31/1.70 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ) ), ~( 'c_lessequals'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X )
% 1.31/1.70 , Z ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.31/1.70 hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Oinverse'( X ), Z ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_lessequals'( Z, Y, X ) ) ],
% 1.31/1.70 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.31/1.70 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.31/1.70 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.31/1.70 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.31/1.70 T ), Z, X ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.31/1.70 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.31/1.70 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.70 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.31/1.70 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.70 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.31/1.70 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.70 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.31/1.70 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.31/1.70 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.31/1.70 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.31/1.70 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.31/1.70 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.31/1.70 , ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.31/1.70 , 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.31/1.70 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.31/1.70 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.31/1.70 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.31/1.70 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), Y ), T ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.31/1.70 , X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.31/1.70 Y ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.31/1.70 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.31/1.70 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.31/1.70 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.31/1.70 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.70 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ), T ) ), U ), W, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ), W, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.70 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), U ) ), W ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.70 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.31/1.70 'tc_nat' ) ), Y ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.31/1.70 'tc_nat' ) ), Y ) ],
% 1.31/1.70 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y
% 1.31/1.70 , X, 'tc_nat' ) ), Z ) ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z
% 1.31/1.70 ) ), T ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.70 ), Y ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.31/1.70 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.70 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.70 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.31/1.70 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.31/1.70 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 1.31/1.70 'tc_nat' ), ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.31/1.70 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 1.31/1.70 X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.31/1.70 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.31/1.70 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ), 'tc_nat' ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.31/1.70 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.31/1.70 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.70 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ) ), =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ) ), =( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.70 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ) ), T ), U, 'tc_nat'
% 1.31/1.70 ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.31/1.70 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), T ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ), 'tc_nat' ) ),
% 1.31/1.70 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.31/1.70 ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ) ), Y ) ), Z ), U, 'tc_nat'
% 1.31/1.70 ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.31/1.70 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), T ) ), U ), 'tc_nat' )
% 1.31/1.70 , ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), X ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ), 'tc_nat' ) ),
% 1.31/1.70 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.31/1.70 ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.31/1.70 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ) ), Y ) ), U ), 'tc_nat' )
% 1.31/1.70 ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Oinverse'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ), Z ) ), =( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Oinverse'( X ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ), =( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.70 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.31/1.70 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.31/1.70 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.31/1.70 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.70 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.31/1.70 [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.31/1.70 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 'tc_nat' ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.70 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.31/1.70 ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.70 ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.31/1.70 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.31/1.70 , X ) ), Z ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( X, 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.31/1.70 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( Y, 'c_Divides_Odiv__class_Omod'( Y, X,
% 1.31/1.70 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.31/1.70 ) ), Z ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.31/1.70 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.31/1.70 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~(
% 1.31/1.70 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc',
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.31/1.70 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.31/1.70 'tc_nat' ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.31/1.70 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.31/1.70 ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Int_Oiszero'( Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.70 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Oone__class_Oone'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X
% 1.31/1.70 ), Y ), X ) ) ],
% 1.31/1.70 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ) ) ],
% 1.31/1.70 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.31/1.70 , Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.31/1.70 , X ) ) ],
% 1.31/1.70 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.31/1.70 , Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.31/1.70 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.31/1.70 [ ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.31/1.70 ), Y ), X ), 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), X, 'tc_nat' ), Y ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.31/1.70 , X ), Y ), 'tc_nat' ) ],
% 1.31/1.70 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.31/1.70 , X ), Y ), 'tc_nat' ) ],
% 1.31/1.70 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.31/1.70 , Y ), X ), 'tc_nat' ) ],
% 1.31/1.70 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.31/1.70 , X ), Y ), 'tc_nat' ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.31/1.70 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.31/1.70 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.31/1.70 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.31/1.70 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.31/1.70 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.31/1.70 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ),
% 1.31/1.70 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.31/1.70 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ), =( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.31/1.70 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.31/1.70 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.31/1.70 X ), Z, X ) ) ],
% 1.31/1.70 [ 'c_lessequals'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.31/1.70 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'(
% 1.31/1.70 X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'c_lessequals'( hAPP( 'c_Suc', X ), X, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', X
% 1.31/1.70 ), Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_lessequals'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.31/1.70 X, Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.31/1.70 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ),
% 1.31/1.70 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.31/1.70 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 1.31/1.70 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.31/1.70 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y
% 1.31/1.70 ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.31/1.70 , U ) ), hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z
% 1.31/1.70 ), T ), U ) ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.31/1.70 'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 'tc_nat' ), X ), Y ) ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.31/1.70 X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 'tc_nat' ), X ), Y ) ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.31/1.70 X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.31/1.70 'c_Suc', Y ) ) ) ],
% 1.31/1.70 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.31/1.70 'c_Suc', X ), Y, 'tc_nat' ), hAPP( 'c_Suc', Z ), 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.31/1.70 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.31/1.70 [ =( X, hAPP( 'c_Suc', Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.31/1.70 'c_lessequals'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.31/1.70 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.31/1.70 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.31/1.70 V0, V1 ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.31/1.70 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.31/1.70 V0, V1 ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.31/1.70 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W
% 1.31/1.70 , V0, V1 ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.31/1.70 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W
% 1.31/1.70 , V0, V1 ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.31/1.70 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =(
% 1.31/1.70 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), =( hAPP(
% 1.31/1.70 'c_Suc', X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), 'c_lessequals'( Y,
% 1.31/1.70 X, 'tc_nat' ) ],
% 1.31/1.70 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP(
% 1.31/1.70 'c_Suc', Y ), X, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_lessequals'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', X ), 'tc_nat' ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ),
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.31/1.70 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.31/1.70 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_Int_OBit1'( 'c_Int_OMin' ), 'c_Int_OMin' ) ],
% 1.31/1.70 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OMin' ) ), =( X, 'c_Int_OMin' ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( =( 'c_Int_OMin', 'c_Int_OBit1'( X ) ) ), =( 'c_Int_OMin', X ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ =( 'c_Int_OMin', 'c_Int_OBit1'( 'c_Int_OMin' ) ) ],
% 1.31/1.70 [ ~( =( 'c_Int_OPls', 'c_Int_OMin' ) ) ],
% 1.31/1.70 [ ~( =( 'c_Int_OMin', 'c_Int_OPls' ) ) ],
% 1.31/1.70 [ ~( =( 'c_Int_OMin', 'c_Int_OBit0'( X ) ) ) ],
% 1.31/1.70 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OMin' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.31/1.70 ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.31/1.70 ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.31/1.70 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.31/1.70 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.31/1.70 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.31/1.70 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.31/1.70 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.31/1.70 , ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.31/1.70 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.31/1.70 ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.31/1.70 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), Y ) ) ],
% 1.31/1.70 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.31/1.70 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.31/1.70 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( 'c_Suc',
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.31/1.70 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.31/1.70 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 1.31/1.70 ), 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', Z ), Y, 'tc_nat' ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.31/1.70 ), X, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc',
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.31/1.70 ), X, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc',
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.31/1.70 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc',
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), 'tc_nat' ) ],
% 1.31/1.70 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ) ), 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.31/1.70 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.31/1.70 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.31/1.70 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.31/1.70 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.31/1.70 , Z ) ],
% 1.31/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.31/1.70 , Z ) ],
% 1.31/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.31/1.70 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.31/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.31/1.70 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.31/1.70 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.31/1.70 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.31/1.70 ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) )
% 1.31/1.70 , 'tc_nat' ) ],
% 1.31/1.70 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T )
% 1.31/1.70 , 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.31/1.70 , Z, 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.31/1.70 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.31/1.70 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.31/1.70 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.31/1.70 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.31/1.70 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ), Y ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.31/1.70 ), Z ), Y ), 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.31/1.70 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.70 , X ) ) ],
% 1.31/1.70 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X,
% 1.31/1.70 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X,
% 1.31/1.70 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.31/1.70 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.31/1.70 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.31/1.70 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.70 T, X ) ) ],
% 1.31/1.70 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.31/1.70 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.31/1.70 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.31/1.70 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.31/1.70 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Oinverse'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.31/1.70 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Oinverse'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.31/1.70 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.31/1.70 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.31/1.70 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.31/1.70 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.31/1.70 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.31/1.70 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.31/1.70 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.31/1.70 , X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.70 , X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.31/1.70 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.70 , X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Y ), X ), ~(
% 1.31/1.70 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ), ~( 'c_lessequals'(
% 1.31/1.70 X, Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y,
% 1.31/1.70 X, 'tc_nat' ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.70 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.31/1.70 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.31/1.70 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat'
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 'tc_nat' ), X ), Y ), Z, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.31/1.70 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.31/1.70 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.31/1.70 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 hAPP( 'c_Suc', T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z
% 1.31/1.70 ), hAPP( 'c_Suc', T ) ), X ) ) ],
% 1.31/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.70 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.31/1.70 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.70 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.31/1.70 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.31/1.70 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.31/1.70 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.31/1.70 , T ) ],
% 1.31/1.70 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.31/1.70 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.31/1.70 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.31/1.70 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.70 , 'tc_nat' ), 'tc_nat' ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.70 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.31/1.70 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.70 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.31/1.70 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.31/1.70 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.31/1.70 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.31/1.70 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ),
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'( Y
% 1.31/1.70 , Z, X ), ~( 'c_SEQ_OLIMSEQ'( 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), Y, X, X, 'tc_nat' ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z )
% 1.31/1.70 , X ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.31/1.70 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ), Y, X, X, 'tc_nat' ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~( 'c_SEQ_OLIMSEQ'( Y, Z,
% 1.31/1.70 X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =( hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.31/1.70 Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.31/1.70 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' )
% 1.31/1.70 , 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), 'c_Int_Oiszero'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.31/1.70 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.31/1.70 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.31/1.70 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 1.31/1.70 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.31/1.70 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.31/1.70 ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.31/1.70 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.31/1.70 ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.31/1.70 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.31/1.70 ), =( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.31/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.31/1.70 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.31/1.70 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.31/1.70 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.31/1.70 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.31/1.70 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.31/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.70 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.31/1.70 ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.31/1.70 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.31/1.70 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.31/1.70 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.31/1.70 Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.31/1.70 X ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.31/1.70 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ), =( Z,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.31/1.70 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.31/1.70 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.31/1.70 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.31/1.70 X ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.31/1.70 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.31/1.70 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.31/1.70 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.31/1.70 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.31/1.70 , X ) ],
% 1.31/1.70 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, hAPP( V1
% 1.31/1.70 , V2 ), V3, V1, V4 ) ), hBOOL( hAPP( hAPP( W, Z ), V2 ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.31/1.70 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, W ), Z ) ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Y, V0, V5,
% 1.31/1.70 V6 ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.31/1.70 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, U ), Y ) ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Z, V0, V5,
% 1.31/1.70 V6 ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.31/1.70 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Z, V5,
% 1.31/1.70 V6 ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.31/1.70 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Z, V5,
% 1.31/1.70 V6 ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.31/1.70 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, W ), Y ) ), W ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Z, V0, V5,
% 1.31/1.70 V6 ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.31/1.70 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, U ), Z ) ), U ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Y, V0, V5,
% 1.31/1.70 V6 ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.31/1.70 hAPP( U, Z ), W ) ), hBOOL( hAPP( hAPP( U, W ), Z ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Y, V5,
% 1.31/1.70 V6 ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.31/1.70 hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Y, V5,
% 1.31/1.70 V6 ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.31/1.70 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, Z ), W ) ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Y, V0, V5,
% 1.31/1.70 V6 ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.31/1.70 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, Y ), U ) ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Z, V0, V5,
% 1.31/1.70 V6 ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.31/1.70 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Z, V5,
% 1.31/1.70 V6 ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.31/1.70 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Z, V5,
% 1.31/1.70 V6 ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.31/1.70 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Y ), W ) ), W ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Z, V0, V5,
% 1.31/1.70 V6 ) ) ],
% 1.31/1.70 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.31/1.70 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.31/1.70 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.31/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.31/1.70 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.31/1.70 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.31/1.70 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.31/1.70 ), X ), Z ), 'tc_nat' ) ) ],
% 1.31/1.70 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.31/1.70 ), X ), X ), 'tc_nat' ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.31/1.70 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.31/1.70 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.31/1.70 ), X ), Z ), 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.31/1.70 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.31/1.70 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.31/1.70 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.70 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.70 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), X ), X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.31/1.70 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.31/1.70 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.31/1.70 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.31/1.70 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.31/1.70 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.31/1.70 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.31/1.70 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.31/1.70 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.31/1.70 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.31/1.70 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.31/1.70 ), Y ), Y ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.70 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.70 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( Y, hAPP( hAPP( Y, T ), T ) )
% 1.31/1.70 , T ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), X ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.31/1.70 ), Z ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.31/1.70 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.31/1.70 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.70 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.31/1.70 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.31/1.70 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.70 , X ) ), T ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.31/1.70 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.70 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.70 , X ) ), T ) ) ) ],
% 1.31/1.70 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.31/1.70 'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X,
% 1.31/1.70 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.31/1.70 , ~( 'c_SEQ_OLIMSEQ'( Z, T, X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.31/1.70 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.31/1.70 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.31/1.70 ) ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OBit1'( Y ), X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.70 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), 'c_Int_Oiszero'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OPls', X ) ), Y ) ],
% 1.31/1.70 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.31/1.70 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.31/1.70 ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y
% 1.31/1.70 ), X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.31/1.70 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 Y ), X ), X ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.70 , X ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.31/1.70 X ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ), X ) )
% 1.31/1.70 ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.31/1.70 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.31/1.70 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 'c_Int_OMin', X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.31/1.70 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.31/1.70 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ), Y, 'tc_nat'
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.31/1.70 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.31/1.70 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.31/1.70 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.31/1.70 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.70 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.31/1.70 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.31/1.70 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.31/1.70 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.31/1.70 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.31/1.70 U ), W ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( W, Y ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, V2, V3, X, V4, Z, T, V5,
% 1.31/1.70 U ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.31/1.70 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( V1, Y ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, V4, X, V5, T, U, V6, W
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.31/1.70 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( V0, Y ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, V4, X, V5, T, U, V6, W
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.31/1.70 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.70 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.31/1.70 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( T, U, W ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.31/1.70 , U, W ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, Z, V2, X, V3, T, U, V4, W
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z
% 1.31/1.70 , T, U ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), V1 ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V2, V3, V1, Y, V4, X, V5, Z, T, V6,
% 1.31/1.70 U ) ) ],
% 1.31/1.70 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z,
% 1.31/1.70 T, U ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( W, V0, Y, V1, V2, X, V3, Z, T, V4, U
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T
% 1.31/1.70 ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), W ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, V3, X, V4, Y, Z, V5,
% 1.31/1.70 T ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.70 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.31/1.70 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.31/1.70 V3, V4 ) ), =( hAPP( hAPP( T, hAPP( hAPP( 'c_Power_Opower_Opower'( V1, V2
% 1.31/1.70 , V4 ), Z ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.31/1.70 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, V4, T, X, Y, V5,
% 1.31/1.70 Z ) ) ],
% 1.31/1.70 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y
% 1.31/1.70 , Z, T ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, V4, X, Y, Z, V5,
% 1.31/1.70 T ) ) ],
% 1.31/1.70 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), V0, V1, V2, V3, Z, T, V4, U ) ), =( W,
% 1.31/1.70 hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.31/1.70 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( Y, T ), T ) ), ~(
% 1.31/1.70 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.31/1.70 U ), W ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, V2, X, V3, V4, Z, T, V5,
% 1.31/1.70 U ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.31/1.70 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.31/1.70 V3, V4 ) ), hBOOL( hAPP( hAPP( U, hAPP( hAPP( T, hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( V1
% 1.31/1.70 , V2, V4 ), Z ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Z ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.31/1.70 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, X, V4, V5, T, U, V6, W
% 1.31/1.70 ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), Y ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.31/1.70 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP( Z, hAPP(
% 1.31/1.70 hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.31/1.70 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z, V2, V3, V4, T, U, V5
% 1.31/1.70 , W ) ), =( V1, hAPP( hAPP( Z, hAPP( hAPP( 'c_Power_Opower_Opower'( T, U
% 1.31/1.70 , W ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( T, U, W ), V1 ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.31/1.70 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP( Z, hAPP(
% 1.31/1.70 hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.31/1.70 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z, V2, V3, V4, T, U, V5
% 1.31/1.70 , W ) ), =( V0, hAPP( hAPP( Z, hAPP( hAPP( 'c_Power_Opower_Opower'( T, U
% 1.31/1.70 , W ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( T, U, W ), V1 ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.31/1.70 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.31/1.70 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 1.31/1.70 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.31/1.70 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.31/1.70 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.31/1.70 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( U, W, V0 ), V1 ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U
% 1.31/1.70 , W, V0 ), X ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Y ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, T, Z, V4, V5, U, W, V6,
% 1.31/1.70 V0 ) ) ],
% 1.31/1.70 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( U, W, V0 ), X ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U
% 1.31/1.70 , W, V0 ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.70 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Y ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, T, Z, V4, V5, U, W, V6,
% 1.31/1.70 V0 ) ) ],
% 1.31/1.70 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.31/1.70 V3, V4 ) ), =( hAPP( hAPP( 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ],
% 1.31/1.70 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.31/1.70 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.70 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ), hAPP(
% 1.31/1.70 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 1.31/1.70 ,
% 1.31/1.70 [ =( hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.31/1.70 , 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.70 'tc_nat' ) ) ],
% 1.31/1.70 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.31/1.70 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.70 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.31/1.70 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ),
% 1.31/1.70 hAPP( hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.70 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ),
% 1.31/1.70 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.70 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.31/1.70 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Z ), U ) ), U ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Y, V0, V5,
% 1.31/1.70 V6 ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.31/1.70 hAPP( U, T ), W ) ), hBOOL( hAPP( hAPP( U, W ), T ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Y, V5,
% 1.31/1.70 V6 ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.31/1.70 hAPP( X, U ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Y, V5,
% 1.31/1.70 V6 ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.31/1.70 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, W ), Z ) ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Y, V0, V5,
% 1.31/1.70 V6 ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.31/1.70 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, U ), Y ) ) ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Z, V0, V5,
% 1.31/1.70 V6 ) ) ],
% 1.31/1.70 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.31/1.70 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.31/1.70 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Z, V5,
% 1.31/1.71 V6 ) ) ],
% 1.31/1.71 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.31/1.71 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.31/1.71 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Z, V5,
% 1.31/1.71 V6 ) ) ],
% 1.31/1.71 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.31/1.71 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, W ), Y ) ), W ) ) ), ~(
% 1.31/1.71 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Z, V0, V5,
% 1.31/1.71 V6 ) ) ],
% 1.31/1.71 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.31/1.71 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, U ), Z ) ), U ) ) ), ~(
% 1.31/1.71 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Y, V0, V5,
% 1.31/1.71 V6 ) ) ],
% 1.31/1.71 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.31/1.71 hAPP( U, Z ), W ) ), hBOOL( hAPP( hAPP( U, W ), Z ) ), ~(
% 1.31/1.71 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Y, V5,
% 1.31/1.71 V6 ) ) ],
% 1.31/1.71 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.31/1.71 hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.31/1.71 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Y, V5,
% 1.31/1.71 V6 ) ) ],
% 1.31/1.71 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.31/1.71 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, Z ), W ) ) ) ), ~(
% 1.31/1.71 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Y, V0, V5,
% 1.31/1.71 V6 ) ) ],
% 1.31/1.71 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.31/1.71 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, Y ), U ) ) ) ), ~(
% 1.31/1.71 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Z, V0, V5,
% 1.31/1.71 V6 ) ) ],
% 1.31/1.71 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.31/1.71 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.31/1.71 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Z, V5,
% 1.31/1.71 V6 ) ) ],
% 1.31/1.71 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.31/1.71 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.31/1.71 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Z, V5,
% 1.31/1.71 V6 ) ) ],
% 1.31/1.71 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.31/1.71 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Y ), W ) ), W ) ) ), ~(
% 1.31/1.71 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Z, V0, V5,
% 1.31/1.71 V6 ) ) ],
% 1.31/1.71 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.31/1.71 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Z ), U ) ), U ) ) ), ~(
% 1.31/1.71 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Y, V0, V5,
% 1.31/1.71 V6 ) ) ],
% 1.31/1.71 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.31/1.71 hAPP( U, T ), W ) ), hBOOL( hAPP( hAPP( U, W ), T ) ), ~(
% 1.31/1.71 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Y, V5,
% 1.31/1.71 V6 ) ) ],
% 1.31/1.71 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.31/1.71 hAPP( X, U ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.31/1.71 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Y, V5,
% 1.31/1.71 V6 ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.71 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.71 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.31/1.71 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.71 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.31/1.71 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.31/1.71 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.31/1.71 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.71 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.31/1.71 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.71 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.71 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.71 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.31/1.71 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.31/1.71 ],
% 1.31/1.71 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.31/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.71 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.31/1.71 , Z ), Y ), 'tc_nat' ) ) ],
% 1.31/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.71 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.31/1.71 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.31/1.71 ],
% 1.31/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.31/1.71 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.71 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.31/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.31/1.71 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.71 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.31/1.71 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.31/1.71 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.31/1.71 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.31/1.71 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.31/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.31/1.71 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.71 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.31/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.31/1.71 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.31/1.71 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.31/1.71 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.31/1.71 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.31/1.71 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.31/1.71 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.31/1.71 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.31/1.71 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.71 'tc_nat' ) ) ) ],
% 1.31/1.71 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.31/1.71 , Y ) ) ],
% 1.31/1.71 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.31/1.71 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.31/1.71 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 1.31/1.71 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.31/1.71 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.31/1.71 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.31/1.71 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.31/1.71 , X ) ) ],
% 1.31/1.71 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.31/1.71 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.31/1.71 , X ) ) ],
% 1.31/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.71 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.31/1.71 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.31/1.71 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.31/1.71 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.31/1.71 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.31/1.71 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.31/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.71 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.31/1.71 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.31/1.71 ) ) ],
% 1.31/1.71 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.31/1.71 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.31/1.71 ) ) ],
% 1.31/1.71 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.31/1.71 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.31/1.71 ), 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.71 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.31/1.71 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.31/1.71 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X,
% 1.31/1.71 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ) ) ],
% 1.31/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.71 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.31/1.71 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.71 , X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.71 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.71 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.31/1.71 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.71 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.31/1.71 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.71 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.71 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.71 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.71 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.31/1.71 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.31/1.71 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.71 [ =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.31/1.71 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.31/1.71 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ), =( X,
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.31/1.71 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.31/1.71 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.31/1.71 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.71 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.31/1.71 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.31/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.31/1.71 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.31/1.71 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.31/1.71 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.31/1.71 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.31/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.31/1.71 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 1.31/1.71 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.31/1.71 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X )
% 1.31/1.71 , Y ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ), X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.31/1.71 X ), Y ) ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ), hAPP(
% 1.31/1.71 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), =( Z,
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.71 ) ],
% 1.31/1.71 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.31/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~(
% 1.31/1.71 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.31/1.71 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.71 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.31/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.31/1.71 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.31/1.71 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.71 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.31/1.71 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.31/1.71 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.31/1.71 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.31/1.71 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), Y, X ), hAPP(
% 1.31/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.31/1.71 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.31/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.31/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), =( Y,
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~( 'c_Int_Oiszero'(
% 1.31/1.71 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ), ~(
% 1.31/1.71 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.31/1.71 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.31/1.71 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.31/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.31/1.71 'tc_nat' ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Z ), Y ), X ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.31/1.71 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ),
% 1.31/1.71 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.31/1.71 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.31/1.71 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.31/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.31/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.31/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.31/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), ~(
% 1.31/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.31/1.71 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.31/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, hAPP(
% 1.31/1.71 'c_Suc', Y ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.31/1.71 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.31/1.71 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.71 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.31/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.31/1.71 ), =( 'c_HOL_Oinverse__class_Odivide'( Y, U, X ),
% 1.31/1.71 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.31/1.71 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.31/1.71 X, 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.71 'tc_nat' ), X ), 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ), Y,
% 1.31/1.71 'tc_nat' ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.31/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.31/1.71 Y ), X ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.31/1.71 Y ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.31/1.71 ), X ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.31/1.71 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.71 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y, X ),
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.31/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.31/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.31/1.71 ), Z ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ],
% 1.31/1.71 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.31/1.71 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.31/1.71 ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.31/1.71 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.31/1.71 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.31/1.71 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.31/1.71 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.31/1.71 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.31/1.71 'c_lessequals'( Z, Y, X ) ],
% 1.31/1.71 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.31/1.71 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.31/1.71 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.31/1.71 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.31/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.31/1.71 ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.71 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.71 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ),
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), X ) ) ],
% 1.31/1.71 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.31/1.71 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.31/1.71 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP(
% 1.31/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ),
% 1.31/1.71 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ) ],
% 1.31/1.71 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.31/1.71 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.31/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.31/1.71 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.31/1.71 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 1.31/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.31/1.71 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.31/1.71 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, hAPP(
% 1.31/1.71 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.31/1.71 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.31/1.71 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.31/1.71 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.31/1.71 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.31/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.71 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y ),
% 1.31/1.71 'tc_nat' ) ) ],
% 1.31/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.71 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ),
% 1.31/1.71 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.31/1.71 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP(
% 1.31/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y )
% 1.31/1.71 , 'tc_nat' ) ) ],
% 1.31/1.71 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.71 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ), 'tc_nat' ), ~( 'c_lessequals'( Y,
% 1.31/1.71 Z, 'tc_nat' ) ) ],
% 1.31/1.71 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.31/1.71 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ), Z, X ), ~(
% 1.31/1.71 'c_SEQ_OLIMSEQ'( Y, Z, X ) ) ],
% 1.31/1.71 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_SEQ_OLIMSEQ'( Y, Z, X
% 1.31/1.71 ), ~( 'c_SEQ_OLIMSEQ'( 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ), Z
% 1.31/1.71 , X ) ) ],
% 1.31/1.71 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.31/1.71 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.31/1.71 X, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.71 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, X ) ),
% 1.31/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ), X ), ~(
% 1.31/1.71 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.31/1.71 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.31/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower_Opower'( X, Y, Z ), U ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ) ), ~(
% 1.31/1.71 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, V0, T, V1, V2, Z ) ) ],
% 1.31/1.71 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.31/1.71 U ), W ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), V0 ) ) ) ), ~(
% 1.31/1.71 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, X, V4, V5, Z, T, V6,
% 1.31/1.71 U ) ) ],
% 1.31/1.71 [ =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 1.31/1.71 'c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1'( X ) ) ), ~(
% 1.31/1.71 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.31/1.71 X ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ) ],
% 1.31/1.71 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.31/1.71 X, Y, Z ), T ), U ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.71 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.31/1.71 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.71 'class_Int_Onumber__ring'( X ) ), =( hAPP(
% 1.31/1.71 'c_HOL_Oinverse__class_Oinverse'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.71 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.71 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.71 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.31/1.71 ), Y ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.31/1.71 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.31/1.71 ), Y ) ],
% 1.31/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.31/1.71 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.31/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.31/1.71 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.31/1.71 ) ],
% 1.31/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.31/1.71 ) ) ],
% 1.31/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.31/1.71 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.71 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.31/1.71 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.31/1.71 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.31/1.71 'tc_nat' ) ) ],
% 1.31/1.71 [ =( X, hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.71 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.71 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 1.31/1.71 'c_Parity_Osko__Parity__Xodd__Suc__mult__two__ex__1__1'( X ) ) ) ),
% 1.31/1.71 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.31/1.71 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.31/1.71 hAPP( 'c_Power_Opower_Opower'( T, U, W ), Z ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), V0 ) ) ) ) ) ), ~(
% 1.31/1.71 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, X, V4, V5, T, U, V6,
% 1.31/1.71 W ) ) ],
% 1.31/1.71 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.31/1.71 U ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.31/1.71 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ) ) ), V0 ) ), ~( hBOOL( hAPP( hAPP(
% 1.31/1.71 X, U ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3
% 1.31/1.71 , V4, X, V5, Y, Z, V6, T ) ) ],
% 1.31/1.71 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.31/1.71 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ) ), hAPP( hAPP( Y, T ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.31/1.71 X, Y, Z ), T ), U ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.71 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.31/1.71 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.31/1.71 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.31/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.71 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.31/1.71 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.31/1.71 'tc_nat' ) ) ],
% 1.31/1.71 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, X ) ),
% 1.31/1.71 hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ) ), hAPP( T, X ) ), ~(
% 1.31/1.71 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.31/1.71 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.31/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.31/1.71 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.31/1.71 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ) ), =( X,
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.31/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.71 'c_Int_OMin', X ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.31/1.71 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.71 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.31/1.71 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc'
% 1.31/1.71 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.31/1.71 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.31/1.71 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.31/1.71 , X, Z, U, W, V0 ) ) ],
% 1.31/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.71 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.31/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.31/1.71 , Y ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.31/1.71 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.71 X ), Y ), Y ) ) ],
% 1.31/1.71 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.31/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.31/1.71 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.31/1.71 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.71 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.31/1.71 ) ],
% 1.31/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) )
% 1.31/1.71 ) ],
% 1.31/1.71 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.31/1.71 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.31/1.71 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.31/1.71 ) ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.31/1.71 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.71 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.31/1.71 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.31/1.71 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.31/1.71 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.31/1.71 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.31/1.71 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ) ],
% 1.31/1.71 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.31/1.71 'tc_nat' ), X ), X ) ) ],
% 1.31/1.71 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.31/1.71 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.31/1.71 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.31/1.71 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.31/1.71 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'tc_nat' ) ) ],
% 1.31/1.71 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.31/1.71 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.31/1.71 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.31/1.71 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.31/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.31/1.71 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.31/1.71 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.31/1.71 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.31/1.71 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.31/1.71 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.31/1.71 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.31/1.71 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.31/1.71 [ 'c_Fun_Oinj__on'( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), X, 'tc_nat', 'tc_nat' ) ],
% 1.31/1.71 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.31/1.71 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.31/1.71 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.31/1.71 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.31/1.71 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.31/1.71 , hAPP( 'c_Suc', X ) ), Z ) ) ), =( Y, Z ) ],
% 1.31/1.71 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.31/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.31/1.71 [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 1.31/1.71 [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 1.31/1.71 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.31/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.31/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.31/1.71 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.31/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.31/1.71 , Y ) ],
% 1.31/1.71 [ 'c_Fun_Oinj__on'( 'c_Suc', X, 'tc_nat', 'tc_nat' ) ],
% 1.31/1.71 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.31/1.71 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.31/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.31/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.31/1.71 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.31/1.71 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.31/1.71 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.31/1.71 [ ~( 'c_Fun_Oinj__on'( 'c_COMBB'( 'c_Suc', hAPP(
% 1.31/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.31/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.31/1.71 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), 'v_A',
% 1.31/1.71 'tc_nat', 'tc_nat' ) ) ],
% 1.31/1.71 [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ), ~(
% 1.31/1.71 'class_Lattices_Oboolean__algebra'( Y ) ) ],
% 1.31/1.71 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.31/1.71 'class_Orderings_Opreorder'( Y ) ) ],
% 1.31/1.71 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.31/1.71 'class_Orderings_Oorder'( Y ) ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.31/1.71 ],
% 1.31/1.71 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.31/1.71 ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.31/1.71 ],
% 1.31/1.71 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.31/1.71 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.31/1.71 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.31/1.71 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.31/1.71 ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.31/1.71 ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.31/1.71 [ =( 'c_COMBC'( X, Y, Z, T, U, W ), hAPP( hAPP( X, Z ), Y ) ) ],
% 1.31/1.71 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.31/1.71 ,
% 1.31/1.71 [ 'c_fequal'( X, X, Y ) ],
% 1.31/1.71 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.31/1.71 ] .
% 1.31/1.71
% 1.31/1.71
% 1.31/1.71 percentage equality = 0.229431, percentage horn = 0.817610
% 1.31/1.71 This is a problem with some equality
% 1.31/1.71
% 1.31/1.71
% 1.31/1.71
% 1.31/1.71 Options Used:
% 1.31/1.71
% 1.31/1.71 useres = 1
% 1.31/1.71 useparamod = 1
% 1.31/1.71 useeqrefl = 1
% 1.31/1.71 useeqfact = 1
% 1.31/1.71 usefactor = 1
% 1.31/1.71 usesimpsplitting = 0
% 1.31/1.71 usesimpdemod = 5
% 1.31/1.71 usesimpres = 3
% 1.31/1.71
% 1.31/1.71 resimpinuse = 1000
% 1.31/1.71 resimpclauses = 20000
% 1.31/1.71 substype = eqrewr
% 1.31/1.71 backwardsubs = 1
% 1.31/1.71 selectoldest = 5
% 1.31/1.71
% 1.31/1.71 litorderings [0] = split
% 1.31/1.71 litorderings [1] = extend the termordering, first sorting on arguments
% 1.31/1.71
% 1.31/1.71 termordering = kbo
% 1.31/1.71
% 1.31/1.71 litapriori = 0
% 1.31/1.71 termapriori = 1
% 1.31/1.71 litaposteriori = 0
% 1.31/1.71 termaposteriori = 0
% 1.31/1.71 demodaposteriori = 0
% 1.31/1.71 ordereqreflfact = 0
% 1.31/1.71
% 1.31/1.71 litselect = negord
% 1.31/1.71
% 1.31/1.71 maxweight = 15
% 1.31/1.71 maxdepth = 30000
% 1.31/1.71 maxlength = 115
% 1.31/1.71 maxnrvars = 195
% 1.31/1.71 excuselevel = 1
% 1.31/1.71 increasemaxweight = 1
% 1.31/1.71
% 1.31/1.71 maxselected = 10000000
% 1.31/1.71 maxnrclauses = 10000000
% 1.31/1.71
% 1.31/1.71 showgenerated = 0
% 1.31/1.71 showkept = 0
% 1.31/1.71 showselected = 0
% 1.31/1.71 showdeleted = 0
% 1.31/1.71 showresimp = 1
% 1.31/1.71 showstatus = 2000
% 1.31/1.71
% 1.31/1.71 prologoutput = 1
% 1.31/1.71 nrgoals = 5000000
% 1.31/1.71 totalproof = 1
% 1.31/1.71
% 1.31/1.71 Symbols occurring in the translation:
% 1.31/1.71
% 1.31/1.71 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.31/1.71 . [1, 2] (w:1, o:157, a:1, s:1, b:0),
% 1.31/1.71 ! [4, 1] (w:0, o:77, a:1, s:1, b:0),
% 1.31/1.71 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.31/1.71 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.31/1.71 'class_Ring__and__Field_Ofield' [40, 1] (w:1, o:82, a:1, s:1, b:0),
% 1.31/1.71 'class_Ring__and__Field_Odivision__by__zero' [41, 1] (w:1, o:86, a:1
% 1.31/1.71 , s:1, b:0),
% 1.31/1.71 'c_HOL_Otimes__class_Otimes' [42, 1] (w:1, o:87, a:1, s:1, b:0),
% 1.31/1.71 hAPP [44, 2] (w:1, o:182, a:1, s:1, b:0),
% 1.31/1.71 'c_HOL_Oinverse__class_Odivide' [46, 3] (w:1, o:188, a:1, s:1, b:0),
% 1.31/1.71
% 1.31/1.71 'c_HOL_Ozero__class_Ozero' [47, 1] (w:1, o:88, a:1, s:1, b:0),
% 1.31/1.71 'tc_nat' [49, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.31/1.71 'c_lessequals' [50, 3] (w:1, o:189, a:1, s:1, b:0),
% 1.31/1.71 'class_OrderedGroup_Ogroup__add' [51, 1] (w:1, o:89, a:1, s:1, b:0),
% 1.31/1.71
% 1.31/1.71 'c_HOL_Ouminus__class_Ouminus' [52, 1] (w:1, o:90, a:1, s:1, b:0),
% 1.31/1.71 'class_Lattices_Oboolean__algebra' [54, 1] (w:1, o:91, a:1, s:1, b:0)
% 1.31/2.15 ,
% 1.31/2.15 'c_Power_Opower__class_Opower' [57, 1] (w:1, o:92, a:1, s:1, b:0),
% 1.31/2.15 'class_Ring__and__Field_Oordered__semidom' [58, 1] (w:1, o:98, a:1
% 1.31/2.15 , s:1, b:0),
% 1.31/2.15 'c_HOL_Oone__class_Oone' [59, 1] (w:1, o:99, a:1, s:1, b:0),
% 1.31/2.15 'c_HOL_Oord__class_Oless' [60, 3] (w:1, o:190, a:1, s:1, b:0),
% 1.31/2.15 'class_Orderings_Oorder' [61, 1] (w:1, o:100, a:1, s:1, b:0),
% 1.31/2.15 'class_Orderings_Olinorder' [62, 1] (w:1, o:101, a:1, s:1, b:0),
% 1.31/2.15 'c_HOL_Ominus__class_Ominus' [64, 3] (w:1, o:191, a:1, s:1, b:0),
% 1.31/2.15 hBOOL [66, 1] (w:1, o:102, a:1, s:1, b:0),
% 1.31/2.15 'class_RealVector_Ometric__space' [67, 1] (w:1, o:103, a:1, s:1, b:0)
% 1.31/2.15 ,
% 1.31/2.15 'c_SEQ_OLIMSEQ' [69, 3] (w:1, o:192, a:1, s:1, b:0),
% 1.31/2.15 'class_Ring__and__Field_Oordered__idom' [70, 1] (w:1, o:104, a:1, s:1
% 1.31/2.15 , b:0),
% 1.31/2.15 'c_Fact_Ofact__class_Ofact' [71, 2] (w:1, o:183, a:1, s:1, b:0),
% 1.31/2.15 'c_Suc' [72, 0] (w:1, o:36, a:1, s:1, b:0),
% 1.31/2.15 'c_HOL_Oplus__class_Oplus' [75, 1] (w:1, o:105, a:1, s:1, b:0),
% 1.31/2.15 'class_OrderedGroup_Opordered__ab__semigroup__add' [77, 1] (w:1, o:
% 1.31/2.15 107, a:1, s:1, b:0),
% 1.31/2.15 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [78, 1]
% 1.31/2.15 (w:1, o:108, a:1, s:1, b:0),
% 1.31/2.15 'c_Power_Opower_Opower' [81, 3] (w:1, o:194, a:1, s:1, b:0),
% 1.31/2.15 'c_OrderedGroup_Omonoid__mult' [82, 3] (w:1, o:193, a:1, s:1, b:0),
% 1.31/2.15 'c_Divides_Odiv__class_Odiv' [83, 3] (w:1, o:195, a:1, s:1, b:0),
% 1.31/2.15 'c_Divides_Odiv__class_Omod' [84, 3] (w:1, o:196, a:1, s:1, b:0),
% 1.31/2.15 'class_OrderedGroup_Omonoid__mult' [85, 1] (w:1, o:110, a:1, s:1, b:0
% 1.31/2.15 ),
% 1.31/2.15 'class_OrderedGroup_Olordered__ab__group__add' [87, 1] (w:1, o:109
% 1.31/2.15 , a:1, s:1, b:0),
% 1.31/2.15 'class_Ring__and__Field_Oordered__field' [88, 1] (w:1, o:111, a:1, s:
% 1.31/2.15 1, b:0),
% 1.31/2.15 'class_Int_Onumber' [89, 1] (w:1, o:112, a:1, s:1, b:0),
% 1.31/2.15 'c_Int_Onumber__class_Onumber__of' [91, 2] (w:1, o:184, a:1, s:1, b:0
% 1.31/2.15 ),
% 1.31/2.15 'c_HOL_Oinverse__class_Oinverse' [92, 1] (w:1, o:113, a:1, s:1, b:0)
% 1.31/2.15 ,
% 1.31/2.15 'class_Ring__and__Field_Ozero__neq__one' [93, 1] (w:1, o:114, a:1, s:
% 1.31/2.15 1, b:0),
% 1.31/2.15 'class_Ring__and__Field_Ono__zero__divisors' [94, 1] (w:1, o:96, a:1
% 1.31/2.15 , s:1, b:0),
% 1.31/2.15 'class_Ring__and__Field_Omult__zero' [95, 1] (w:1, o:93, a:1, s:1, b:
% 1.31/2.15 0),
% 1.31/2.15 'class_Power_Opower' [96, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.31/2.15 'class_Ring__and__Field_Oring__1__no__zero__divisors' [97, 1] (w:1
% 1.31/2.15 , o:129, a:1, s:1, b:0),
% 1.31/2.15 'class_OrderedGroup_Opordered__ab__group__add' [98, 1] (w:1, o:115
% 1.31/2.15 , a:1, s:1, b:0),
% 1.31/2.15 'class_Ring__and__Field_Ocomm__semiring__1' [99, 1] (w:1, o:84, a:1
% 1.31/2.15 , s:1, b:0),
% 1.31/2.15 'class_Ring__and__Field_Oordered__ring__strict' [100, 1] (w:1, o:97
% 1.31/2.15 , a:1, s:1, b:0),
% 1.31/2.15 'class_Divides_Osemiring__div' [101, 1] (w:1, o:131, a:1, s:1, b:0),
% 1.31/2.15
% 1.31/2.15 'class_OrderedGroup_Opordered__comm__monoid__add' [102, 1] (w:1, o:
% 1.31/2.15 116, a:1, s:1, b:0),
% 1.31/2.15 'c_Ring__and__Field_Oordered__idom' [111, 11] (w:1, o:203, a:1, s:1
% 1.31/2.15 , b:0),
% 1.31/2.15 'class_Int_Onumber__ring' [112, 1] (w:1, o:132, a:1, s:1, b:0),
% 1.31/2.15 'c_Int_OMin' [113, 0] (w:1, o:57, a:1, s:1, b:0),
% 1.31/2.15 'c_Parity_Oeven__odd__class_Oeven' [114, 2] (w:1, o:185, a:1, s:1, b:
% 1.31/2.15 0),
% 1.31/2.15 'class_Ring__and__Field_Oordered__semiring__strict' [115, 1] (w:1, o:
% 1.31/2.15 133, a:1, s:1, b:0),
% 1.31/2.15 'class_RealVector_Oreal__normed__field' [117, 1] (w:1, o:134, a:1, s:
% 1.31/2.15 1, b:0),
% 1.31/2.15 'class_OrderedGroup_Oab__group__add' [120, 1] (w:1, o:117, a:1, s:1
% 1.31/2.15 , b:0),
% 1.31/2.15 'class_Ring__and__Field_Oidom' [121, 1] (w:1, o:135, a:1, s:1, b:0),
% 1.31/2.15
% 1.31/2.15 'class_Ring__and__Field_Oordered__semiring' [122, 1] (w:1, o:136, a:1
% 1.31/2.15 , s:1, b:0),
% 1.31/2.15 'class_Ring__and__Field_Opordered__ring' [124, 1] (w:1, o:138, a:1
% 1.31/2.15 , s:1, b:0),
% 1.31/2.15 'class_Ring__and__Field_Osemiring__0' [127, 1] (w:1, o:142, a:1, s:1
% 1.31/2.15 , b:0),
% 1.31/2.15 'class_OrderedGroup_Ocomm__monoid__add' [128, 1] (w:1, o:118, a:1, s:
% 1.31/2.15 1, b:0),
% 1.31/2.15 'class_Ring__and__Field_Omult__mono1' [131, 1] (w:1, o:94, a:1, s:1
% 1.31/2.15 , b:0),
% 1.31/2.15 'class_Ring__and__Field_Omult__mono' [132, 1] (w:1, o:95, a:1, s:1
% 1.31/2.15 , b:0),
% 1.31/2.15 'class_Ring__and__Field_Odivision__ring' [133, 1] (w:1, o:143, a:1
% 11.09/11.49 , s:1, b:0),
% 11.09/11.49 'class_Ring__and__Field_Oring' [136, 1] (w:1, o:139, a:1, s:1, b:0),
% 11.09/11.49
% 11.09/11.49 'class_Orderings_Opreorder' [137, 1] (w:1, o:119, a:1, s:1, b:0),
% 11.09/11.49 'class_OrderedGroup_Oab__semigroup__add' [138, 1] (w:1, o:120, a:1
% 11.09/11.49 , s:1, b:0),
% 11.09/11.49 'class_Ring__and__Field_Opordered__cancel__semiring' [139, 1] (w:1
% 11.09/11.49 , o:144, a:1, s:1, b:0),
% 11.09/11.49 'c_Groebner__Basis_Ogb__semiring' [145, 6] (w:1, o:200, a:1, s:1, b:0
% 11.09/11.49 ),
% 11.09/11.49 'class_OrderedGroup_Oordered__ab__group__add' [146, 1] (w:1, o:106
% 11.09/11.49 , a:1, s:1, b:0),
% 11.09/11.49 'class_Ring__and__Field_Opordered__semiring' [147, 1] (w:1, o:145, a:
% 11.09/11.49 1, s:1, b:0),
% 11.09/11.49 'class_Divides_Oring__div' [148, 1] (w:1, o:130, a:1, s:1, b:0),
% 11.09/11.49 'class_RealVector_Oreal__normed__algebra' [151, 1] (w:1, o:146, a:1
% 11.09/11.49 , s:1, b:0),
% 11.09/11.49 'c_Int_Oiszero' [152, 2] (w:1, o:186, a:1, s:1, b:0),
% 11.09/11.49 'class_RealVector_Oreal__normed__div__algebra' [153, 1] (w:1, o:147
% 11.09/11.49 , a:1, s:1, b:0),
% 11.09/11.49 'c_COMBB' [154, 5] (w:1, o:199, a:1, s:1, b:0),
% 11.09/11.49 'class_OrderedGroup_Ocancel__ab__semigroup__add' [159, 1] (w:1, o:121
% 11.09/11.49 , a:1, s:1, b:0),
% 11.09/11.49 'class_OrderedGroup_Ocancel__semigroup__add' [160, 1] (w:1, o:122, a:
% 11.09/11.49 1, s:1, b:0),
% 11.09/11.49 'class_Ring__and__Field_Ocomm__ring__1' [161, 1] (w:1, o:83, a:1, s:1
% 11.09/11.49 , b:0),
% 11.09/11.49 'class_Ring__and__Field_Oordered__comm__semiring__strict' [164, 1]
% 11.09/11.49 (w:1, o:137, a:1, s:1, b:0),
% 11.09/11.49 'class_OrderedGroup_Omonoid__add' [165, 1] (w:1, o:123, a:1, s:1, b:0
% 11.09/11.49 ),
% 11.09/11.49 'class_RealVector_Oreal__field' [166, 1] (w:1, o:148, a:1, s:1, b:0)
% 11.09/11.49 ,
% 11.09/11.49 'class_Ring__and__Field_Oring__1' [167, 1] (w:1, o:140, a:1, s:1, b:0
% 11.09/11.49 ),
% 11.09/11.49 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [168, 1]
% 11.09/11.49 (w:1, o:124, a:1, s:1, b:0),
% 11.09/11.49 'c_Int_OPls' [169, 0] (w:1, o:65, a:1, s:1, b:0),
% 11.09/11.49 'c_Int_OBit1' [170, 1] (w:1, o:150, a:1, s:1, b:0),
% 11.09/11.49 'c_Int_OBit0' [171, 1] (w:1, o:149, a:1, s:1, b:0),
% 11.09/11.49 'class_Ring__and__Field_Oring__no__zero__divisors' [172, 1] (w:1, o:
% 11.09/11.49 141, a:1, s:1, b:0),
% 11.09/11.49 'class_Ring__and__Field_Ocomm__semiring' [175, 1] (w:1, o:85, a:1, s:
% 11.09/11.49 1, b:0),
% 11.09/11.49 'class_OrderedGroup_Ocomm__monoid__mult' [176, 1] (w:1, o:125, a:1
% 11.09/11.49 , s:1, b:0),
% 11.09/11.49 'class_Ring__and__Field_Osemiring' [177, 1] (w:1, o:151, a:1, s:1, b:
% 11.09/11.49 0),
% 11.09/11.49 'class_Ring__and__Field_Osemiring__1' [178, 1] (w:1, o:152, a:1, s:1
% 11.09/11.49 , b:0),
% 11.09/11.49 'class_RealVector_Oreal__normed__vector' [181, 1] (w:1, o:153, a:1
% 11.09/11.49 , s:1, b:0),
% 11.09/11.49 'class_Int_Oring__char__0' [182, 1] (w:1, o:154, a:1, s:1, b:0),
% 11.09/11.49 'c_Ring__and__Field_Ocomm__ring__1' [183, 7] (w:1, o:202, a:1, s:1
% 11.09/11.49 , b:0),
% 11.09/11.49 'c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1' [185, 1] (w:1, o:
% 11.09/11.49 155, a:1, s:1, b:0),
% 11.09/11.49 'c_Parity_Osko__Parity__Xodd__Suc__mult__two__ex__1__1' [186, 1] (w:1
% 11.09/11.49 , o:156, a:1, s:1, b:0),
% 11.09/11.49 'c_Fun_Oinj__on' [189, 4] (w:1, o:198, a:1, s:1, b:0),
% 11.09/11.49 'class_OrderedGroup_Oab__semigroup__mult' [190, 1] (w:1, o:126, a:1
% 11.09/11.49 , s:1, b:0),
% 11.09/11.49 'class_OrderedGroup_Oab__semigroup__idem__mult' [191, 1] (w:1, o:127
% 11.09/11.49 , a:1, s:1, b:0),
% 11.09/11.49 'v_A' [196, 0] (w:1, o:72, a:1, s:1, b:0),
% 11.09/11.49 'tc_fun' [199, 2] (w:1, o:187, a:1, s:1, b:0),
% 11.09/11.49 'tc_Int_Oint' [200, 0] (w:1, o:75, a:1, s:1, b:0),
% 11.09/11.49 'c_COMBC' [201, 6] (w:1, o:201, a:1, s:1, b:0),
% 11.09/11.49 'c_fequal' [202, 3] (w:1, o:197, a:1, s:1, b:0).
% 11.09/11.49
% 11.09/11.49
% 11.09/11.49 Starting Search:
% 11.09/11.49
% 11.09/11.49 Resimplifying inuse:
% 11.09/11.49 Done
% 11.09/11.49
% 11.09/11.49
% 11.09/11.49 Intermediate Status:
% 11.09/11.49 Generated: 3885
% 11.09/11.49 Kept: 2040
% 11.09/11.49 Inuse: 50
% 11.09/11.49 Deleted: 1
% 11.09/11.49 Deletedinuse: 0
% 11.09/11.49
% 11.09/11.49 Resimplifying inuse:
% 11.09/11.49 Done
% 11.09/11.49
% 11.09/11.49 Resimplifying inuse:
% 11.09/11.49 Done
% 11.09/11.49
% 11.09/11.49
% 11.09/11.49 Intermediate Status:
% 11.09/11.49 Generated: 11332
% 11.09/11.49 Kept: 4047
% 11.09/11.49 Inuse: 142
% 11.09/11.49 Deleted: 2
% 11.09/11.49 Deletedinuse: 0
% 11.09/11.49
% 11.09/11.49 Resimplifying inuse:
% 11.09/11.49 Done
% 11.09/11.49
% 11.09/11.49 Resimplifying inuse:
% 11.09/11.49 Done
% 11.09/11.49
% 11.09/11.49
% 11.09/11.49 Intermediate Status:
% 11.09/11.49 Generated: 18594
% 11.09/11.49 Kept: 6057
% 11.09/11.49 Inuse: 241
% 11.09/11.49 Deleted: 10
% 11.09/11.49 Deletedinuse: 0
% 11.09/11.49
% 11.09/11.49 Resimplifying inuse:
% 11.09/11.49 Done
% 11.09/11.49
% 11.09/11.49
% 11.09/11.49 Intermediate Status:
% 11.09/11.49 Generated: 25404
% 11.09/11.49 Kept: 8707
% 11.09/11.49 Inuse: 277
% 11.09/11.49 Deleted: 12
% 11.09/11.49 Deletedinuse: 0
% 11.09/11.49
% 11.09/11.49 Resimplifying inuse:
% 11.09/11.49 Done
% 11.09/11.49
% 11.09/11.49 Resimplifying inuse:
% 11.09/11.49 Done
% 11.09/11.49
% 11.09/11.49
% 11.09/11.49 Intermediate Status:
% 33.11/33.45 Generated: 32895
% 33.11/33.45 Kept: 10818
% 33.11/33.45 Inuse: 343
% 33.11/33.45 Deleted: 13
% 33.11/33.45 Deletedinuse: 0
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 38229
% 33.11/33.45 Kept: 12838
% 33.11/33.45 Inuse: 388
% 33.11/33.45 Deleted: 13
% 33.11/33.45 Deletedinuse: 0
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 45842
% 33.11/33.45 Kept: 14862
% 33.11/33.45 Inuse: 438
% 33.11/33.45 Deleted: 13
% 33.11/33.45 Deletedinuse: 0
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 53235
% 33.11/33.45 Kept: 17024
% 33.11/33.45 Inuse: 468
% 33.11/33.45 Deleted: 13
% 33.11/33.45 Deletedinuse: 0
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 59561
% 33.11/33.45 Kept: 19233
% 33.11/33.45 Inuse: 502
% 33.11/33.45 Deleted: 14
% 33.11/33.45 Deletedinuse: 0
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45 Resimplifying clauses:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 68246
% 33.11/33.45 Kept: 21306
% 33.11/33.45 Inuse: 555
% 33.11/33.45 Deleted: 381
% 33.11/33.45 Deletedinuse: 0
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 75654
% 33.11/33.45 Kept: 23954
% 33.11/33.45 Inuse: 580
% 33.11/33.45 Deleted: 381
% 33.11/33.45 Deletedinuse: 0
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 80795
% 33.11/33.45 Kept: 26124
% 33.11/33.45 Inuse: 600
% 33.11/33.45 Deleted: 381
% 33.11/33.45 Deletedinuse: 0
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 86974
% 33.11/33.45 Kept: 28175
% 33.11/33.45 Inuse: 625
% 33.11/33.45 Deleted: 381
% 33.11/33.45 Deletedinuse: 0
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 93466
% 33.11/33.45 Kept: 30239
% 33.11/33.45 Inuse: 650
% 33.11/33.45 Deleted: 381
% 33.11/33.45 Deletedinuse: 0
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 100721
% 33.11/33.45 Kept: 32242
% 33.11/33.45 Inuse: 662
% 33.11/33.45 Deleted: 381
% 33.11/33.45 Deletedinuse: 0
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 108385
% 33.11/33.45 Kept: 34251
% 33.11/33.45 Inuse: 697
% 33.11/33.45 Deleted: 381
% 33.11/33.45 Deletedinuse: 0
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 116940
% 33.11/33.45 Kept: 36362
% 33.11/33.45 Inuse: 722
% 33.11/33.45 Deleted: 384
% 33.11/33.45 Deletedinuse: 0
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 134097
% 33.11/33.45 Kept: 39150
% 33.11/33.45 Inuse: 733
% 33.11/33.45 Deleted: 389
% 33.11/33.45 Deletedinuse: 1
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45 Resimplifying clauses:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 142653
% 33.11/33.45 Kept: 41164
% 33.11/33.45 Inuse: 753
% 33.11/33.45 Deleted: 690
% 33.11/33.45 Deletedinuse: 1
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 152143
% 33.11/33.45 Kept: 43164
% 33.11/33.45 Inuse: 782
% 33.11/33.45 Deleted: 690
% 33.11/33.45 Deletedinuse: 1
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 171143
% 33.11/33.45 Kept: 45212
% 33.11/33.45 Inuse: 788
% 33.11/33.45 Deleted: 690
% 33.11/33.45 Deletedinuse: 1
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 190797
% 33.11/33.45 Kept: 47239
% 33.11/33.45 Inuse: 793
% 33.11/33.45 Deleted: 690
% 33.11/33.45 Deletedinuse: 1
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 201237
% 33.11/33.45 Kept: 49984
% 33.11/33.45 Inuse: 803
% 33.11/33.45 Deleted: 690
% 33.11/33.45 Deletedinuse: 1
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 210564
% 33.11/33.45 Kept: 52163
% 33.11/33.45 Inuse: 823
% 33.11/33.45 Deleted: 690
% 33.11/33.45 Deletedinuse: 1
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 220109
% 33.11/33.45 Kept: 54289
% 33.11/33.45 Inuse: 853
% 33.11/33.45 Deleted: 690
% 33.11/33.45 Deletedinuse: 1
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 232784
% 33.11/33.45 Kept: 56907
% 33.11/33.45 Inuse: 883
% 33.11/33.45 Deleted: 690
% 33.11/33.45 Deletedinuse: 1
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 248544
% 33.11/33.45 Kept: 59332
% 33.11/33.45 Inuse: 908
% 33.11/33.45 Deleted: 690
% 33.11/33.45 Deletedinuse: 1
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 290715
% 33.11/33.45 Kept: 61452
% 33.11/33.45 Inuse: 913
% 33.11/33.45 Deleted: 691
% 33.11/33.45 Deletedinuse: 2
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45 Resimplifying clauses:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 33.11/33.45 Generated: 302827
% 33.11/33.45 Kept: 64359
% 33.11/33.45 Inuse: 939
% 33.11/33.45 Deleted: 843
% 33.11/33.45 Deletedinuse: 2
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45 Resimplifying inuse:
% 33.11/33.45 Done
% 33.11/33.45
% 33.11/33.45
% 33.11/33.45 Intermediate Status:
% 78.41/78.80 Generated: 316365
% 78.41/78.80 Kept: 68126
% 78.41/78.80 Inuse: 958
% 78.41/78.80 Deleted: 843
% 78.41/78.80 Deletedinuse: 2
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 325814
% 78.41/78.80 Kept: 72555
% 78.41/78.80 Inuse: 963
% 78.41/78.80 Deleted: 843
% 78.41/78.80 Deletedinuse: 2
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 334575
% 78.41/78.80 Kept: 74951
% 78.41/78.80 Inuse: 968
% 78.41/78.80 Deleted: 843
% 78.41/78.80 Deletedinuse: 2
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 343117
% 78.41/78.80 Kept: 76978
% 78.41/78.80 Inuse: 996
% 78.41/78.80 Deleted: 848
% 78.41/78.80 Deletedinuse: 7
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 352379
% 78.41/78.80 Kept: 79307
% 78.41/78.80 Inuse: 1018
% 78.41/78.80 Deleted: 848
% 78.41/78.80 Deletedinuse: 7
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 361851
% 78.41/78.80 Kept: 82015
% 78.41/78.80 Inuse: 1033
% 78.41/78.80 Deleted: 848
% 78.41/78.80 Deletedinuse: 7
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80 Resimplifying clauses:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 369829
% 78.41/78.80 Kept: 84281
% 78.41/78.80 Inuse: 1043
% 78.41/78.80 Deleted: 1364
% 78.41/78.80 Deletedinuse: 7
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 377518
% 78.41/78.80 Kept: 86300
% 78.41/78.80 Inuse: 1064
% 78.41/78.80 Deleted: 1364
% 78.41/78.80 Deletedinuse: 7
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 389876
% 78.41/78.80 Kept: 88306
% 78.41/78.80 Inuse: 1092
% 78.41/78.80 Deleted: 1364
% 78.41/78.80 Deletedinuse: 7
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 401393
% 78.41/78.80 Kept: 90313
% 78.41/78.80 Inuse: 1115
% 78.41/78.80 Deleted: 1364
% 78.41/78.80 Deletedinuse: 7
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 411520
% 78.41/78.80 Kept: 92392
% 78.41/78.80 Inuse: 1128
% 78.41/78.80 Deleted: 1364
% 78.41/78.80 Deletedinuse: 7
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 424577
% 78.41/78.80 Kept: 94673
% 78.41/78.80 Inuse: 1163
% 78.41/78.80 Deleted: 1364
% 78.41/78.80 Deletedinuse: 7
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 438405
% 78.41/78.80 Kept: 96846
% 78.41/78.80 Inuse: 1198
% 78.41/78.80 Deleted: 1364
% 78.41/78.80 Deletedinuse: 7
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 452898
% 78.41/78.80 Kept: 99025
% 78.41/78.80 Inuse: 1228
% 78.41/78.80 Deleted: 1366
% 78.41/78.80 Deletedinuse: 9
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 466480
% 78.41/78.80 Kept: 101148
% 78.41/78.80 Inuse: 1258
% 78.41/78.80 Deleted: 1367
% 78.41/78.80 Deletedinuse: 10
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80 Resimplifying clauses:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 477657
% 78.41/78.80 Kept: 103206
% 78.41/78.80 Inuse: 1288
% 78.41/78.80 Deleted: 1792
% 78.41/78.80 Deletedinuse: 10
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 487715
% 78.41/78.80 Kept: 105368
% 78.41/78.80 Inuse: 1313
% 78.41/78.80 Deleted: 1792
% 78.41/78.80 Deletedinuse: 10
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 517579
% 78.41/78.80 Kept: 110235
% 78.41/78.80 Inuse: 1328
% 78.41/78.80 Deleted: 1792
% 78.41/78.80 Deletedinuse: 10
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 527319
% 78.41/78.80 Kept: 112239
% 78.41/78.80 Inuse: 1336
% 78.41/78.80 Deleted: 1793
% 78.41/78.80 Deletedinuse: 11
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 543409
% 78.41/78.80 Kept: 115681
% 78.41/78.80 Inuse: 1353
% 78.41/78.80 Deleted: 1793
% 78.41/78.80 Deletedinuse: 11
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 553637
% 78.41/78.80 Kept: 118019
% 78.41/78.80 Inuse: 1378
% 78.41/78.80 Deleted: 1794
% 78.41/78.80 Deletedinuse: 12
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 570475
% 78.41/78.80 Kept: 121484
% 78.41/78.80 Inuse: 1402
% 78.41/78.80 Deleted: 1798
% 78.41/78.80 Deletedinuse: 15
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 578384
% 78.41/78.80 Kept: 123806
% 78.41/78.80 Inuse: 1407
% 78.41/78.80 Deleted: 1798
% 78.41/78.80 Deletedinuse: 15
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80 Resimplifying clauses:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 594522
% 78.41/78.80 Kept: 127191
% 78.41/78.80 Inuse: 1422
% 78.41/78.80 Deleted: 3504
% 78.41/78.80 Deletedinuse: 16
% 78.41/78.80
% 78.41/78.80 Resimplifying inuse:
% 78.41/78.80 Done
% 78.41/78.80
% 78.41/78.80
% 78.41/78.80 Intermediate Status:
% 78.41/78.80 Generated: 606199
% 78.41/78.80 Kept: 129282
% 78.41/78.80 Inuse: 1427
% 78.41/78.80 Deleted: 3504
% 148.68/149.04 Deletedinuse: 16
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 643073
% 148.68/149.04 Kept: 134101
% 148.68/149.04 Inuse: 1442
% 148.68/149.04 Deleted: 3505
% 148.68/149.04 Deletedinuse: 17
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 655254
% 148.68/149.04 Kept: 136643
% 148.68/149.04 Inuse: 1452
% 148.68/149.04 Deleted: 3505
% 148.68/149.04 Deletedinuse: 17
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 665244
% 148.68/149.04 Kept: 138679
% 148.68/149.04 Inuse: 1457
% 148.68/149.04 Deleted: 3505
% 148.68/149.04 Deletedinuse: 17
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 675187
% 148.68/149.04 Kept: 140708
% 148.68/149.04 Inuse: 1462
% 148.68/149.04 Deleted: 3505
% 148.68/149.04 Deletedinuse: 17
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 700436
% 148.68/149.04 Kept: 144442
% 148.68/149.04 Inuse: 1477
% 148.68/149.04 Deleted: 3505
% 148.68/149.04 Deletedinuse: 17
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04 Resimplifying clauses:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 711777
% 148.68/149.04 Kept: 146530
% 148.68/149.04 Inuse: 1482
% 148.68/149.04 Deleted: 3702
% 148.68/149.04 Deletedinuse: 17
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 732149
% 148.68/149.04 Kept: 148548
% 148.68/149.04 Inuse: 1488
% 148.68/149.04 Deleted: 3702
% 148.68/149.04 Deletedinuse: 17
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 743008
% 148.68/149.04 Kept: 150572
% 148.68/149.04 Inuse: 1504
% 148.68/149.04 Deleted: 3702
% 148.68/149.04 Deletedinuse: 17
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 755521
% 148.68/149.04 Kept: 152742
% 148.68/149.04 Inuse: 1522
% 148.68/149.04 Deleted: 3702
% 148.68/149.04 Deletedinuse: 17
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 768039
% 148.68/149.04 Kept: 155028
% 148.68/149.04 Inuse: 1542
% 148.68/149.04 Deleted: 3702
% 148.68/149.04 Deletedinuse: 17
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 778261
% 148.68/149.04 Kept: 157079
% 148.68/149.04 Inuse: 1562
% 148.68/149.04 Deleted: 3702
% 148.68/149.04 Deletedinuse: 17
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 791071
% 148.68/149.04 Kept: 159414
% 148.68/149.04 Inuse: 1587
% 148.68/149.04 Deleted: 3702
% 148.68/149.04 Deletedinuse: 17
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 832509
% 148.68/149.04 Kept: 163910
% 148.68/149.04 Inuse: 1597
% 148.68/149.04 Deleted: 3702
% 148.68/149.04 Deletedinuse: 17
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04 Resimplifying clauses:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 842126
% 148.68/149.04 Kept: 165913
% 148.68/149.04 Inuse: 1615
% 148.68/149.04 Deleted: 3811
% 148.68/149.04 Deletedinuse: 17
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 853450
% 148.68/149.04 Kept: 168144
% 148.68/149.04 Inuse: 1617
% 148.68/149.04 Deleted: 3811
% 148.68/149.04 Deletedinuse: 17
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 880312
% 148.68/149.04 Kept: 171315
% 148.68/149.04 Inuse: 1642
% 148.68/149.04 Deleted: 3811
% 148.68/149.04 Deletedinuse: 17
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 891091
% 148.68/149.04 Kept: 173689
% 148.68/149.04 Inuse: 1667
% 148.68/149.04 Deleted: 3811
% 148.68/149.04 Deletedinuse: 17
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 902518
% 148.68/149.04 Kept: 176192
% 148.68/149.04 Inuse: 1692
% 148.68/149.04 Deleted: 3811
% 148.68/149.04 Deletedinuse: 17
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 936084
% 148.68/149.04 Kept: 181173
% 148.68/149.04 Inuse: 1702
% 148.68/149.04 Deleted: 3811
% 148.68/149.04 Deletedinuse: 17
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 955087
% 148.68/149.04 Kept: 183194
% 148.68/149.04 Inuse: 1709
% 148.68/149.04 Deleted: 3812
% 148.68/149.04 Deletedinuse: 18
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04 Resimplifying clauses:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 963156
% 148.68/149.04 Kept: 185194
% 148.68/149.04 Inuse: 1726
% 148.68/149.04 Deleted: 4085
% 148.68/149.04 Deletedinuse: 18
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 974970
% 148.68/149.04 Kept: 187886
% 148.68/149.04 Inuse: 1732
% 148.68/149.04 Deleted: 4085
% 148.68/149.04 Deletedinuse: 18
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 982131
% 148.68/149.04 Kept: 190149
% 148.68/149.04 Inuse: 1747
% 148.68/149.04 Deleted: 4085
% 148.68/149.04 Deletedinuse: 18
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 989737
% 148.68/149.04 Kept: 192168
% 148.68/149.04 Inuse: 1765
% 148.68/149.04 Deleted: 4085
% 148.68/149.04 Deletedinuse: 18
% 148.68/149.04
% 148.68/149.04 Resimplifying inuse:
% 148.68/149.04 Done
% 148.68/149.04
% 148.68/149.04
% 148.68/149.04 Intermediate Status:
% 148.68/149.04 Generated: 1016379
% 148.68/149.04 Kept: 195472
% 278.63/279.02 Inuse: 1799
% 278.63/279.02 Deleted: 4090
% 278.63/279.02 Deletedinuse: 19
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1025783
% 278.63/279.02 Kept: 197496
% 278.63/279.02 Inuse: 1803
% 278.63/279.02 Deleted: 4090
% 278.63/279.02 Deletedinuse: 19
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1036943
% 278.63/279.02 Kept: 199708
% 278.63/279.02 Inuse: 1813
% 278.63/279.02 Deleted: 4090
% 278.63/279.02 Deletedinuse: 19
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1047049
% 278.63/279.02 Kept: 201768
% 278.63/279.02 Inuse: 1818
% 278.63/279.02 Deleted: 4090
% 278.63/279.02 Deletedinuse: 19
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1059460
% 278.63/279.02 Kept: 204211
% 278.63/279.02 Inuse: 1843
% 278.63/279.02 Deleted: 4094
% 278.63/279.02 Deletedinuse: 23
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02 Resimplifying clauses:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1083547
% 278.63/279.02 Kept: 211447
% 278.63/279.02 Inuse: 1853
% 278.63/279.02 Deleted: 5543
% 278.63/279.02 Deletedinuse: 27
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1101819
% 278.63/279.02 Kept: 214936
% 278.63/279.02 Inuse: 1858
% 278.63/279.02 Deleted: 5543
% 278.63/279.02 Deletedinuse: 27
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1115801
% 278.63/279.02 Kept: 217568
% 278.63/279.02 Inuse: 1863
% 278.63/279.02 Deleted: 5543
% 278.63/279.02 Deletedinuse: 27
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1128552
% 278.63/279.02 Kept: 220279
% 278.63/279.02 Inuse: 1868
% 278.63/279.02 Deleted: 5543
% 278.63/279.02 Deletedinuse: 27
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1150064
% 278.63/279.02 Kept: 225186
% 278.63/279.02 Inuse: 1872
% 278.63/279.02 Deleted: 5543
% 278.63/279.02 Deletedinuse: 27
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02 Resimplifying clauses:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1162936
% 278.63/279.02 Kept: 227616
% 278.63/279.02 Inuse: 1873
% 278.63/279.02 Deleted: 5568
% 278.63/279.02 Deletedinuse: 27
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1175126
% 278.63/279.02 Kept: 229781
% 278.63/279.02 Inuse: 1898
% 278.63/279.02 Deleted: 5568
% 278.63/279.02 Deletedinuse: 27
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1187209
% 278.63/279.02 Kept: 232230
% 278.63/279.02 Inuse: 1918
% 278.63/279.02 Deleted: 5569
% 278.63/279.02 Deletedinuse: 28
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1198405
% 278.63/279.02 Kept: 234396
% 278.63/279.02 Inuse: 1938
% 278.63/279.02 Deleted: 5570
% 278.63/279.02 Deletedinuse: 29
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1211785
% 278.63/279.02 Kept: 237204
% 278.63/279.02 Inuse: 1948
% 278.63/279.02 Deleted: 5570
% 278.63/279.02 Deletedinuse: 29
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1223518
% 278.63/279.02 Kept: 239653
% 278.63/279.02 Inuse: 1953
% 278.63/279.02 Deleted: 5570
% 278.63/279.02 Deletedinuse: 29
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1279851
% 278.63/279.02 Kept: 246396
% 278.63/279.02 Inuse: 1973
% 278.63/279.02 Deleted: 5570
% 278.63/279.02 Deletedinuse: 29
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02 Resimplifying clauses:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1290156
% 278.63/279.02 Kept: 248432
% 278.63/279.02 Inuse: 1992
% 278.63/279.02 Deleted: 6088
% 278.63/279.02 Deletedinuse: 29
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1311101
% 278.63/279.02 Kept: 251350
% 278.63/279.02 Inuse: 2013
% 278.63/279.02 Deleted: 6089
% 278.63/279.02 Deletedinuse: 30
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1321564
% 278.63/279.02 Kept: 254957
% 278.63/279.02 Inuse: 2023
% 278.63/279.02 Deleted: 6089
% 278.63/279.02 Deletedinuse: 30
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1329089
% 278.63/279.02 Kept: 257208
% 278.63/279.02 Inuse: 2033
% 278.63/279.02 Deleted: 6089
% 278.63/279.02 Deletedinuse: 30
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1339009
% 278.63/279.02 Kept: 259218
% 278.63/279.02 Inuse: 2049
% 278.63/279.02 Deleted: 6089
% 278.63/279.02 Deletedinuse: 30
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1348415
% 278.63/279.02 Kept: 261230
% 278.63/279.02 Inuse: 2066
% 278.63/279.02 Deleted: 6089
% 278.63/279.02 Deletedinuse: 30
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1357399
% 278.63/279.02 Kept: 263285
% 278.63/279.02 Inuse: 2073
% 278.63/279.02 Deleted: 6089
% 278.63/279.02 Deletedinuse: 30
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02
% 278.63/279.02 Intermediate Status:
% 278.63/279.02 Generated: 1371004
% 278.63/279.02 Kept: 266318
% 278.63/279.02 Inuse: 2088
% 278.63/279.02 Deleted: 6089
% 278.63/279.02 Deletedinuse: 30
% 278.63/279.02
% 278.63/279.02 Resimplifying inuse:
% 278.63/279.02 Done
% 278.63/279.02
% 278.63/279.02 ResimplifCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------