TSTP Solution File: SWV583-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV583-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.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 16:26:53 EDT 2022
% Result : Timeout 300.05s 300.52s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV583-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Wed Jun 15 14:06:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.23/1.61 *** allocated 10000 integers for termspace/termends
% 1.23/1.61 *** allocated 10000 integers for clauses
% 1.23/1.61 *** allocated 10000 integers for justifications
% 1.23/1.61 *** allocated 15000 integers for termspace/termends
% 1.23/1.61 *** allocated 22500 integers for termspace/termends
% 1.23/1.61 *** allocated 33750 integers for termspace/termends
% 1.23/1.61 *** allocated 50625 integers for termspace/termends
% 1.23/1.61 Bliksem 1.12
% 1.23/1.61
% 1.23/1.61
% 1.23/1.61 Automatic Strategy Selection
% 1.23/1.61
% 1.23/1.61 Clauses:
% 1.23/1.61 [
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Z, hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), W ), X ) ), T ), X ) ), ~(
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Z, hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ) ), W ), X ), ~(
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), W ), X ) ), ~(
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ],
% 1.23/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.61 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.23/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.61 , Y ), T ), Z, X ) ) ],
% 1.23/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.61 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.23/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.61 , Y ), Z ), T, X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.23/1.61 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.23/1.61 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oone__class_Oone'(
% 1.23/1.61 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.23/1.61 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.61 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.61 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.23/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ),
% 1.23/1.61 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.23/1.61 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.23/1.61 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.23/1.61 'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.23/1.61 'tc_nat' ) ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.23/1.61 , Z ) ), Z ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.23/1.61 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.23/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.61 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.23/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.61 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.23/1.61 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.23/1.61 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.23/1.61 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.23/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.23/1.61 ), X ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.61 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.61 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.23/1.61 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.23/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.61 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.23/1.61 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.61 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.23/1.61 ), X ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.61 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.23/1.61 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.23/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.23/1.61 X ) ],
% 1.23/1.61 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'(
% 1.23/1.61 'tc_nat' ), X, 'tc_nat' ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X
% 1.23/1.61 ) ), 'c_Divides_Odiv__class_Odiv'( T, U, X ) ),
% 1.23/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.61 ), Y ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X
% 1.23/1.61 ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( U, T, X ) ), ~(
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.23/1.61 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.61 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ), hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.61 'tc_nat' ) ) ), 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.23/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.23/1.61 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.23/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.23/1.61 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.61 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.23/1.61 ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.61 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.23/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.23/1.61 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.23/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z,
% 1.23/1.61 'tc_nat' ) ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.61 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.23/1.61 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.61 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.62 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.23/1.62 'c_lessequals'( Z, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.62 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.23/1.62 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.23/1.62 'c_lessequals'( Z, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( T, X ), X ) )
% 1.23/1.62 , ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 1.23/1.62 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' ) ],
% 1.23/1.62 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.23/1.62 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.23/1.62 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.23/1.62 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.23/1.62 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.23/1.62 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.23/1.62 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 1.23/1.62 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.23/1.62 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.23/1.62 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), =( Y, X ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ],
% 1.23/1.62 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 1.23/1.62 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 1.23/1.62 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y, X ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.23/1.62 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.23/1.62 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.23/1.62 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.23/1.62 , X ) ) ), =( Y, Z ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.23/1.62 , X ) ) ), =( Y, Z ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( T, X ) ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), Z, X ) ) ],
% 1.23/1.62 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.23/1.62 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.23/1.62 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 Z, Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.23/1.62 , X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.23/1.62 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.23/1.62 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.23/1.62 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), T ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.23/1.62 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), T ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.23/1.62 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.23/1.62 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.23/1.62 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.23/1.62 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.23/1.62 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.23/1.62 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.23/1.62 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.23/1.62 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.23/1.62 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.23/1.62 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.23/1.62 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.23/1.62 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.23/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ), Y )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.23/1.62 , X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X ) ],
% 1.23/1.62 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Odiv'(
% 1.23/1.62 Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.23/1.62 X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Odiv'(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.23/1.62 X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.23/1.62 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.23/1.62 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X ), X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.23/1.62 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.23/1.62 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 Y, X ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 1.23/1.62 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.23/1.62 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.23/1.62 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.23/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.23/1.62 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.23/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.23/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ),
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), ~(
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.23/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ],
% 1.23/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ],
% 1.23/1.62 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ) ), X ), Z, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ) ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.23/1.62 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.23/1.62 X ) ) ) ],
% 1.23/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 1.23/1.62 Y, Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.23/1.62 X ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.23/1.62 X ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, T
% 1.23/1.62 , X ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, Z
% 1.23/1.62 , X ), 'c_Divides_Odiv__class_Odiv'( T, Z, X ), X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 Z, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 Z, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.23/1.62 , X ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.23/1.62 , X ), Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.23/1.62 , T, X ), X ), T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.23/1.62 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.23/1.62 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.23/1.62 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.23/1.62 'c_lessequals'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.23/1.62 'c_lessequals'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.23/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.62 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ), X ) ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.23/1.62 ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =(
% 1.23/1.62 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), X ), Y ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ],
% 1.23/1.62 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ),
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 1.23/1.62 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.23/1.62 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.23/1.62 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.23/1.62 Z ), X ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.23/1.62 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 1.23/1.62 hBOOL( hAPP( X, Z ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 1.23/1.62 hBOOL( hAPP( X, Z ) ) ],
% 1.23/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.23/1.62 Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc',
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ),
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 1.23/1.62 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.23/1.62 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'(
% 1.23/1.62 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.23/1.62 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.23/1.62 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.23/1.62 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.23/1.62 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.23/1.62 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.23/1.62 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.23/1.62 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.23/1.62 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.23/1.62 Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.62 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.23/1.62 ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 1.23/1.62 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.62 X ) ), Y ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.23/1.62 , T, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.23/1.62 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.23/1.62 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.23/1.62 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( T, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.23/1.62 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X
% 1.23/1.62 ) ), U ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), T ), U ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ), W, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.23/1.62 ) ), T ) ), U ), W, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), T ) ), U ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.23/1.62 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.23/1.62 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.23/1.62 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.23/1.62 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.23/1.62 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.23/1.62 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.62 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.62 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oabs__class_Oabs'(
% 1.23/1.62 Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.23/1.62 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), 'c_Divides_Odiv__class_Odiv'(
% 1.23/1.62 Z, T, X ) ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.23/1.62 , X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X
% 1.23/1.62 ) ],
% 1.23/1.62 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'tc_nat' ),
% 1.23/1.62 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.23/1.62 , X ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( Y
% 1.23/1.62 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.23/1.62 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), hAPP(
% 1.23/1.62 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), Z ) ) ],
% 1.23/1.62 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.23/1.62 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.23/1.62 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.23/1.62 ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.23/1.62 X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X
% 1.23/1.62 ), X ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.23/1.62 ), Z ), Y ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.23/1.62 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.23/1.62 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), Y ), Z ) ), T ) ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), Y ), Z ) ), T ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.23/1.62 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.23/1.62 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.23/1.62 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.23/1.62 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.23/1.62 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.23/1.62 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.23/1.62 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.23/1.62 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.23/1.62 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.23/1.62 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.23/1.62 , X ) ), T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.23/1.62 ), Z ), T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.23/1.62 ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.23/1.62 ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.23/1.62 ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.23/1.62 ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.62 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.23/1.62 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.23/1.62 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.23/1.62 Z, X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.23/1.62 Y, Z, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.62 'c_Int_OMin', X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.23/1.62 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.23/1.62 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Y,
% 1.23/1.62 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.23/1.62 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'(
% 1.23/1.62 Y, T, X ) ), 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X
% 1.23/1.62 ) ), T ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.23/1.62 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.23/1.62 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'(
% 1.23/1.62 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.23/1.62 , Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ) ), Z ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.23/1.62 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OMin',
% 1.23/1.62 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OMin',
% 1.23/1.62 'tc_Int_Oint' ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OMin', 'tc_Int_Oint' ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OMin',
% 1.23/1.62 'tc_Int_Oint' ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.23/1.62 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__field'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), W, X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.23/1.62 Z, U, X ), W, X ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, T, X )
% 1.23/1.62 , W, X ) ), U ) ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.23/1.62 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.23/1.62 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OPls', 'tc_Int_Oint' )
% 1.23/1.62 ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.62 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.23/1.62 'tc_Int_Oint' ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( Y, T, X ), X ) ), 'c_HOL_Oabs__class_Oabs'(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ) ), X ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.62 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.23/1.62 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.23/1.62 X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.23/1.62 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.23/1.62 ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 'tc_Int_Oint' ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit0'( X ),
% 1.23/1.62 'tc_Int_Oint' ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit0'( X ),
% 1.23/1.62 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X,
% 1.23/1.62 'tc_Int_Oint' ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 'tc_Int_Oint' ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit1'( X ),
% 1.23/1.62 'tc_Int_Oint' ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit1'( X ),
% 1.23/1.62 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X,
% 1.23/1.62 'tc_Int_Oint' ) ) ],
% 1.23/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ),
% 1.23/1.62 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.23/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 X, T, 'tc_nat' ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.23/1.62 ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ), X ) ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.23/1.62 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.23/1.62 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 1.23/1.62 X ) ) ],
% 1.23/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.23/1.62 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.23/1.62 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.23/1.62 Y ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.62 'tc_nat' ) ), Y ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.62 'tc_nat' ) ), Y ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.23/1.62 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), 'c_Divides_Odiv__class_Odiv'( Y, Z,
% 1.23/1.62 X ) ), T ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ),
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X, 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.23/1.62 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ),
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( Y, 'c_Divides_Odiv__class_Omod'( Y, X,
% 1.23/1.62 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.23/1.62 , 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ), X ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.23/1.62 , Y ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.23/1.62 ) ), Z ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( X, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.23/1.62 Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.23/1.62 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.23/1.62 ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.23/1.62 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_Int_Oint' ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.23/1.62 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ), X ) ) ],
% 1.23/1.62 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.23/1.62 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.23/1.62 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ),
% 1.23/1.62 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ), =( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.23/1.62 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.23/1.62 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.23/1.62 X ), Z, X ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.23/1.62 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.23/1.62 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.23/1.62 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.62 T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.23/1.62 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.23/1.62 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.23/1.62 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.23/1.62 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.23/1.62 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.23/1.62 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.23/1.62 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.23/1.62 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.23/1.62 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 1.23/1.62 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OMin',
% 1.23/1.62 'tc_Int_Oint' ) ) ],
% 1.23/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y
% 1.23/1.62 , Z, X ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ), X ) ), Y ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ), X ) ), 'c_Parity_Oeven__odd__class_Oeven'(
% 1.23/1.62 Y, 'tc_nat' ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 1.23/1.62 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.23/1.62 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.23/1.62 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.23/1.62 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.23/1.62 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.23/1.62 X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X
% 1.23/1.62 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.23/1.62 Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.23/1.62 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.23/1.62 X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.23/1.62 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.23/1.62 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.23/1.62 , X ) ],
% 1.23/1.62 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OMin',
% 1.23/1.62 'tc_Int_Oint' ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.23/1.62 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.23/1.62 ],
% 1.23/1.62 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ),
% 1.23/1.62 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'(
% 1.23/1.62 'tc_nat' ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ), =( X,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y,
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.62 'c_Int_OMin', X ) ), Y ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z,
% 1.23/1.62 Y, X ) ), Z ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X
% 1.23/1.62 ) ), Z ), Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.23/1.62 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.23/1.62 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.23/1.62 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.23/1.62 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.23/1.62 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.23/1.62 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Y ), Z ), Z, X ), Y ) ],
% 1.23/1.62 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Z ), T ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( Z, T, X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.23/1.62 ), Y ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.23/1.62 ), Y ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.23/1.62 ), Y ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.23/1.62 X ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.23/1.62 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.23/1.62 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.23/1.62 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.23/1.62 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.23/1.62 , X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.23/1.62 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.23/1.62 , X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.23/1.62 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.23/1.62 , X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.23/1.62 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.23/1.62 , X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.23/1.62 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.23/1.62 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.23/1.62 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.23/1.62 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 , X ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.23/1.62 , X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.62 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.62 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.23/1.62 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.23/1.62 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.23/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.23/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.23/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.23/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.62 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ), Z
% 1.23/1.62 ), 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), Z ), X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.23/1.62 ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.23/1.62 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.23/1.62 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.23/1.62 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.23/1.62 , T, X ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), T, X ) ), =( T,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.23/1.62 ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Z, X ) ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.23/1.62 , ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.23/1.62 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.23/1.62 , ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.23/1.62 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.23/1.62 ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.23/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.23/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_Divides_Osemiring__div'( X )
% 1.23/1.62 ), ~( =( 'c_Divides_Odiv__class_Omod'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.62 Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.23/1.62 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_Divides_Osemiring__div'( X )
% 1.23/1.62 ), =( 'c_Divides_Odiv__class_Omod'( 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.62 Y, X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.62 Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.23/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.23/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.23/1.62 ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.23/1.62 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.62 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.23/1.62 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.23/1.62 , Z ), Y ), 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.23/1.62 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.62 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.62 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.23/1.62 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.23/1.62 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.62 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.62 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.23/1.62 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.23/1.62 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.23/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.23/1.62 , X ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.23/1.62 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.23/1.62 , X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.23/1.62 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.23/1.62 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.23/1.62 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.23/1.62 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.23/1.62 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.23/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), Y, X ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.23/1.62 Y, X ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.23/1.62 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 Y, X ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.23/1.62 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 Z, X ) ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.23/1.62 'c_lessequals'( Z, Y, X ) ],
% 1.23/1.62 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.62 X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.62 'tc_nat' ) ), X ), X, 'tc_nat' ) ],
% 1.23/1.62 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.62 X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.62 'tc_nat' ) ), X, 'tc_nat' ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.23/1.62 'tc_nat' ) ) ],
% 1.23/1.62 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.23/1.62 'tc_nat' ) ) ],
% 1.23/1.62 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), Y, 'tc_nat' ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.23/1.62 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.23/1.62 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.23/1.62 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.23/1.62 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.23/1.62 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.23/1.62 'tc_nat' ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), X, 'tc_nat' ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X
% 1.23/1.62 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), Y ) ) ), =( X,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.62 [ =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.23/1.62 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.23/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ), =( X,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.62 'c_Int_OMin', X ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.23/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.62 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.62 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.23/1.62 , ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.23/1.62 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.23/1.62 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.23/1.62 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.23/1.62 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.23/1.62 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.23/1.62 , X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.23/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.23/1.62 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.23/1.62 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.23/1.62 , X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.23/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.23/1.62 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.23/1.62 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.23/1.62 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.23/1.62 ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.23/1.62 ), 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ), Z ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.23/1.62 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.62 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), X ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.23/1.62 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.62 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.23/1.62 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.23/1.62 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.23/1.62 ), 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.23/1.62 ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.23/1.62 , X ) ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.23/1.62 , X ) ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.23/1.62 ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.23/1.62 ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.23/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.23/1.62 , X ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y,
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), T ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.62 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.62 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.23/1.62 T, X ) ), T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.23/1.62 ) ), Z ), T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.23/1.62 , X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.62 'c_Int_OMin', X ) ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ),
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.23/1.62 , Y ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.62 'tc_nat' ) ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.23/1.62 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.23/1.62 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.23/1.62 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.23/1.62 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 'tc_nat' ), 'tc_nat' ) ],
% 1.23/1.62 [ ~( =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.23/1.62 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.23/1.62 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.62 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.23/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.62 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.23/1.62 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'(
% 1.23/1.62 X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.23/1.62 'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), X ), Y ) ) ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.23/1.62 X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 'tc_nat' ), X ), Y ) ) ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.23/1.62 X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.23/1.62 'c_Suc', Y ) ) ) ],
% 1.23/1.62 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.23/1.62 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =(
% 1.23/1.62 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ =( 'c_Int_OBit1'( 'c_Int_OMin' ), 'c_Int_OMin' ) ],
% 1.23/1.62 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OMin' ) ), =( X, 'c_Int_OMin' ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( =( 'c_Int_OMin', 'c_Int_OBit1'( X ) ) ), =( 'c_Int_OMin', X ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.23/1.62 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.23/1.62 'tc_Int_Oint' ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.23/1.62 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.23/1.62 'tc_Int_Oint' ) ) ],
% 1.23/1.62 [ =( 'c_Int_OMin', 'c_Int_OBit1'( 'c_Int_OMin' ) ) ],
% 1.23/1.62 [ ~( =( 'c_Int_OPls', 'c_Int_OMin' ) ) ],
% 1.23/1.62 [ ~( =( 'c_Int_OMin', 'c_Int_OPls' ) ) ],
% 1.23/1.62 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OPls',
% 1.23/1.62 'tc_Int_Oint' ) ) ],
% 1.23/1.62 [ ~( =( 'c_Int_OMin', 'c_Int_OBit0'( X ) ) ) ],
% 1.23/1.62 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OMin' ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.23/1.62 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.23/1.62 'tc_Int_Oint' ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.23/1.62 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.23/1.62 'tc_Int_Oint' ) ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.23/1.62 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 1.23/1.62 ), 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', Z ), Y, 'tc_nat' ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Y ), ~(
% 1.23/1.62 'c_lessequals'( Z, Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ) ),
% 1.23/1.62 'c_lessequals'( Y, Z, X ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ), ~(
% 1.23/1.62 'c_lessequals'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 1.23/1.62 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 1.23/1.62 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 1.23/1.62 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.23/1.62 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T,
% 1.23/1.62 Y, X ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.23/1.62 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.62 T, X ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 1.23/1.62 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 1.23/1.62 'c_lessequals'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.23/1.62 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.62 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.23/1.62 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Z ), Y ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Z ), Y ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.23/1.62 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.23/1.62 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.23/1.62 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.23/1.62 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 ), Y ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.23/1.62 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.23/1.62 , X ) ), Z ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 ), =( 'c_HOL_Oinverse__class_Odivide'( Y, U, X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.62 , 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) )
% 1.23/1.62 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 1.23/1.62 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.23/1.62 , X ), X ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.62 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.23/1.62 ), X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.62 , X ), X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.23/1.62 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.62 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.62 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 , X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.62 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.23/1.62 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.62 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.23/1.62 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.23/1.62 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.23/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.62 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.62 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.62 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.23/1.62 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.23/1.62 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.23/1.62 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.23/1.63 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.63 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.23/1.63 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.23/1.63 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.63 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.23/1.63 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.23/1.63 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.23/1.63 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.23/1.63 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.63 , X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.63 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.23/1.63 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.63 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.23/1.63 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.23/1.63 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.23/1.63 ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.23/1.63 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.63 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.23/1.63 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.23/1.63 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.23/1.63 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.23/1.63 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.63 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.63 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.63 , X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.23/1.63 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.23/1.63 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.23/1.63 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.23/1.63 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X
% 1.23/1.63 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( T, Y, X ), X ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.23/1.63 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , X ) ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.23/1.63 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.63 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X
% 1.23/1.63 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), 'c_HOL_Ominus__class_Ominus'( Y, T, X ) ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, T, X
% 1.23/1.63 ) ), U ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( T, Y, X
% 1.23/1.63 ) ), Z ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X
% 1.23/1.63 ) ), Z ) ), T ), W ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X
% 1.23/1.63 ) ), Z ) ), W ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.63 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.23/1.63 ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.23/1.63 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ), =( Z,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.23/1.63 , T ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.23/1.63 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T,
% 1.23/1.63 Y, X ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.23/1.63 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.63 T, X ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'( X ) ), =(
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ), T ),
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'( X ) ), =(
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ),
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ),
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ), T ),
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.23/1.63 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.23/1.63 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.23/1.63 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.23/1.63 , Z ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.23/1.63 , Z ) ],
% 1.23/1.63 [ 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.23/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.23/1.63 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.63 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.63 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 1.23/1.63 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.63 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.23/1.63 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 1.23/1.63 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.63 ), X ), Z ), 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.23/1.63 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.23/1.63 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.23/1.63 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.23/1.63 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.23/1.63 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.23/1.63 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.23/1.63 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.63 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.23/1.63 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.23/1.63 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.23/1.63 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.23/1.63 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.23/1.63 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.23/1.63 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.23/1.63 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.23/1.63 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.23/1.63 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.23/1.63 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.23/1.63 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.23/1.63 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), T ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.23/1.63 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.23/1.63 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.63 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.23/1.63 , 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.23/1.63 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.23/1.63 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.23/1.63 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.23/1.63 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.23/1.63 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.23/1.63 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), T ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.23/1.63 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), T ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.23/1.63 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.23/1.63 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.63 ), T ), Z ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.23/1.63 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.63 ), T ), Z ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.63 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.23/1.63 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.63 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 T, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.23/1.63 , X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.23/1.63 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.23/1.63 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.23/1.63 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.23/1.63 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.23/1.63 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.63 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.23/1.63 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 T, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.63 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.63 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.23/1.63 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.23/1.63 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.23/1.63 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.23/1.63 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.23/1.63 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.23/1.63 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.23/1.63 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.23/1.63 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.23/1.63 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.23/1.63 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.23/1.63 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.23/1.63 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.23/1.63 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.23/1.63 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.63 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.23/1.63 , 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , X ) ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.23/1.63 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.23/1.63 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.23/1.63 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , X ) ), T ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.23/1.63 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.63 ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.63 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.63 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), U ) ), W ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ), W, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ), T ) ), U ), W, X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.23/1.63 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.23/1.63 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.23/1.63 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.63 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 1.23/1.63 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.23/1.63 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.63 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), Y ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.23/1.63 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y,
% 1.23/1.63 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.23/1.63 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.23/1.63 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.63 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OPls', X ) ), Y ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.23/1.63 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.23/1.63 , 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.23/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( X, hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.23/1.63 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( =( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) )
% 1.23/1.63 , Y ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat'
% 1.23/1.63 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.23/1.63 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.23/1.63 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.23/1.63 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.23/1.63 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.63 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.23/1.63 ],
% 1.23/1.63 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.23/1.63 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.23/1.63 , Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.23/1.63 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.23/1.63 , 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 'tc_nat' ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.23/1.63 , 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.23/1.63 , 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.23/1.63 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' )
% 1.23/1.63 , 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.63 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.23/1.63 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.23/1.63 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.23/1.63 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.23/1.63 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.23/1.63 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.23/1.63 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.23/1.63 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.23/1.63 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.23/1.63 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.23/1.63 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.23/1.63 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.23/1.63 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.23/1.63 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X,
% 1.23/1.63 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.23/1.63 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.23/1.63 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.23/1.63 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.23/1.63 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.23/1.63 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.23/1.63 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.23/1.63 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.23/1.63 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.63 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.23/1.63 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), =( Z,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.23/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.23/1.63 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.23/1.63 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.23/1.63 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.23/1.63 ) ],
% 1.23/1.63 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.23/1.63 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.23/1.63 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.23/1.63 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.23/1.63 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ),
% 1.23/1.63 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.63 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.23/1.63 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.23/1.63 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.23/1.63 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ),
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.23/1.63 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.23/1.63 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.23/1.63 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 1.23/1.63 ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.23/1.63 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.23/1.63 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Odiv'(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.23/1.63 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.23/1.63 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.63 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.23/1.63 Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'( Y
% 1.23/1.63 , T, X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.23/1.63 ) ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.23/1.63 ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.23/1.63 ) ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.23/1.63 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, X ), 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, T, X ) )
% 1.23/1.63 , ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.23/1.63 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.23/1.63 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( 'c_Suc',
% 1.23/1.63 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ), 'tc_nat' ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc',
% 1.23/1.63 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.23/1.63 'tc_nat' ), Y, 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 1.23/1.63 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.23/1.63 , Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.23/1.63 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.63 , X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.23/1.63 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.23/1.63 ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.23/1.63 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), X ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.63 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.23/1.63 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 hAPP( 'c_Suc', T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z
% 1.23/1.63 ), hAPP( 'c_Suc', T ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.23/1.63 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ) )
% 1.23/1.63 , =( Y, T ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) )
% 1.23/1.63 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.23/1.63 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.23/1.63 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.23/1.63 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.23/1.63 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.23/1.63 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.23/1.63 ), Y ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.23/1.63 ), Y ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.23/1.63 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.23/1.63 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.23/1.63 ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.23/1.63 ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.23/1.63 ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.63 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.23/1.63 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.23/1.63 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.23/1.63 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.23/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.23/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.23/1.63 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ),
% 1.23/1.63 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 1.23/1.63 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.23/1.63 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.23/1.63 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.23/1.63 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' )
% 1.23/1.63 ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.63 'c_HOL_Oone__class_Oone'( X ), X ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ), Y ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.23/1.63 Z, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.23/1.63 'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OMin', X ) ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OMin', X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( X
% 1.23/1.63 , 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat'
% 1.23/1.63 ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.23/1.63 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.23/1.63 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.23/1.63 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.23/1.63 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.23/1.63 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP(
% 1.23/1.63 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OMin', X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.23/1.63 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.63 'c_HOL_Oone__class_Oone'( X ), X ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.63 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.63 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.63 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.63 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.23/1.63 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.63 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.23/1.63 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.23/1.63 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.23/1.63 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.23/1.63 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T
% 1.23/1.63 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.63 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.23/1.63 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.63 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.63 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.23/1.63 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.23/1.63 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.63 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.23/1.63 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.23/1.63 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.23/1.63 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) )
% 1.23/1.63 ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.23/1.63 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) )
% 1.23/1.63 ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_OPls'
% 1.23/1.63 , Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.23/1.63 ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.23/1.63 ), Y ), hAPP( 'c_Suc', Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.23/1.63 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.23/1.63 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.23/1.63 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.23/1.63 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.23/1.63 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.23/1.63 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.23/1.63 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.23/1.63 , Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.23/1.63 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.63 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X,
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X,
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), Z ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.23/1.63 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.23/1.63 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , 'tc_nat' ), 'tc_nat' ), 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.23/1.63 X ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.23/1.63 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , 'tc_nat' ), 'tc_nat' ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.23/1.63 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.63 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.23/1.63 'c_Suc', X ), Y, 'tc_nat' ), 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.23/1.63 hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ), 'c_Fact_Ofact__class_Ofact'(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( X, hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ) ) ), 'c_Parity_Osko__Parity__Xodd__nat__equiv__def2__1__1'(
% 1.23/1.63 X ) ) ) ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.23/1.63 , hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.23/1.63 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), X ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.23/1.63 [ =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.23/1.63 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.23/1.63 'c_Parity_Osko__Parity__Xeven__nat__equiv__def2__1__1'( X ) ) ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.23/1.63 , hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.23/1.63 ) ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ), X ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.23/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X
% 1.23/1.63 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.23/1.63 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ),
% 1.23/1.63 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.23/1.63 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.23/1.63 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.23/1.63 , Y ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.23/1.63 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) )
% 1.23/1.63 ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.23/1.63 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.23/1.63 ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.23/1.63 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.23/1.63 , Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.23/1.63 ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.23/1.63 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.23/1.63 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.23/1.63 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.23/1.63 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 'tc_nat' ), X ), X ) ) ],
% 1.23/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 1.23/1.63 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.23/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' )
% 1.23/1.63 ) ],
% 1.23/1.63 [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), X ), X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.23/1.63 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.23/1.63 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.63 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.23/1.63 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.23/1.63 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ) ],
% 1.23/1.63 [ =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 1.23/1.63 'c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1'( X ) ) ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.63 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.23/1.63 ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.23/1.63 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), X ) ],
% 1.23/1.63 [ =( X, hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 1.23/1.63 'c_Parity_Osko__Parity__Xodd__Suc__mult__two__ex__1__1'( X ) ) ) ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.23/1.63 X ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ), X ) )
% 1.23/1.63 ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OMin', X ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.23/1.63 [ =( hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.23/1.63 , 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.23/1.63 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), =( hAPP(
% 1.23/1.63 'c_Suc', X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.23/1.63 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.23/1.63 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W
% 1.23/1.63 , V0, V1 ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.23/1.63 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W
% 1.23/1.63 , V0, V1 ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.23/1.63 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.23/1.63 V0, V1 ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.23/1.63 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.23/1.63 V0, V1 ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.23/1.63 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.23/1.63 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.23/1.63 'c_Suc', X ), Y, 'tc_nat' ), hAPP( 'c_Suc', Z ), 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.23/1.63 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y
% 1.23/1.63 ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 1.23/1.63 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.23/1.63 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ),
% 1.23/1.63 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.23/1.63 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X, hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, hAPP(
% 1.23/1.63 'c_Suc', Y ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.23/1.63 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.23/1.63 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.23/1.63 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.23/1.63 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.23/1.63 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.23/1.63 ), 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.23/1.63 ), 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), 'tc_nat' ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.23/1.63 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.23/1.63 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.23/1.63 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), X ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.23/1.63 ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.23/1.63 ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.23/1.63 T, X ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.23/1.63 T, X ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.23/1.63 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.23/1.63 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.23/1.63 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.23/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.23/1.63 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.63 ), Z ), Y ), 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.63 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.63 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.63 ), X ), Z ), 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.23/1.63 ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.23/1.63 ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.23/1.63 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.23/1.63 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.23/1.63 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.63 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.23/1.63 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.23/1.63 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.63 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.23/1.63 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , X ) ), T ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.23/1.63 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 hAPP( 'c_Suc', Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.23/1.63 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.23/1.63 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 X, hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.23/1.63 ), 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.23/1.63 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.23/1.63 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ), Y, 'tc_nat'
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.23/1.63 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.23/1.63 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ) ), =( Y, Z ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.23/1.63 ), 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.23/1.63 ), 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.63 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.23/1.63 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.23/1.63 , X, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.63 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.63 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.63 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.63 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.23/1.63 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.23/1.63 , X, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.63 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.23/1.63 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.23/1.63 , Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y ),
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ),
% 1.23/1.63 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.23/1.63 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.23/1.63 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.23/1.63 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.23/1.63 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.23/1.63 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.23/1.63 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.23/1.63 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), 'tc_nat' ) ],
% 1.23/1.63 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ) ), 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.23/1.63 ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.23/1.63 , X, Z, U, W, V0 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Y ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.23/1.63 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.23/1.63 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.23/1.63 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.23/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.23/1.63 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.23/1.63 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.63 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.63 ) ), =( Y, Z ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.63 ) ), =( Y, Z ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.63 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.63 ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.23/1.63 ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.63 ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.63 ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.23/1.63 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.23/1.63 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.23/1.63 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 1.23/1.63 ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.23/1.63 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.23/1.63 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.23/1.63 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.23/1.63 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.23/1.63 , 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat'
% 1.23/1.63 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.23/1.63 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.23/1.63 , T, X ) ) ), =( Y, Z ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.23/1.63 , T, X ) ) ), =( Z, T ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.23/1.63 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.64 , 'tc_nat' ), 'tc_nat' ) ],
% 1.23/1.64 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.23/1.64 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.23/1.64 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.23/1.64 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.23/1.64 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.23/1.64 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.23/1.64 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.64 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.64 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.23/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.23/1.64 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.64 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.23/1.64 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.23/1.64 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.64 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.23/1.64 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.23/1.64 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.23/1.64 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.64 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.23/1.64 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.23/1.64 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.23/1.64 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.23/1.64 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.23/1.64 ) ],
% 1.23/1.64 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.23/1.64 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.23/1.64 ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.64 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.23/1.64 ), =( Z, Y ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.23/1.64 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.23/1.64 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.23/1.64 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.64 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.23/1.64 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 1.23/1.64 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.23/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.64 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.23/1.64 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.23/1.64 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 1.23/1.64 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 1.23/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.23/1.64 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.23/1.64 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 1.23/1.64 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.64 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.64 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.64 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.64 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.23/1.64 ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.64 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.23/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.23/1.64 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.23/1.64 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.23/1.64 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.23/1.64 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.23/1.64 , V0, U, V1 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.23/1.64 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.23/1.64 , V0, U, V1 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.23/1.64 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.23/1.64 X, T, U, Y, W, V0 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.23/1.64 X, T, U, Z, W, V0 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.23/1.64 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.23/1.64 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.23/1.64 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.23/1.64 T, X, U, Y, W, V0 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.23/1.64 T, X, U, Z, W, V0 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.23/1.64 T, X, U, W, Y, V0 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.23/1.64 T, X, U, W, Z, V0 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.23/1.64 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.23/1.64 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.23/1.64 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.23/1.64 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.23/1.64 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.23/1.64 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.23/1.64 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.23/1.64 , V0, V1, V2 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.23/1.64 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.23/1.64 W, V0, V1, V2 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.23/1.64 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.23/1.64 , V0, V1, V2 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.23/1.64 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.23/1.64 W, V0, V1, V2 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.23/1.64 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.23/1.64 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.23/1.64 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.23/1.64 W, V0, V1, V2 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.23/1.64 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.23/1.64 W, V0, V1, V2 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.23/1.64 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.23/1.64 , V0, V1, V2 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.23/1.64 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.23/1.64 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.23/1.64 , V0, V1, V2 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.23/1.64 X, T, U, Y, W, V0 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.23/1.64 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.23/1.64 , V0, V1, V2 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.23/1.64 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.23/1.64 T, X, U, Y, W, V0 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.23/1.64 T, X, U, W, Y, V0 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.23/1.64 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.23/1.64 , V0, V1, V2 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.23/1.64 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.23/1.64 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.23/1.64 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.23/1.64 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.23/1.64 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.64 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), =( Y,
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.23/1.64 Z, 'tc_nat' ) ) ],
% 1.23/1.64 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.23/1.64 'tc_nat' ), hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.23/1.64 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.23/1.64 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.23/1.64 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 1.23/1.64 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.64 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.23/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.23/1.64 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.23/1.64 ) ],
% 1.23/1.64 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.23/1.64 , Y, X ) ) ],
% 1.23/1.64 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.23/1.64 , X ) ) ],
% 1.23/1.64 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.23/1.64 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.23/1.64 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.23/1.64 , Y, X ) ) ],
% 1.23/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.23/1.64 , X ) ) ],
% 1.23/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.64 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.64 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.64 , X ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.64 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.23/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.23/1.64 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.64 , 'tc_nat' ), 'tc_nat' ) ],
% 1.23/1.64 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.23/1.64 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X,
% 1.23/1.64 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ) ) ],
% 1.23/1.64 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.23/1.64 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.23/1.64 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~(
% 1.23/1.64 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.23/1.64 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.64 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.23/1.64 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.23/1.64 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.23/1.64 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.23/1.64 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.64 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), =( Y,
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.64 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.23/1.64 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.23/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.23/1.64 'tc_nat' ) ) ],
% 1.23/1.64 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.23/1.64 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.23/1.64 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.23/1.64 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.23/1.64 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.23/1.64 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.23/1.64 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.23/1.64 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.23/1.64 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.23/1.64 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.64 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.64 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.23/1.64 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.23/1.64 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.64 X, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.64 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.64 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.64 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.64 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.23/1.64 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.64 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'tc_nat' ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.64 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.23/1.64 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.23/1.64 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.64 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.64 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.64 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.23/1.64 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.64 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.64 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.23/1.64 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.64 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.23/1.64 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.23/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.64 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.64 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.23/1.64 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.64 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.64 'tc_nat' ) ) ],
% 1.23/1.64 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.23/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.23/1.64 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.64 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.23/1.64 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ) ), =( X,
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.64 [ =( 'c_Set_Oimage'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y
% 1.23/1.64 , Z, 'tc_fun'( T, 'tc_bool' ) ), T, U ),
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oimage'( X, Y, T, U
% 1.23/1.64 ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 1.23/1.64 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.64 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.23/1.64 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.23/1.64 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.64 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.23/1.64 [ =( 'c_Set_Oimage'( X, 'c_Set_Oimage'( Y, Z, T, U ), U, W ),
% 1.23/1.64 'c_Set_Oimage'( 'c_COMBB'( X, Y, U, W, T ), Z, T, W ) ) ],
% 1.23/1.64 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.23/1.64 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.23/1.64 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.64 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.23/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.64 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.23/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.64 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.64 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.23/1.64 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.23/1.64 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.64 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.64 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.64 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.64 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.64 'tc_nat' ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.64 'tc_nat' ) ) ],
% 1.23/1.64 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.23/1.64 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.64 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.23/1.64 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.64 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.23/1.64 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.23/1.64 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.64 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.23/1.64 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.23/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.23/1.64 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.23/1.64 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.23/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.23/1.64 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.23/1.64 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.23/1.64 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.23/1.64 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.23/1.64 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.23/1.64 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.23/1.64 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.23/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.23/1.64 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.23/1.64 , hAPP( 'c_Suc', X ) ), Z ) ) ), =( Y, Z ) ],
% 1.23/1.64 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.64 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc'
% 1.23/1.64 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.23/1.64 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.23/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.23/1.64 [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 1.23/1.64 [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.64 'tc_nat' ) ), Y ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.64 'tc_nat' ) ) ) ],
% 1.23/1.64 [ =( 'c_Set_Oimage'( 'c_Suc',
% 1.23/1.64 'c_SetInterval_Oord__class_OatLeastLessThan'( X, Y, 'tc_nat' ), 'tc_nat'
% 1.23/1.64 , 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc'
% 1.23/1.64 , X ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.23/1.64 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.23/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.23/1.64 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z, Y ) ), ~( hBOOL( hAPP(
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Z, X, 'tc_fun'( T,
% 1.23/1.64 'tc_bool' ) ), Y ) ) ) ],
% 1.23/1.64 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.23/1.64 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ) ],
% 1.23/1.64 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.23/1.64 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( X, T ) ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.23/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.64 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.23/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.64 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.23/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.64 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.64 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.64 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.23/1.64 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.23/1.64 , Y ) ],
% 1.23/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.64 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, hAPP(
% 1.23/1.64 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.64 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.23/1.64 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.64 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.23/1.64 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.23/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.23/1.64 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Y, X ), Y ) ],
% 1.23/1.64 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, X, 'tc_fun'( Y,
% 1.23/1.64 'tc_bool' ) ), X ) ],
% 1.23/1.64 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.23/1.64 ) ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.64 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.23/1.64 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.23/1.64 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.23/1.64 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.23/1.64 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.23/1.64 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.23/1.64 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.23/1.64 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.64 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.23/1.64 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 1.23/1.64 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.23/1.64 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.23/1.64 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.23/1.64 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 1.23/1.64 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.23/1.64 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, X,
% 1.23/1.64 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.64 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 1.23/1.64 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 1.23/1.64 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.23/1.64 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.23/1.64 'tc_bool' ) ) ) ],
% 1.23/1.64 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 1.23/1.64 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.23/1.64 [ ~( =( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.23/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.64 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_n' ), 'tc_nat' ),
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oimage'( hAPP(
% 1.23/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.64 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 1.23/1.64 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.64 'tc_nat' ), 'v_n', 'tc_nat' ), 'tc_nat', 'tc_nat' ), 'c_Set_Oimage'(
% 1.23/1.64 'c_COMBB'( 'c_Suc', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.64 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ),
% 1.23/1.64 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.64 'tc_nat' ), 'v_n', 'tc_nat' ), 'tc_nat', 'tc_nat' ), 'tc_fun'( 'tc_nat',
% 1.23/1.64 'tc_bool' ) ) ) ) ],
% 1.23/1.64 [ 'class_Lattices_Oupper__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 1.23/1.64 'class_Lattices_Olattice'( Y ) ) ],
% 1.23/1.64 [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ), ~(
% 1.23/1.64 'class_Lattices_Oboolean__algebra'( Y ) ) ],
% 1.23/1.64 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.23/1.64 'class_Orderings_Opreorder'( Y ) ) ],
% 1.23/1.64 [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 1.23/1.64 'class_Lattices_Olattice'( Y ) ) ],
% 1.23/1.64 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.23/1.64 'class_Orderings_Oorder'( Y ) ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.23/1.64 ],
% 1.23/1.64 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.23/1.64 ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.23/1.64 ],
% 1.23/1.64 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Lattices_Oupper__semilattice'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Lattices_Olattice'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.23/1.64 [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ],
% 1.23/1.64 [ 'class_Lattices_Oboolean__algebra'( 'tc_bool' ) ],
% 1.23/1.64 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.23/1.64 [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 1.23/1.64 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.23/1.64 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.23/1.64 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.23/1.64 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.23/1.64 ],
% 1.23/1.64 [ 'class_OrderedGroup_Olordered__ab__group__add__join'( 'tc_Int_Oint' )
% 1.23/1.64 ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.23/1.64 ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Lattices_Oupper__semilattice'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Odvd'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Lattices_Olattice'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ =( 'c_COMBC'( X, Y, Z, T, U, W ), hAPP( hAPP( X, Z ), Y ) ) ],
% 1.23/1.64 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'c_fequal'( X, X, Y ) ],
% 1.23/1.64 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.23/1.64 ] .
% 1.23/1.64
% 1.23/1.64
% 1.23/1.64 percentage equality = 0.243419, percentage horn = 0.852298
% 1.23/1.64 This is a problem with some equality
% 1.23/1.64
% 1.23/1.64
% 1.23/1.64
% 1.23/1.64 Options Used:
% 1.23/1.64
% 1.23/1.64 useres = 1
% 1.23/1.64 useparamod = 1
% 1.23/1.64 useeqrefl = 1
% 1.23/1.64 useeqfact = 1
% 1.23/1.64 usefactor = 1
% 1.23/1.64 usesimpsplitting = 0
% 1.23/1.64 usesimpdemod = 5
% 1.23/1.64 usesimpres = 3
% 1.23/1.64
% 1.23/1.64 resimpinuse = 1000
% 1.23/1.64 resimpclauses = 20000
% 1.23/1.64 substype = eqrewr
% 1.23/1.64 backwardsubs = 1
% 1.23/1.64 selectoldest = 5
% 1.23/1.64
% 1.23/1.64 litorderings [0] = split
% 1.23/1.64 litorderings [1] = extend the termordering, first sorting on arguments
% 1.23/1.64
% 1.23/1.64 termordering = kbo
% 1.23/1.64
% 1.23/1.64 litapriori = 0
% 1.23/1.64 termapriori = 1
% 1.23/1.64 litaposteriori = 0
% 1.23/1.64 termaposteriori = 0
% 1.23/1.64 demodaposteriori = 0
% 1.23/1.64 ordereqreflfact = 0
% 1.23/1.64
% 1.23/1.64 litselect = negord
% 1.23/1.64
% 1.23/1.64 maxweight = 15
% 1.23/1.64 maxdepth = 30000
% 1.23/1.64 maxlength = 115
% 1.23/1.64 maxnrvars = 195
% 1.23/1.64 excuselevel = 1
% 1.23/1.64 increasemaxweight = 1
% 1.23/1.64
% 1.23/1.64 maxselected = 10000000
% 1.23/1.64 maxnrclauses = 10000000
% 1.23/1.64
% 1.23/1.64 showgenerated = 0
% 1.23/1.64 showkept = 0
% 1.23/1.64 showselected = 0
% 1.23/1.64 showdeleted = 0
% 1.23/1.64 showresimp = 1
% 1.23/1.64 showstatus = 2000
% 1.23/1.64
% 1.23/1.64 prologoutput = 1
% 1.23/1.64 nrgoals = 5000000
% 1.23/1.64 totalproof = 1
% 1.23/1.64
% 1.23/1.64 Symbols occurring in the translation:
% 1.23/1.64
% 1.23/1.64 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.23/1.64 . [1, 2] (w:1, o:162, a:1, s:1, b:0),
% 1.23/1.64 ! [4, 1] (w:0, o:76, a:1, s:1, b:0),
% 1.23/1.64 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.23/1.64 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.23/1.64 'class_Ring__and__Field_Odvd' [40, 1] (w:1, o:85, a:1, s:1, b:0),
% 1.23/1.64 'class_Ring__and__Field_Ocomm__ring' [41, 1] (w:1, o:81, a:1, s:1, b:
% 1.23/1.64 0),
% 1.23/1.64 'c_HOL_Oplus__class_Oplus' [43, 1] (w:1, o:87, a:1, s:1, b:0),
% 1.23/1.64 hAPP [45, 2] (w:1, o:187, a:1, s:1, b:0),
% 1.23/1.64 'c_Ring__and__Field_Odvd__class_Odvd' [47, 3] (w:1, o:194, a:1, s:1
% 1.23/1.64 , b:0),
% 1.23/1.64 'c_HOL_Otimes__class_Otimes' [48, 1] (w:1, o:88, a:1, s:1, b:0),
% 1.23/1.64 'c_HOL_Ominus__class_Ominus' [51, 3] (w:1, o:195, a:1, s:1, b:0),
% 1.23/1.64 'class_Divides_Osemiring__div' [52, 1] (w:1, o:90, a:1, s:1, b:0),
% 1.23/1.64 'c_Divides_Odiv__class_Omod' [55, 3] (w:1, o:196, a:1, s:1, b:0),
% 1.23/1.64 'class_OrderedGroup_Opordered__ab__group__add' [57, 1] (w:1, o:92, a:
% 1.23/1.64 1, s:1, b:0),
% 1.23/1.64 'c_lessequals' [61, 3] (w:1, o:197, a:1, s:1, b:0),
% 1.23/1.64 'tc_nat' [63, 0] (w:1, o:37, a:1, s:1, b:0),
% 1.23/1.64 'c_HOL_Oone__class_Oone' [64, 1] (w:1, o:86, a:1, s:1, b:0),
% 1.23/1.64 'class_Ring__and__Field_Oordered__field' [65, 1] (w:1, o:95, a:1, s:1
% 1.23/1.64 , b:0),
% 1.23/1.64 'c_HOL_Oinverse__class_Odivide' [66, 3] (w:1, o:198, a:1, s:1, b:0),
% 1.23/1.64
% 1.23/1.64 'c_HOL_Ozero__class_Ozero' [67, 1] (w:1, o:96, a:1, s:1, b:0),
% 1.23/1.64 'c_HOL_Oord__class_Oless' [68, 3] (w:1, o:199, a:1, s:1, b:0),
% 1.23/1.64 'class_Ring__and__Field_Oordered__idom' [69, 1] (w:1, o:97, a:1, s:1
% 1.23/1.64 , b:0),
% 1.23/1.64 'class_Int_Onumber__ring' [70, 1] (w:1, o:98, a:1, s:1, b:0),
% 1.23/1.64 'c_Int_OMin' [71, 0] (w:1, o:38, a:1, s:1, b:0),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of' [72, 2] (w:1, o:190, a:1, s:1, b:0
% 1.23/1.64 ),
% 1.23/1.64 'c_HOL_Oabs__class_Oabs' [73, 2] (w:1, o:188, a:1, s:1, b:0),
% 1.23/1.64 'c_Divides_Odiv__class_Odiv' [74, 3] (w:1, o:200, a:1, s:1, b:0),
% 1.23/1.64 'class_OrderedGroup_Ogroup__add' [75, 1] (w:1, o:99, a:1, s:1, b:0),
% 1.23/1.64
% 1.23/1.64 'c_HOL_Ouminus__class_Ouminus' [76, 2] (w:1, o:189, a:1, s:1, b:0),
% 1.23/1.64 'class_OrderedGroup_Opordered__ab__group__add__abs' [77, 1] (w:1, o:
% 1.23/1.64 100, a:1, s:1, b:0),
% 1.23/1.64 'class_Ring__and__Field_Odivision__by__zero' [78, 1] (w:1, o:101, a:1
% 1.23/1.64 , s:1, b:0),
% 1.23/1.64 'class_Int_Onumber' [79, 1] (w:1, o:102, a:1, s:1, b:0),
% 1.23/1.64 'class_Ring__and__Field_Ocomm__semiring__1' [81, 1] (w:1, o:83, a:1
% 1.23/1.64 , s:1, b:0),
% 1.23/1.64 'c_Fact_Ofact__class_Ofact' [84, 2] (w:1, o:191, a:1, s:1, b:0),
% 1.23/1.64 'class_Ring__and__Field_Oordered__semidom' [85, 1] (w:1, o:104, a:1
% 1.23/1.64 , s:1, b:0),
% 1.23/1.64 'class_OrderedGroup_Olordered__ab__group__add' [86, 1] (w:1, o:105
% 1.23/1.64 , a:1, s:1, b:0),
% 1.23/1.64 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [87, 1]
% 2.65/3.07 (w:1, o:106, a:1, s:1, b:0),
% 2.65/3.07 'class_OrderedGroup_Opordered__ab__semigroup__add' [88, 1] (w:1, o:
% 2.65/3.07 107, a:1, s:1, b:0),
% 2.65/3.07 'c_Power_Opower__class_Opower' [89, 1] (w:1, o:108, a:1, s:1, b:0),
% 2.65/3.07 'c_Parity_Oeven__odd__class_Oeven' [90, 2] (w:1, o:192, a:1, s:1, b:0
% 2.65/3.07 ),
% 2.65/3.07 'class_Orderings_Oorder' [91, 1] (w:1, o:109, a:1, s:1, b:0),
% 2.65/3.07 'tc_Int_Oint' [92, 0] (w:1, o:43, a:1, s:1, b:0),
% 2.65/3.07 'class_Ring__and__Field_Ofield' [93, 1] (w:1, o:110, a:1, s:1, b:0),
% 2.65/3.07
% 2.65/3.07 'class_Lattices_Oboolean__algebra' [94, 1] (w:1, o:111, a:1, s:1, b:0
% 2.65/3.07 ),
% 2.65/3.07 'class_OrderedGroup_Olordered__ab__group__add__abs' [95, 1] (w:1, o:
% 2.65/3.07 112, a:1, s:1, b:0),
% 2.65/3.07 'c_Lattices_Oupper__semilattice__class_Osup' [96, 3] (w:1, o:201, a:1
% 2.65/3.07 , s:1, b:0),
% 2.65/3.07 'class_OrderedGroup_Opordered__comm__monoid__add' [97, 1] (w:1, o:113
% 2.65/3.07 , a:1, s:1, b:0),
% 2.65/3.07 'class_RealVector_Oreal__normed__field' [98, 1] (w:1, o:114, a:1, s:1
% 2.65/3.07 , b:0),
% 2.65/3.07 'class_Orderings_Olinorder' [100, 1] (w:1, o:115, a:1, s:1, b:0),
% 2.65/3.07 'class_Divides_Oring__div' [101, 1] (w:1, o:89, a:1, s:1, b:0),
% 2.65/3.07 'class_OrderedGroup_Oab__group__add' [102, 1] (w:1, o:116, a:1, s:1
% 2.65/3.07 , b:0),
% 2.65/3.07 'class_Ring__and__Field_Ocomm__ring__1' [103, 1] (w:1, o:82, a:1, s:1
% 2.65/3.07 , b:0),
% 2.65/3.07 'class_Ring__and__Field_Oidom' [104, 1] (w:1, o:117, a:1, s:1, b:0),
% 2.65/3.07
% 2.65/3.07 'class_OrderedGroup_Ocancel__ab__semigroup__add' [105, 1] (w:1, o:118
% 2.65/3.07 , a:1, s:1, b:0),
% 2.65/3.07 'class_OrderedGroup_Ocancel__semigroup__add' [106, 1] (w:1, o:119, a:
% 2.65/3.07 1, s:1, b:0),
% 2.65/3.07 'class_OrderedGroup_Omonoid__mult' [107, 1] (w:1, o:121, a:1, s:1, b:
% 2.65/3.07 0),
% 2.65/3.07 hBOOL [110, 1] (w:1, o:122, a:1, s:1, b:0),
% 2.65/3.07 'c_Suc' [111, 0] (w:1, o:46, a:1, s:1, b:0),
% 2.65/3.07 'class_Ring__and__Field_Oabs__if' [112, 1] (w:1, o:123, a:1, s:1, b:0
% 2.65/3.07 ),
% 2.65/3.07 'class_Ring__and__Field_Opordered__ring' [113, 1] (w:1, o:127, a:1
% 2.65/3.07 , s:1, b:0),
% 2.65/3.07 'class_OrderedGroup_Ocomm__monoid__add' [117, 1] (w:1, o:128, a:1, s:
% 2.65/3.07 1, b:0),
% 2.65/3.07 'c_Int_OPls' [119, 0] (w:1, o:51, a:1, s:1, b:0),
% 2.65/3.07 'class_Ring__and__Field_Olordered__ring' [120, 1] (w:1, o:129, a:1
% 2.65/3.07 , s:1, b:0),
% 2.65/3.07 'class_OrderedGroup_Oab__semigroup__add' [121, 1] (w:1, o:130, a:1
% 2.65/3.07 , s:1, b:0),
% 2.65/3.07 'class_Orderings_Opreorder' [122, 1] (w:1, o:131, a:1, s:1, b:0),
% 2.65/3.07 'c_Int_OBit1' [123, 1] (w:1, o:133, a:1, s:1, b:0),
% 2.65/3.07 'class_RealVector_Oreal__field' [124, 1] (w:1, o:134, a:1, s:1, b:0)
% 2.65/3.07 ,
% 2.65/3.07 'class_OrderedGroup_Oordered__ab__group__add' [126, 1] (w:1, o:91, a:
% 2.65/3.07 1, s:1, b:0),
% 2.65/3.07 'c_Int_OBit0' [127, 1] (w:1, o:132, a:1, s:1, b:0),
% 2.65/3.07 'class_Ring__and__Field_Oring__1' [129, 1] (w:1, o:135, a:1, s:1, b:0
% 2.65/3.07 ),
% 2.65/3.07 'c_Groebner__Basis_Ogb__semiring' [138, 6] (w:1, o:206, a:1, s:1, b:0
% 2.65/3.07 ),
% 2.65/3.07 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [140, 1]
% 2.65/3.07 (w:1, o:136, a:1, s:1, b:0),
% 2.65/3.07 'class_Ring__and__Field_Ozero__neq__one' [144, 1] (w:1, o:137, a:1
% 2.65/3.07 , s:1, b:0),
% 2.65/3.07 'class_OrderedGroup_Omonoid__add' [145, 1] (w:1, o:138, a:1, s:1, b:0
% 2.65/3.07 ),
% 2.65/3.07 'class_Ring__and__Field_Opordered__ring__abs' [146, 1] (w:1, o:139
% 2.65/3.07 , a:1, s:1, b:0),
% 2.65/3.07 'class_Ring__and__Field_Oordered__ring__strict' [147, 1] (w:1, o:103
% 2.65/3.07 , a:1, s:1, b:0),
% 2.65/3.07 'class_Ring__and__Field_Oring' [148, 1] (w:1, o:140, a:1, s:1, b:0),
% 2.65/3.07
% 2.65/3.07 'class_RealVector_Oreal__normed__algebra' [149, 1] (w:1, o:141, a:1
% 2.65/3.07 , s:1, b:0),
% 2.65/3.07 'class_Ring__and__Field_Ocomm__semiring' [150, 1] (w:1, o:84, a:1, s:
% 2.65/3.07 1, b:0),
% 2.65/3.07 'class_OrderedGroup_Ocomm__monoid__mult' [151, 1] (w:1, o:142, a:1
% 2.65/3.07 , s:1, b:0),
% 2.65/3.07 'class_Ring__and__Field_Osemiring' [152, 1] (w:1, o:145, a:1, s:1, b:
% 2.65/3.07 0),
% 2.65/3.07 'class_Lattices_Oupper__semilattice' [156, 1] (w:1, o:146, a:1, s:1
% 2.65/3.07 , b:0),
% 2.65/3.07 'class_Lattices_Olattice' [157, 1] (w:1, o:147, a:1, s:1, b:0),
% 2.65/3.07 'class_Ring__and__Field_Omult__mono1' [158, 1] (w:1, o:148, a:1, s:1
% 2.65/3.07 , b:0),
% 2.65/3.07 'class_Ring__and__Field_Omult__mono' [159, 1] (w:1, o:149, a:1, s:1
% 2.65/3.07 , b:0),
% 2.65/3.07 'class_Ring__and__Field_Opordered__cancel__semiring' [160, 1] (w:1
% 9.67/10.03 , o:150, a:1, s:1, b:0),
% 9.67/10.03 'class_Ring__and__Field_Opordered__semiring' [161, 1] (w:1, o:151, a:
% 9.67/10.03 1, s:1, b:0),
% 9.67/10.03 'class_OrderedGroup_Olordered__ab__group__add__join' [162, 1] (w:1
% 9.67/10.03 , o:120, a:1, s:1, b:0),
% 9.67/10.03 'class_Ring__and__Field_Oordered__semiring__strict' [163, 1] (w:1, o:
% 9.67/10.03 124, a:1, s:1, b:0),
% 9.67/10.03 'class_Ring__and__Field_Oordered__semiring' [164, 1] (w:1, o:125, a:1
% 9.67/10.03 , s:1, b:0),
% 9.67/10.03 'class_Power_Opower' [165, 1] (w:1, o:154, a:1, s:1, b:0),
% 9.67/10.03 'c_SetInterval_Oord__class_OatLeastLessThan' [166, 3] (w:1, o:202, a:
% 9.67/10.03 1, s:1, b:0),
% 9.67/10.03 'tc_bool' [167, 0] (w:1, o:58, a:1, s:1, b:0),
% 9.67/10.03 'tc_fun' [168, 2] (w:1, o:193, a:1, s:1, b:0),
% 9.67/10.03 'class_Ring__and__Field_Osemiring__0' [169, 1] (w:1, o:155, a:1, s:1
% 9.67/10.03 , b:0),
% 9.67/10.03 'c_Parity_Osko__Parity__Xodd__nat__equiv__def2__1__1' [171, 1] (w:1
% 9.67/10.03 , o:156, a:1, s:1, b:0),
% 9.67/10.03 'c_Parity_Osko__Parity__Xeven__nat__equiv__def2__1__1' [172, 1] (w:1
% 9.67/10.03 , o:158, a:1, s:1, b:0),
% 9.67/10.03 'class_Ring__and__Field_Osemiring__1' [173, 1] (w:1, o:159, a:1, s:1
% 9.67/10.03 , b:0),
% 9.67/10.03 'c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1' [174, 1] (w:1, o:
% 9.67/10.03 157, a:1, s:1, b:0),
% 9.67/10.03 'c_Parity_Osko__Parity__Xodd__Suc__mult__two__ex__1__1' [175, 1] (w:1
% 9.67/10.03 , o:160, a:1, s:1, b:0),
% 9.67/10.03 'class_Ring__and__Field_Oordered__comm__semiring__strict' [176, 1]
% 9.67/10.03 (w:1, o:126, a:1, s:1, b:0),
% 9.67/10.03 'class_Ring__and__Field_Ono__zero__divisors' [177, 1] (w:1, o:94, a:1
% 9.67/10.03 , s:1, b:0),
% 9.67/10.03 'class_Ring__and__Field_Omult__zero' [178, 1] (w:1, o:93, a:1, s:1
% 9.67/10.03 , b:0),
% 9.67/10.03 'class_Ring__and__Field_Oring__1__no__zero__divisors' [179, 1] (w:1
% 9.67/10.03 , o:143, a:1, s:1, b:0),
% 9.67/10.03 'c_Set_Oimage' [188, 4] (w:1, o:204, a:1, s:1, b:0),
% 9.67/10.03 'c_COMBB' [191, 5] (w:1, o:205, a:1, s:1, b:0),
% 9.67/10.03 'class_Ring__and__Field_Oring__no__zero__divisors' [193, 1] (w:1, o:
% 9.67/10.03 144, a:1, s:1, b:0),
% 9.67/10.03 'class_OrderedGroup_Oab__semigroup__mult' [195, 1] (w:1, o:152, a:1
% 9.67/10.03 , s:1, b:0),
% 9.67/10.03 'class_OrderedGroup_Oab__semigroup__idem__mult' [196, 1] (w:1, o:153
% 9.67/10.03 , a:1, s:1, b:0),
% 9.67/10.03 'class_Int_Oring__char__0' [199, 1] (w:1, o:161, a:1, s:1, b:0),
% 9.67/10.03 'v_n' [201, 0] (w:1, o:71, a:1, s:1, b:0),
% 9.67/10.03 'c_COMBC' [204, 6] (w:1, o:207, a:1, s:1, b:0),
% 9.67/10.03 'c_fequal' [205, 3] (w:1, o:203, a:1, s:1, b:0).
% 9.67/10.03
% 9.67/10.03
% 9.67/10.03 Starting Search:
% 9.67/10.03
% 9.67/10.03 Resimplifying inuse:
% 9.67/10.03 Done
% 9.67/10.03
% 9.67/10.03
% 9.67/10.03 Intermediate Status:
% 9.67/10.03 Generated: 3729
% 9.67/10.03 Kept: 2015
% 9.67/10.03 Inuse: 169
% 9.67/10.03 Deleted: 7
% 9.67/10.03 Deletedinuse: 0
% 9.67/10.03
% 9.67/10.03 Resimplifying inuse:
% 9.67/10.03 Done
% 9.67/10.03
% 9.67/10.03 Resimplifying inuse:
% 9.67/10.03 Done
% 9.67/10.03
% 9.67/10.03
% 9.67/10.03 Intermediate Status:
% 9.67/10.03 Generated: 11702
% 9.67/10.03 Kept: 4086
% 9.67/10.03 Inuse: 243
% 9.67/10.03 Deleted: 8
% 9.67/10.03 Deletedinuse: 0
% 9.67/10.03
% 9.67/10.03 Resimplifying inuse:
% 9.67/10.03 Done
% 9.67/10.03
% 9.67/10.03 Resimplifying inuse:
% 9.67/10.03 Done
% 9.67/10.03
% 9.67/10.03
% 9.67/10.03 Intermediate Status:
% 9.67/10.03 Generated: 17559
% 9.67/10.03 Kept: 6100
% 9.67/10.03 Inuse: 337
% 9.67/10.03 Deleted: 8
% 9.67/10.03 Deletedinuse: 0
% 9.67/10.03
% 9.67/10.03 Resimplifying inuse:
% 9.67/10.03 Done
% 9.67/10.03
% 9.67/10.03
% 9.67/10.03 Intermediate Status:
% 9.67/10.03 Generated: 21455
% 9.67/10.03 Kept: 8156
% 9.67/10.03 Inuse: 343
% 9.67/10.03 Deleted: 8
% 9.67/10.03 Deletedinuse: 0
% 9.67/10.03
% 9.67/10.03 Resimplifying inuse:
% 9.67/10.03 Done
% 9.67/10.03
% 9.67/10.03 Resimplifying inuse:
% 9.67/10.03 Done
% 9.67/10.03
% 9.67/10.03
% 9.67/10.03 Intermediate Status:
% 9.67/10.03 Generated: 27450
% 9.67/10.03 Kept: 10757
% 9.67/10.03 Inuse: 358
% 9.67/10.03 Deleted: 8
% 9.67/10.03 Deletedinuse: 0
% 9.67/10.03
% 9.67/10.03 Resimplifying inuse:
% 9.67/10.03 Done
% 9.67/10.03
% 9.67/10.03 Resimplifying inuse:
% 9.67/10.03 Done
% 9.67/10.03
% 9.67/10.03
% 9.67/10.03 Intermediate Status:
% 9.67/10.03 Generated: 34288
% 9.67/10.03 Kept: 12759
% 9.67/10.03 Inuse: 420
% 9.67/10.03 Deleted: 9
% 9.67/10.03 Deletedinuse: 0
% 9.67/10.03
% 9.67/10.03 Resimplifying inuse:
% 9.67/10.03 Done
% 9.67/10.03
% 9.67/10.03 Resimplifying inuse:
% 9.67/10.03 Done
% 9.67/10.03
% 9.67/10.03
% 9.67/10.03 Intermediate Status:
% 9.67/10.03 Generated: 40534
% 9.67/10.03 Kept: 14764
% 9.67/10.03 Inuse: 495
% 9.67/10.03 Deleted: 11
% 9.67/10.03 Deletedinuse: 0
% 9.67/10.03
% 9.67/10.03 Resimplifying inuse:
% 9.67/10.03 Done
% 9.67/10.03
% 9.67/10.03 Resimplifying inuse:
% 9.67/10.03 Done
% 9.67/10.03
% 9.67/10.03
% 9.67/10.03 Intermediate Status:
% 9.67/10.03 Generated: 49748
% 9.67/10.03 Kept: 16835
% 9.67/10.03 Inuse: 554
% 9.67/10.03 Deleted: 12
% 9.67/10.03 Deletedinuse: 0
% 9.67/10.03
% 9.67/10.03 Resimplifying inuse:
% 9.67/10.03 Done
% 9.67/10.03
% 9.67/10.03 Resimplifying inuse:
% 9.67/10.03 Done
% 9.67/10.03
% 9.67/10.03
% 9.67/10.03 Intermediate Status:
% 9.67/10.03 Generated: 63584
% 9.67/10.03 Kept: 19279
% 9.67/10.03 Inuse: 574
% 9.67/10.03 Deleted: 12
% 9.67/10.03 Deletedinuse: 0
% 9.67/10.03
% 9.67/10.03 Resimplifying inuse:
% 9.67/10.03 Done
% 9.67/10.03
% 9.67/10.03 Resimplifying clauses:
% 9.67/10.03 Done
% 9.67/10.03
% 9.67/10.03 Resimplifying inuse:
% 9.67/10.03 Done
% 9.67/10.03
% 9.67/10.03
% 9.67/10.03 Intermediate Status:
% 9.67/10.03 Generated: 71744
% 9.67/10.03 Kept: 21329
% 9.67/10.03 Inuse: 637
% 9.67/10.03 Deleted: 169
% 9.67/10.03 Deletedinuse: 1
% 9.67/10.03
% 9.67/10.03 Resimplifying inuse:
% 9.67/10.03 Done
% 9.67/10.03
% 9.67/10.03
% 9.67/10.03 Intermediate Status:
% 9.67/10.03 Generated: 80263
% 9.67/10.03 Kept: 23527
% 9.67/10.03 Inuse: 662
% 9.67/10.03 Deleted: 169
% 9.67/10.03 Deletedinuse: 1
% 9.67/10.03
% 9.67/10.03 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 89506
% 37.16/37.55 Kept: 25644
% 37.16/37.55 Inuse: 697
% 37.16/37.55 Deleted: 169
% 37.16/37.55 Deletedinuse: 1
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 95175
% 37.16/37.55 Kept: 27698
% 37.16/37.55 Inuse: 702
% 37.16/37.55 Deleted: 169
% 37.16/37.55 Deletedinuse: 1
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 102726
% 37.16/37.55 Kept: 29912
% 37.16/37.55 Inuse: 742
% 37.16/37.55 Deleted: 169
% 37.16/37.55 Deletedinuse: 1
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 109440
% 37.16/37.55 Kept: 32050
% 37.16/37.55 Inuse: 772
% 37.16/37.55 Deleted: 169
% 37.16/37.55 Deletedinuse: 1
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 114892
% 37.16/37.55 Kept: 34050
% 37.16/37.55 Inuse: 788
% 37.16/37.55 Deleted: 169
% 37.16/37.55 Deletedinuse: 1
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 122786
% 37.16/37.55 Kept: 36232
% 37.16/37.55 Inuse: 822
% 37.16/37.55 Deleted: 169
% 37.16/37.55 Deletedinuse: 1
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 130652
% 37.16/37.55 Kept: 38340
% 37.16/37.55 Inuse: 857
% 37.16/37.55 Deleted: 169
% 37.16/37.55 Deletedinuse: 1
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 141306
% 37.16/37.55 Kept: 40631
% 37.16/37.55 Inuse: 887
% 37.16/37.55 Deleted: 169
% 37.16/37.55 Deletedinuse: 1
% 37.16/37.55
% 37.16/37.55 Resimplifying clauses:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 153057
% 37.16/37.55 Kept: 42639
% 37.16/37.55 Inuse: 933
% 37.16/37.55 Deleted: 281
% 37.16/37.55 Deletedinuse: 1
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 165006
% 37.16/37.55 Kept: 45407
% 37.16/37.55 Inuse: 972
% 37.16/37.55 Deleted: 281
% 37.16/37.55 Deletedinuse: 1
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 174857
% 37.16/37.55 Kept: 47419
% 37.16/37.55 Inuse: 1019
% 37.16/37.55 Deleted: 283
% 37.16/37.55 Deletedinuse: 2
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 184504
% 37.16/37.55 Kept: 49500
% 37.16/37.55 Inuse: 1069
% 37.16/37.55 Deleted: 293
% 37.16/37.55 Deletedinuse: 10
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 192842
% 37.16/37.55 Kept: 51695
% 37.16/37.55 Inuse: 1089
% 37.16/37.55 Deleted: 293
% 37.16/37.55 Deletedinuse: 10
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 201671
% 37.16/37.55 Kept: 53703
% 37.16/37.55 Inuse: 1126
% 37.16/37.55 Deleted: 293
% 37.16/37.55 Deletedinuse: 10
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 212201
% 37.16/37.55 Kept: 55762
% 37.16/37.55 Inuse: 1174
% 37.16/37.55 Deleted: 293
% 37.16/37.55 Deletedinuse: 10
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 222865
% 37.16/37.55 Kept: 57828
% 37.16/37.55 Inuse: 1209
% 37.16/37.55 Deleted: 293
% 37.16/37.55 Deletedinuse: 10
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 228284
% 37.16/37.55 Kept: 59829
% 37.16/37.55 Inuse: 1215
% 37.16/37.55 Deleted: 293
% 37.16/37.55 Deletedinuse: 10
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying clauses:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 235251
% 37.16/37.55 Kept: 61833
% 37.16/37.55 Inuse: 1243
% 37.16/37.55 Deleted: 857
% 37.16/37.55 Deletedinuse: 11
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 242950
% 37.16/37.55 Kept: 63867
% 37.16/37.55 Inuse: 1272
% 37.16/37.55 Deleted: 857
% 37.16/37.55 Deletedinuse: 11
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 252605
% 37.16/37.55 Kept: 66449
% 37.16/37.55 Inuse: 1279
% 37.16/37.55 Deleted: 857
% 37.16/37.55 Deletedinuse: 11
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 260383
% 37.16/37.55 Kept: 68478
% 37.16/37.55 Inuse: 1311
% 37.16/37.55 Deleted: 857
% 37.16/37.55 Deletedinuse: 11
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 266908
% 37.16/37.55 Kept: 70600
% 37.16/37.55 Inuse: 1334
% 37.16/37.55 Deleted: 857
% 37.16/37.55 Deletedinuse: 11
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 274112
% 37.16/37.55 Kept: 72641
% 37.16/37.55 Inuse: 1369
% 37.16/37.55 Deleted: 857
% 37.16/37.55 Deletedinuse: 11
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 37.16/37.55 Done
% 37.16/37.55
% 37.16/37.55
% 37.16/37.55 Intermediate Status:
% 37.16/37.55 Generated: 284906
% 37.16/37.55 Kept: 74653
% 37.16/37.55 Inuse: 1401
% 37.16/37.55 Deleted: 857
% 37.16/37.55 Deletedinuse: 11
% 37.16/37.55
% 37.16/37.55 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 297329
% 82.49/82.92 Kept: 76988
% 82.49/82.92 Inuse: 1434
% 82.49/82.92 Deleted: 857
% 82.49/82.92 Deletedinuse: 11
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 307253
% 82.49/82.92 Kept: 79143
% 82.49/82.92 Inuse: 1474
% 82.49/82.92 Deleted: 858
% 82.49/82.92 Deletedinuse: 12
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92 Resimplifying clauses:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 316248
% 82.49/82.92 Kept: 81387
% 82.49/82.92 Inuse: 1504
% 82.49/82.92 Deleted: 1063
% 82.49/82.92 Deletedinuse: 12
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 325435
% 82.49/82.92 Kept: 83474
% 82.49/82.92 Inuse: 1514
% 82.49/82.92 Deleted: 1063
% 82.49/82.92 Deletedinuse: 12
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 335682
% 82.49/82.92 Kept: 85641
% 82.49/82.92 Inuse: 1534
% 82.49/82.92 Deleted: 1063
% 82.49/82.92 Deletedinuse: 12
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 344663
% 82.49/82.92 Kept: 87642
% 82.49/82.92 Inuse: 1564
% 82.49/82.92 Deleted: 1063
% 82.49/82.92 Deletedinuse: 12
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 355326
% 82.49/82.92 Kept: 89767
% 82.49/82.92 Inuse: 1599
% 82.49/82.92 Deleted: 1063
% 82.49/82.92 Deletedinuse: 12
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 365902
% 82.49/82.92 Kept: 92161
% 82.49/82.92 Inuse: 1639
% 82.49/82.92 Deleted: 1064
% 82.49/82.92 Deletedinuse: 13
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 378676
% 82.49/82.92 Kept: 95959
% 82.49/82.92 Inuse: 1669
% 82.49/82.92 Deleted: 1064
% 82.49/82.92 Deletedinuse: 13
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 389719
% 82.49/82.92 Kept: 100518
% 82.49/82.92 Inuse: 1694
% 82.49/82.92 Deleted: 1064
% 82.49/82.92 Deletedinuse: 13
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 397141
% 82.49/82.92 Kept: 104030
% 82.49/82.92 Inuse: 1699
% 82.49/82.92 Deleted: 1064
% 82.49/82.92 Deletedinuse: 13
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92 Resimplifying clauses:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 404845
% 82.49/82.92 Kept: 106822
% 82.49/82.92 Inuse: 1704
% 82.49/82.92 Deleted: 1548
% 82.49/82.92 Deletedinuse: 13
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 414853
% 82.49/82.92 Kept: 108898
% 82.49/82.92 Inuse: 1719
% 82.49/82.92 Deleted: 1548
% 82.49/82.92 Deletedinuse: 13
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 424147
% 82.49/82.92 Kept: 110911
% 82.49/82.92 Inuse: 1730
% 82.49/82.92 Deleted: 1548
% 82.49/82.92 Deletedinuse: 13
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 435727
% 82.49/82.92 Kept: 113065
% 82.49/82.92 Inuse: 1764
% 82.49/82.92 Deleted: 1548
% 82.49/82.92 Deletedinuse: 13
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 469568
% 82.49/82.92 Kept: 118133
% 82.49/82.92 Inuse: 1789
% 82.49/82.92 Deleted: 1548
% 82.49/82.92 Deletedinuse: 13
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 478830
% 82.49/82.92 Kept: 120145
% 82.49/82.92 Inuse: 1795
% 82.49/82.92 Deleted: 1548
% 82.49/82.92 Deletedinuse: 13
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 488252
% 82.49/82.92 Kept: 122164
% 82.49/82.92 Inuse: 1801
% 82.49/82.92 Deleted: 1548
% 82.49/82.92 Deletedinuse: 13
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 502945
% 82.49/82.92 Kept: 125380
% 82.49/82.92 Inuse: 1814
% 82.49/82.92 Deleted: 1548
% 82.49/82.92 Deletedinuse: 13
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92 Resimplifying clauses:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 520888
% 82.49/82.92 Kept: 127735
% 82.49/82.92 Inuse: 1839
% 82.49/82.92 Deleted: 1743
% 82.49/82.92 Deletedinuse: 13
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 532351
% 82.49/82.92 Kept: 130585
% 82.49/82.92 Inuse: 1849
% 82.49/82.92 Deleted: 1743
% 82.49/82.92 Deletedinuse: 13
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 541879
% 82.49/82.92 Kept: 132776
% 82.49/82.92 Inuse: 1854
% 82.49/82.92 Deleted: 1743
% 82.49/82.92 Deletedinuse: 13
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 551308
% 82.49/82.92 Kept: 134892
% 82.49/82.92 Inuse: 1874
% 82.49/82.92 Deleted: 1743
% 82.49/82.92 Deletedinuse: 13
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 614900
% 82.49/82.92 Kept: 141304
% 82.49/82.92 Inuse: 1894
% 82.49/82.92 Deleted: 1743
% 82.49/82.92 Deletedinuse: 13
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 82.49/82.92 Done
% 82.49/82.92
% 82.49/82.92
% 82.49/82.92 Intermediate Status:
% 82.49/82.92 Generated: 623801
% 82.49/82.92 Kept: 143305
% 82.49/82.92 Inuse: 1916
% 82.49/82.92 Deleted: 1743
% 82.49/82.92 Deletedinuse: 13
% 82.49/82.92
% 82.49/82.92 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 631149
% 180.86/181.31 Kept: 145351
% 180.86/181.31 Inuse: 1934
% 180.86/181.31 Deleted: 1743
% 180.86/181.31 Deletedinuse: 13
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31 Resimplifying clauses:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 639677
% 180.86/181.31 Kept: 147533
% 180.86/181.31 Inuse: 1954
% 180.86/181.31 Deleted: 1844
% 180.86/181.31 Deletedinuse: 13
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 650307
% 180.86/181.31 Kept: 149951
% 180.86/181.31 Inuse: 1979
% 180.86/181.31 Deleted: 1844
% 180.86/181.31 Deletedinuse: 13
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 663828
% 180.86/181.31 Kept: 152476
% 180.86/181.31 Inuse: 2014
% 180.86/181.31 Deleted: 1844
% 180.86/181.31 Deletedinuse: 13
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 674340
% 180.86/181.31 Kept: 154504
% 180.86/181.31 Inuse: 2021
% 180.86/181.31 Deleted: 1846
% 180.86/181.31 Deletedinuse: 15
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 684912
% 180.86/181.31 Kept: 156533
% 180.86/181.31 Inuse: 2028
% 180.86/181.31 Deleted: 1847
% 180.86/181.31 Deletedinuse: 16
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 694969
% 180.86/181.31 Kept: 158538
% 180.86/181.31 Inuse: 2030
% 180.86/181.31 Deleted: 1847
% 180.86/181.31 Deletedinuse: 16
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 705729
% 180.86/181.31 Kept: 160549
% 180.86/181.31 Inuse: 2056
% 180.86/181.31 Deleted: 1847
% 180.86/181.31 Deletedinuse: 16
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 716891
% 180.86/181.31 Kept: 162637
% 180.86/181.31 Inuse: 2079
% 180.86/181.31 Deleted: 1847
% 180.86/181.31 Deletedinuse: 16
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 726767
% 180.86/181.31 Kept: 164706
% 180.86/181.31 Inuse: 2099
% 180.86/181.31 Deleted: 1847
% 180.86/181.31 Deletedinuse: 16
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31 Resimplifying clauses:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 737173
% 180.86/181.31 Kept: 166942
% 180.86/181.31 Inuse: 2129
% 180.86/181.31 Deleted: 2105
% 180.86/181.31 Deletedinuse: 16
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 751173
% 180.86/181.31 Kept: 168942
% 180.86/181.31 Inuse: 2156
% 180.86/181.31 Deleted: 2105
% 180.86/181.31 Deletedinuse: 16
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 767618
% 180.86/181.31 Kept: 172585
% 180.86/181.31 Inuse: 2174
% 180.86/181.31 Deleted: 2105
% 180.86/181.31 Deletedinuse: 16
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 779984
% 180.86/181.31 Kept: 174644
% 180.86/181.31 Inuse: 2206
% 180.86/181.31 Deleted: 2105
% 180.86/181.31 Deletedinuse: 16
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 790812
% 180.86/181.31 Kept: 176833
% 180.86/181.31 Inuse: 2229
% 180.86/181.31 Deleted: 2105
% 180.86/181.31 Deletedinuse: 16
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 807354
% 180.86/181.31 Kept: 180206
% 180.86/181.31 Inuse: 2244
% 180.86/181.31 Deleted: 2105
% 180.86/181.31 Deletedinuse: 16
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 819503
% 180.86/181.31 Kept: 182638
% 180.86/181.31 Inuse: 2249
% 180.86/181.31 Deleted: 2105
% 180.86/181.31 Deletedinuse: 16
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 831918
% 180.86/181.31 Kept: 184859
% 180.86/181.31 Inuse: 2254
% 180.86/181.31 Deleted: 2105
% 180.86/181.31 Deletedinuse: 16
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 844690
% 180.86/181.31 Kept: 187052
% 180.86/181.31 Inuse: 2259
% 180.86/181.31 Deleted: 2105
% 180.86/181.31 Deletedinuse: 16
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31 Resimplifying clauses:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 857549
% 180.86/181.31 Kept: 189337
% 180.86/181.31 Inuse: 2264
% 180.86/181.31 Deleted: 2408
% 180.86/181.31 Deletedinuse: 16
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 866893
% 180.86/181.31 Kept: 191353
% 180.86/181.31 Inuse: 2287
% 180.86/181.31 Deleted: 2409
% 180.86/181.31 Deletedinuse: 17
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 876451
% 180.86/181.31 Kept: 193638
% 180.86/181.31 Inuse: 2314
% 180.86/181.31 Deleted: 2409
% 180.86/181.31 Deletedinuse: 17
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 884071
% 180.86/181.31 Kept: 195896
% 180.86/181.31 Inuse: 2334
% 180.86/181.31 Deleted: 2409
% 180.86/181.31 Deletedinuse: 17
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 Intermediate Status:
% 180.86/181.31 Generated: 934114
% 180.86/181.31 Kept: 203276
% 180.86/181.31 Inuse: 2364
% 180.86/181.31 Deleted: 2409
% 180.86/181.31 Deletedinuse: 17
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31 Resimplifying inuse:
% 180.86/181.31 Done
% 180.86/181.31
% 180.86/181.31
% 180.86/181.31 IntermedCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------