TSTP Solution File: SWV696-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV696-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:27:51 EDT 2022
% Result : Timeout 300.01s 300.45s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV696-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Thu Jun 16 00:25:03 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.20/1.61 *** allocated 10000 integers for termspace/termends
% 1.20/1.61 *** allocated 10000 integers for clauses
% 1.20/1.61 *** allocated 10000 integers for justifications
% 1.20/1.61 *** allocated 15000 integers for termspace/termends
% 1.20/1.61 *** allocated 22500 integers for termspace/termends
% 1.20/1.61 *** allocated 33750 integers for termspace/termends
% 1.20/1.61 Bliksem 1.12
% 1.20/1.61
% 1.20/1.61
% 1.20/1.61 Automatic Strategy Selection
% 1.20/1.61
% 1.20/1.61 Clauses:
% 1.20/1.61 [
% 1.20/1.61 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.20/1.61 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.20/1.61 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.20/1.61 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.20/1.61 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.20/1.61 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.20/1.61 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 'tc_nat' ), 'tc_nat' ), X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.61 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.61 Y, Z, 'tc_nat' ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y )
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.61 Y, Z, 'tc_nat' ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Z )
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' )
% 1.20/1.61 , Y ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'tc_nat' )
% 1.20/1.61 , Y ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.61 Y, Z, 'tc_nat' ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y )
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.61 Y, Z, 'tc_nat' ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Z )
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.20/1.61 ,
% 1.20/1.61 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.20/1.61 ,
% 1.20/1.61 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 Y, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) )
% 1.20/1.61 ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z
% 1.20/1.61 , X ), Y ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 Y, X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Y ) )
% 1.20/1.61 ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.20/1.61 , X ), Y ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.20/1.61 , X ), Z ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ]
% 1.20/1.61 ,
% 1.20/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z
% 1.20/1.61 , X ), Y ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 Y, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) )
% 1.20/1.61 ) ],
% 1.20/1.61 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'c_Suc'( X ) ), Y ), 'tc_nat' )
% 1.20/1.61 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'c_Suc'( X ) ), Y ) ),
% 1.20/1.61 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.61 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), 'c_Suc'( X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.20/1.61 X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.20/1.61 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.20/1.61 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.20/1.61 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 1.20/1.61 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~(
% 1.20/1.61 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) )
% 1.20/1.61 ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.20/1.61 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.61 Z, T, X ) ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.61 , X ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ) ],
% 1.20/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.20/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 'tc_nat' ), 'tc_nat' ), X ) ) ), =( Y, Z ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.20/1.61 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) )
% 1.20/1.61 ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat'
% 1.20/1.61 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ) ) ) )
% 1.20/1.61 ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.20/1.61 'c_HOL_Oone__class_Oone'( X ) ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.61 'tc_nat' ), X ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z )
% 1.20/1.61 , X ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.20/1.61 Z ), Y ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Z ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.61 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ), hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.20/1.61 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.20/1.61 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.20/1.61 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.20/1.61 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.20/1.61 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.20/1.61 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.20/1.61 , X ) ), Z ), X ), Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.61 , X ) ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X
% 1.20/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ) ],
% 1.20/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.20/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.20/1.61 ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.20/1.61 ,
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.20/1.61 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), X ), X ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.20/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), Y ) ) ), ~(
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.20/1.61 ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ), X
% 1.20/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), Z ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.61 'tc_nat' ), Y ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.61 'tc_nat' ), X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.20/1.61 ), X ), Y ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.20/1.61 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.20/1.61 ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), Z ) ) ) ],
% 1.20/1.61 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.20/1.61 [ =( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.20/1.61 ), X ), Y ), 'tc_nat' ) ) ],
% 1.20/1.61 [ =( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.20/1.61 ), X ), Y ), 'tc_nat' ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ),
% 1.20/1.61 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ),
% 1.20/1.61 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.20/1.61 hAPP( 'c_Power_Opower__class_Opower'( Y, X ), Z ) ), hAPP(
% 1.20/1.61 'c_Power_Opower__class_Opower'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.20/1.61 ), X ), Z ) ) ],
% 1.20/1.61 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.61 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T )
% 1.20/1.61 , U ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( U, X ), Z ) ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ), X ), U ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~(
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.61 X ), Y ) ) ) ],
% 1.20/1.61 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'c_Suc'( hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ) ), Z ), hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'c_Suc'( X ) ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.61 ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.20/1.61 ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.61 ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.20/1.61 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.20/1.61 , X ) ), Z ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y
% 1.20/1.61 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), Y ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.20/1.61 ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), X ), T ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.61 ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.61 ), T ), Z ), X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ) ]
% 1.20/1.61 ,
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.20/1.61 , X ) ), Z ), X ), Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat'
% 1.20/1.61 ), 'tc_nat' ), 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.20/1.61 , X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ),
% 1.20/1.61 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), 'tc_nat' ),
% 1.20/1.61 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ],
% 1.20/1.61 [ =( hAPP( 'c_Power_Opower__class_Opower'( X, 'tc_nat' ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), T, 'tc_nat' )
% 1.20/1.61 , 'tc_nat' ), U ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), X ), Z ), T, 'tc_nat' ), 'tc_nat' ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), Y ), Z ), U, 'tc_nat' ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 Y, 'tc_nat' ), X ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z,
% 1.20/1.61 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ), U, 'tc_nat' ) ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ), Z, 'tc_nat' )
% 1.20/1.61 , 'tc_nat' ), U ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), X )
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z
% 1.20/1.61 ) ), T ), U, 'tc_nat' ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), Z ), T ), X, 'tc_nat' ), 'tc_nat' ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), Y ), T ), U, 'tc_nat' ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 Z, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z,
% 1.20/1.61 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ), U, 'tc_nat' ) ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X
% 1.20/1.61 ) ), Y ), U, 'tc_nat' ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X,
% 1.20/1.61 'tc_nat' ), T ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' )
% 1.20/1.61 , Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.20/1.61 'tc_nat' ), 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( X,
% 1.20/1.61 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y
% 1.20/1.61 ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Obot'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 'c_Orderings_Obot__class_Obot'( X ), X ), Y ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.20/1.61 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ) ) ), ~(
% 1.20/1.61 hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.20/1.61 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ) ) ), ~(
% 1.20/1.61 hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( 'c_Suc'( X ), 'tc_nat' ), Y ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( X ), 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( 'c_Suc'( X ), 'tc_nat' ), Y ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( X ), 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z,
% 1.20/1.61 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.61 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.20/1.61 ,
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.61 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.20/1.61 ,
% 1.20/1.61 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'c_Suc'( X )
% 1.20/1.61 ), Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X
% 1.20/1.61 ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ]
% 1.20/1.61 ,
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.20/1.61 ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.20/1.61 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.61 X ), Y ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.20/1.61 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X )
% 1.20/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.20/1.61 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.20/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.20/1.61 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.61 , X ) ), T ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.61 , X ) ), T ), X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z
% 1.20/1.61 ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T
% 1.20/1.61 ), X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.61 ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T
% 1.20/1.61 ), Z ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.61 X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.20/1.61 , T ), Z ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.20/1.61 , Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.20/1.61 X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.61 ), X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.20/1.61 ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.20/1.61 , Z ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.20/1.61 ],
% 1.20/1.61 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), Y ), Z ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X
% 1.20/1.61 ) ), Z ), T, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.20/1.61 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.20/1.61 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.20/1.61 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), =(
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.20/1.61 ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.20/1.61 , Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ), X ), Y ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.20/1.61 ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.20/1.61 , Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ), X ), Y ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( =( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), T ), Y ), U, 'tc_nat' ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 T, 'tc_nat' ), X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ), Z, 'tc_nat' )
% 1.20/1.61 , U ) ],
% 1.20/1.61 [ ~( =( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), T ), Y ), U, 'tc_nat' ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 X, 'tc_nat' ), T ) ) ), =( Z, 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ), U, 'tc_nat' )
% 1.20/1.61 ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y
% 1.20/1.61 , Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y
% 1.20/1.61 , Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.61 'tc_nat' ), X ) ) ) ],
% 1.20/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X )
% 1.20/1.61 ), Y ), 'c_HOL_Oplus__class_Oplus'( Y, hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.20/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 'c_Suc'(
% 1.20/1.61 Y ) ), 'c_HOL_Oplus__class_Oplus'( X, hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.61 ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), Y ) ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.20/1.61 , Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.20/1.61 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), ~(
% 1.20/1.61 hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.20/1.61 ), Y ), T ), X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 1.20/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 1.20/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.61 ) ) ) ],
% 1.20/1.61 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), Z ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.61 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.20/1.61 , 'tc_nat' ), X ) ) ) ],
% 1.20/1.61 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), Z ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.61 'tc_nat' ), Y ), Z ), 'tc_nat' ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z,
% 1.20/1.61 'tc_nat' ), Y ) ) ) ],
% 1.20/1.61 [ =( 'c_SetInterval_Oord__class_OlessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 'tc_nat' ), 'tc_nat' ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.20/1.61 'tc_nat', 'tc_bool' ) ) ) ],
% 1.20/1.61 [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.20/1.61 ) ), Y ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.61 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ) ],
% 1.20/1.61 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.20/1.61 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 'tc_nat' ), 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 'tc_nat' ), 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.20/1.61 'c_SetInterval_Oord__class_OlessThan'( Y, X ),
% 1.20/1.61 'c_SetInterval_Oord__class_OlessThan'( Z, X ) ) ), =( Y, Z ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP(
% 1.20/1.61 'c_Power_Opower__class_Opower'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.61 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ],
% 1.20/1.61 [ =( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), Z ), Y ), T, 'tc_nat' ), 'tc_nat' ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ), Y ), T,
% 1.20/1.61 'tc_nat' ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 1.20/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.61 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, 'c_Suc'( Y ),
% 1.20/1.61 'tc_nat' ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_nat', 'tc_bool'
% 1.20/1.61 ) ) ), hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.20/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), 'c_Suc'( Z ) ), X ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( Z ) ), Y ) ) ) ) ]
% 1.20/1.61 ,
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X ) ), Y ), 'tc_nat' )
% 1.20/1.61 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X ) ), Z
% 1.20/1.61 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) )
% 1.20/1.61 ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'tc_nat' ), Y )
% 1.20/1.61 ), =( 'c_Suc'( X ), Y ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.20/1.61 'tc_nat' ), Y ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( X ), 'tc_nat' ), Y ) ), hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ],
% 1.20/1.61 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_Suc'( Y ), 'tc_nat' ), X ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.20/1.61 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ),
% 1.20/1.61 hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), 'c_HOL_Oone__class_Oone'(
% 1.20/1.61 X ) ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.20/1.61 X, 'tc_nat' ) ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ),
% 1.20/1.61 Y ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.20/1.61 ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.20/1.61 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.61 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), Z ) ) ) ]
% 1.20/1.61 ,
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.20/1.61 ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.20/1.61 ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ), X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ) ) ],
% 1.20/1.61 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.20/1.61 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 'tc_nat' ) ), 'tc_nat' ), 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) )
% 1.20/1.61 ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.20/1.61 'c_Suc'( Z ) ), X ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), 'c_Suc'( Z ) ), Y ) ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), 'c_Suc'( X ) ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X ) ), Z ) ) ), ~(
% 1.20/1.61 hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.61 ), Z ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.61 ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.61 X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.61 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =( 'c_Orderings_Obot__class_Obot'(
% 1.20/1.61 'tc_fun'( X, 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.61 Y, Z, X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.20/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.20/1.61 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( X ), 'tc_nat' ), 'c_Suc'( X ) )
% 1.20/1.61 ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.20/1.61 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T
% 1.20/1.61 ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), Z ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) ) ) ],
% 1.20/1.61 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.20/1.61 , 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.20/1.61 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 'tc_nat' ), 'tc_nat' ), 'c_Finite__Set_Ocard'(
% 1.20/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ) ) ]
% 1.20/1.61 ,
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.61 'tc_nat' ), X ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), Z ), X ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.61 'tc_nat' ), Z ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.61 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.20/1.61 'tc_nat' ), Z ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.61 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.20/1.61 'tc_nat' ), Z ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.61 'tc_nat' ), X ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.61 'tc_nat' ), Y ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.61 Y ), Z ) ) ), ~( hBOOL( hAPP( X,
% 1.20/1.61 'c_ATP__Linkup_Osko__Nat__Xnat__diff__split__1__1'( X, Y, Z ) ) ) ),
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ],
% 1.20/1.61 [ =( 'c_Finite__Set_Ocard'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X
% 1.20/1.61 , 'tc_bool' ) ), X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Power_Opower__class_Opower'( Z
% 1.20/1.61 , 'tc_nat' ), X ), 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( Z,
% 1.20/1.61 'tc_nat' ), Y ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.20/1.61 , Z ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.61 X ), T ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.61 X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.61 ), X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.61 X ), Z ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.61 X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), Y ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X
% 1.20/1.61 ) ), T ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ) ) ],
% 1.20/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X
% 1.20/1.61 ) ), T ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Z ) ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.20/1.61 , X ), Y ) ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 1.20/1.61 , X ), X ), 'c_HOL_Oplus__class_Oplus'( T, U, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 1.20/1.61 , X ), X ), 'c_HOL_Oplus__class_Oplus'( T, U, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'tc_nat' ),
% 1.20/1.61 'c_Suc'( Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat'
% 1.20/1.61 ), Y ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'tc_nat' ), 'c_Suc'( Y ) )
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'tc_nat' ),
% 1.20/1.61 'c_Suc'( Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat'
% 1.20/1.61 ), Y ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.61 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.61 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.20/1.61 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.20/1.61 ,
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.61 ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.20/1.61 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.20/1.61 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.61 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.20/1.61 ,
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.20/1.61 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.20/1.61 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.20/1.61 ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.20/1.61 ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.20/1.61 ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.61 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ), X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.20/1.61 ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.20/1.61 ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.20/1.61 ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.20/1.61 ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.20/1.61 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U
% 1.20/1.61 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U
% 1.20/1.61 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.61 X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.61 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y )
% 1.20/1.61 , T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X )
% 1.20/1.61 , 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.20/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.20/1.61 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ),
% 1.20/1.61 'c_HOL_Oone__class_Oone'( X ) ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ),
% 1.20/1.61 'c_HOL_Oone__class_Oone'( X ) ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.20/1.61 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.20/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.20/1.61 [ =( 'c_HOL_Oord__class_Oless'( 'v_n', 'tc_nat' ), 'c_lessequals'(
% 1.20/1.61 'c_Suc'( 'v_n' ), 'tc_nat' ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Z, X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.20/1.61 Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), =( Z, Y ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Z, X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.20/1.61 Z ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ), =( Y, X ) ],
% 1.20/1.61 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), =( Z, Y ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ), =( Y, X ) ],
% 1.20/1.61 [ =( X, Y ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ), ~(
% 1.20/1.61 hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ),
% 1.20/1.61 Y ) ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Z, Y ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), =( Z, Y ) ],
% 1.20/1.61 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_Suc'(
% 1.20/1.61 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ), 'c_Suc'( Y ) ) ), ~(
% 1.20/1.61 hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'tc_nat' ), Y )
% 1.20/1.61 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( X ) )
% 1.20/1.61 ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( X ) )
% 1.20/1.61 ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.20/1.61 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'tc_nat' )
% 1.20/1.61 , 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.20/1.61 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 Z, X ), T ) ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( T, Z, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 Y, X ), T ) ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.20/1.61 , hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( T, Y, X ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( T, Z, X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.20/1.61 , hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X )
% 1.20/1.61 , 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.20/1.61 , hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Z, T, X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.20/1.61 , hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X )
% 1.20/1.61 , 'c_HOL_Oplus__class_Oplus'( T, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), X ), Z ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), Z ), X ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.20/1.61 'c_HOL_Oone__class_Oone'( X ), X ) ) ) ],
% 1.20/1.61 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_Suc'( X ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X ) ),
% 1.20/1.61 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ), Y ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.20/1.61 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.61 X ), Z ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.20/1.61 Y, X ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.20/1.61 , X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.20/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), Y ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.20/1.61 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.20/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.20/1.61 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.20/1.61 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 1.20/1.61 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~(
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.61 X ), Z ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.61 Y ), Z ) ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.20/1.61 'c_ATP__Linkup_Osko__Nat__Xnat__diff__split__asm__1__1'( X, Y, Z ),
% 1.20/1.61 'tc_nat' ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z )
% 1.20/1.61 ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.61 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X )
% 1.20/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ) ],
% 1.20/1.61 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), Y ), T ), 'tc_nat' ) ) ), =( Z, T ), =( Y,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 'tc_nat' ), 'tc_nat' ), 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ) ]
% 1.20/1.61 ,
% 1.20/1.61 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.20/1.61 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'( X
% 1.20/1.61 ) ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.20/1.61 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.20/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.20/1.61 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.20/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.61 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.61 X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.61 X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.61 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.20/1.61 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.61 Z, 'c_Suc'( T ), 'tc_nat' ), 'tc_nat', X ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.61 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.61 Z, T, 'tc_nat' ), 'tc_nat', X ), hAPP( Y, T ), X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( T, 'tc_nat' ), Z ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.61 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.20/1.61 ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.61 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.61 ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( Y ) )
% 1.20/1.61 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ]
% 1.20/1.61 ,
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'tc_nat' ), Y ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), X ), T ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z
% 1.20/1.61 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.61 , X ) ), T ), X ), Z ) ) ) ],
% 1.20/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X
% 1.20/1.61 ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.20/1.61 X ) ), Z ) ) ), =( Y, Z ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.61 , X ) ), T ), X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.61 , X ) ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 'tc_nat' ), 'tc_nat' ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.20/1.61 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), hAPP(
% 1.20/1.61 'c_Power_Opower__class_Opower'( X, 'tc_nat' ), Y ) ) ) ) ],
% 1.20/1.61 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.61 'tc_nat' ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), hAPP(
% 1.20/1.61 'c_Power_Opower__class_Opower'( Y, 'tc_nat' ), X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ), Z ) ) ) ]
% 1.20/1.61 ,
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.20/1.61 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ) ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ]
% 1.20/1.61 ,
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.20/1.61 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.20/1.61 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.61 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.20/1.61 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.20/1.61 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.61 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( Y, 'tc_nat' ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.20/1.61 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.61 Z, T, 'tc_nat' ), 'tc_nat', X ), 'c_HOL_Oplus__class_Oplus'( hAPP( Y, Z )
% 1.20/1.61 , 'c_Finite__Set_Osetsum'( Y,
% 1.20/1.61 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_Suc'( Z ), T, 'tc_nat' )
% 1.20/1.61 , 'tc_nat', X ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z,
% 1.20/1.61 'tc_nat' ), T ) ) ) ],
% 1.20/1.61 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.61 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 Y, X ), Z ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), =( X, Y
% 1.20/1.61 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.61 [ =( X, Y ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y )
% 1.20/1.61 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), =( X, Y
% 1.20/1.61 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 Y, X ), Z ) ) ), =( Y, Z ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), Z ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 Y, X ), Z ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 Y, X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 Y, X ), Z ) ) ), =( Z, Y ) ],
% 1.20/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Z, Y ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.61 ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z )
% 1.20/1.61 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.61 ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.20/1.61 ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), Y ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'(
% 1.20/1.61 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.20/1.61 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T
% 1.20/1.61 ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.20/1.61 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), Z ) ) ) ],
% 1.20/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.61 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y )
% 1.20/1.61 , T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.20/1.61 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), U )
% 1.20/1.61 , X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), U ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.20/1.61 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.61 ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.61 , X ) ), Z ) ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.20/1.61 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.61 , X ) ), Z ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), T ), X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ]
% 1.20/1.61 ,
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ]
% 1.20/1.61 ,
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.61 , X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.61 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.61 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , T ), Z ), X ), Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.61 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X
% 1.20/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , T ), Z ), X ), Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X )
% 1.20/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), Y ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.20/1.61 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.61 , X ) ), Z ) ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.61 X ), Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ),
% 1.20/1.61 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.61 X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.20/1.61 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oplus__class_Oplus'( Z, hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), T ) ), =( T,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.20/1.61 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 X ), T ), Z ), X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.20/1.61 ,
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.20/1.61 ) ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ),
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.61 ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X )
% 1.20/1.61 ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ),
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.61 ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), T ), X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), T ), X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.61 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , T ), Z ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.20/1.61 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.61 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X
% 1.20/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , T ), Z ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.20/1.61 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.20/1.61 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.61 , X ) ), Z ) ), Z ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.20/1.61 Y, X ) ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.20/1.61 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.20/1.61 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.20/1.61 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), =(
% 1.20/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z ), =( T,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.20/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U
% 1.20/1.61 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.61 X ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 X ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), U )
% 1.20/1.61 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), T ), X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.61 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.20/1.61 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~(
% 1.20/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.61 X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.61 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.61 X ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ), X ), X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.61 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.20/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 X ), Y ), T ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T
% 1.20/1.61 ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 X ), T ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.20/1.61 ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), T ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T )
% 1.20/1.61 ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , T ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.20/1.61 ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ), X )
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.61 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U
% 1.20/1.61 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.61 X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.20/1.61 , ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.61 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.20/1.61 hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.20/1.61 ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.20/1.61 ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.61 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.20/1.61 hBOOL( hAPP( 'c_lessequals'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.61 ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Z ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X )
% 1.20/1.61 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ), X )
% 1.20/1.61 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ), X )
% 1.20/1.61 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ), X )
% 1.20/1.61 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.20/1.61 , Z ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.20/1.61 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), ~(
% 1.20/1.61 hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.20/1.61 ), Y ), T ), X ), Z ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.61 ), X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.20/1.61 X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.61 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), U ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.20/1.61 ) ), =( Z, U ), =( Y, T ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.61 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), U ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.20/1.61 ) ), =( Z, U ), =( Y, T ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.20/1.61 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.20/1.61 ) ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Z ), T ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.20/1.61 ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , T ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.20/1.61 ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.20/1.61 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ), Z ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X )
% 1.20/1.61 ), T ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oplus__class_Oplus'( Z, T
% 1.20/1.61 , X ) ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.20/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X )
% 1.20/1.61 ), T ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.20/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X )
% 1.20/1.61 ), T ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.20/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oplus__class_Oplus'( Z, T
% 1.20/1.61 , X ) ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.20/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oplus__class_Oplus'( Z, T
% 1.20/1.61 , X ) ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X )
% 1.20/1.61 ), T ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.20/1.61 Y ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.20/1.61 Y ) ],
% 1.20/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.20/1.61 Y ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.20/1.61 Y ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.20/1.61 Y ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.20/1.61 Y ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.61 X ) ), =( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X )
% 1.20/1.61 ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.61 X ) ), =( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X )
% 1.20/1.61 ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), Z ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), U, X ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ), Z ), U, X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , U ), Z ), W, X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X )
% 1.20/1.61 , 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.20/1.61 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ), W, X
% 1.20/1.61 ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ), W, X ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), Y, X ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Z ), U ), W, X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , U ), Z ), W, X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ), T, X )
% 1.20/1.61 , X ), W ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), U, X ), X ), W ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), U, X ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Z ), T ), W, X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_RealVector_Oreal__field'( X ) ), =( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), W ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ), W ) ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), W ) ), U ), X ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , U ), Z ), W, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ), W, X )
% 1.20/1.61 ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ), W, X ) ) ), ~( hBOOL(
% 1.20/1.61 hAPP( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), Y, X ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Z ), U ), W, X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , U ), Z ), W, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ), T, X )
% 1.20/1.61 , X ), W ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), U, X ), X ), W ) ),
% 1.20/1.61 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), U, X ), X ),
% 1.20/1.61 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.61 , Z ), T ), W, X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.61 'c_lessequals'( hAPP( 'c_Power_Opower__class_Opower'( Y, X ), 'c_Suc'( T
% 1.20/1.61 ) ), X ), hAPP( 'c_Power_Opower__class_Opower'( Z, X ), 'c_Suc'( T ) ) )
% 1.20/1.61 ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.20/1.61 'c_Power_Opower__class_Opower'( Y, X ),
% 1.20/1.61 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ),
% 1.20/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP(
% 1.20/1.61 'c_Power_Opower__class_Opower'( Y, X ), 'c_Suc'( Z ) ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( T, X ), 'c_Suc'( Z ) ) ) ), =( Y, T ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T )
% 1.20/1.62 ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.20/1.62 ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_Power_Opower__class_Opower'( Y, X ),
% 1.20/1.62 T ), X ), hAPP( 'c_Power_Opower__class_Opower'( Z, X ), T ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), U ), Z ) ) ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), T ) ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), U ) ), X ), Z ) ), =( Y,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ) ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.20/1.62 ), X ), Z ), 'tc_nat' ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), Z ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.20/1.62 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.62 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T )
% 1.20/1.62 , U ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( U, X ), Z ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), U
% 1.20/1.62 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) )
% 1.20/1.62 ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.62 ), X ), 'c_HOL_Oplus__class_Oplus'( Y, Y, X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, Y, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.20/1.62 ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 hAPP( 'c_Power_Opower__class_Opower'( T, X ), Y ), X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( T, X ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), T ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 hAPP( 'c_Power_Opower__class_Opower'( T, X ), Y ), X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( T, X ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), T ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( 'c_Power_Opower__class_Opower'( Y, X ), Z ), X ),
% 1.20/1.62 hAPP( 'c_Power_Opower__class_Opower'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Z, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.20/1.62 , X ) ), Z ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.20/1.62 ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X, 'tc_nat'
% 1.20/1.62 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.20/1.62 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.20/1.62 'c_HOL_Oone__class_Oone'( X ), X ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X
% 1.20/1.62 , 'tc_nat' ), Z ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.62 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.62 X ), Z ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.20/1.62 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), 'c_Suc'( X ) ) ) )
% 1.20/1.62 ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( Y ) )
% 1.20/1.62 ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ) ],
% 1.20/1.62 [ =( X, 'c_Suc'( Y ) ), hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y )
% 1.20/1.62 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), 'c_Suc'( Y ) ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 X ), X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 X ), X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X
% 1.20/1.62 ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ) ) ],
% 1.20/1.62 [ =( hAPP( 'c_Power_Opower__class_Opower'( 'c_Suc'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ), 'c_Suc'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.20/1.62 [ =( hAPP( 'c_Power_Opower__class_Opower'( 'c_Suc'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ), 'c_Suc'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.20/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Series_Osums'(
% 1.20/1.62 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.20/1.62 'tc_fun'( X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_Series_Osums'(
% 1.20/1.62 Y, T, X ) ) ],
% 1.20/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Series_Osums'(
% 1.20/1.62 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.20/1.62 'tc_fun'( X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_Series_Osums'(
% 1.20/1.62 Y, T, X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.62 ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.62 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ), X )
% 1.20/1.62 , Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X
% 1.20/1.62 ) ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.20/1.62 'c_HOL_Oone__class_Oone'( X ), X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 1.20/1.62 X ), X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.20/1.62 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), X ), X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.62 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T )
% 1.20/1.62 , Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.62 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T )
% 1.20/1.62 , Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( T, X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.20/1.62 ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.62 ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.20/1.62 ), Y ) ],
% 1.20/1.62 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ],
% 1.20/1.62 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 1.20/1.62 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.62 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.20/1.62 X ) ) ), =( Z, T ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.20/1.62 X ) ) ), =( Z, T ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.20/1.62 X ) ) ), =( Y, T ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.20/1.62 ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.20/1.62 ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.20/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.20/1.62 , X ) ), Z ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.20/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), Y ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.20/1.62 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ), X
% 1.20/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.62 ), X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.20/1.62 X ), Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.62 ), X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.20/1.62 , Z ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.20/1.62 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ),
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.62 X ), T ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.20/1.62 , Z ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 X ), Y ), T ), X ), Z ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.20/1.62 ) ), 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), Y ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.20/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.20/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.20/1.62 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.62 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( 'c_Power_Opower__class_Opower'( Y, X ), Z ), X ),
% 1.20/1.62 hAPP( 'c_Power_Opower__class_Opower'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( Z, 'tc_nat' ), T ) ) ) ],
% 1.20/1.62 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.62 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.20/1.62 [ =( 'c_Finite__Set_Ocard'( 'c_SetInterval_Oord__class_OlessThan'( X,
% 1.20/1.62 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.20/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.62 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), Y ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.20/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), Y ) ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.20/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ), X
% 1.20/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.20/1.62 ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ), X
% 1.20/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.20/1.62 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.20/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.62 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), Y ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.20/1.62 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.20/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.20/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.20/1.62 ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.20/1.62 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ) ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_Suc'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ) ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_Suc'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_Power_Opower__class_Opower'( Y, X ),
% 1.20/1.62 'c_Suc'( Z ) ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.62 ), X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X )
% 1.20/1.62 , 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X )
% 1.20/1.62 , 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), 'c_Suc'(
% 1.20/1.62 X ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( Y ) )
% 1.20/1.62 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( Y ) ) ) ) ],
% 1.20/1.62 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.20/1.62 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( T, U, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 Z, X ), U ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 'tc_nat' ), X ), Y ), Z, 'tc_nat' ) ), 'c_HOL_Oplus__class_Oplus'( hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ), U, 'tc_nat' ) )
% 1.20/1.62 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T
% 1.20/1.62 ) ), Y ), Z, 'tc_nat' ) ), U ) ), ~( hBOOL( hAPP( 'c_lessequals'( T,
% 1.20/1.62 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 'tc_nat' ), X ), Y ), Z, 'tc_nat' ) ), 'c_HOL_Oplus__class_Oplus'( hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ), U, 'tc_nat' ) )
% 1.20/1.62 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X
% 1.20/1.62 ) ), Y ), U, 'tc_nat' ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat'
% 1.20/1.62 ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, Y, X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, Y, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.20/1.62 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( U, X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), Y
% 1.20/1.62 ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Z, X ), Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( U, X ), T
% 1.20/1.62 ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( T, X ), U ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( T, X ), U ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.20/1.62 , Y ), Z ), Z, X ), Y ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X )
% 1.20/1.62 ), 'c_HOL_Oplus__class_Oplus'( T, U, X ) ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.62 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ), X ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X )
% 1.20/1.62 ), Z ), Y ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_Power_Opower__class_Opower'( Y, X ),
% 1.20/1.62 Z ), X ), hAPP( 'c_Power_Opower__class_Opower'( T, X ), Z ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.62 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_Power_Opower__class_Opower'( Y, X ),
% 1.20/1.62 Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.62 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.20/1.62 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), 'tc_nat' ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.20/1.62 ) ) ],
% 1.20/1.62 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.20/1.62 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ) ) ],
% 1.20/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.20/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.20/1.62 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.20/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.20/1.62 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.20/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.20/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.20/1.62 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.20/1.62 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.20/1.62 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.20/1.62 [ ~( =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ) ), Y ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ) ) ) ],
% 1.20/1.62 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) )
% 1.20/1.62 ) ],
% 1.20/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.62 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.62 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.62 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.62 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.62 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.20/1.62 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.20/1.62 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.20/1.62 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.62 'tc_nat' ), X ) ) ],
% 1.20/1.62 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), 'tc_nat' ) ) ],
% 1.20/1.62 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.20/1.62 ), 'tc_nat' ), X ) ],
% 1.20/1.62 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.20/1.62 , X, 'tc_nat' ), X ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X )
% 1.20/1.62 ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T, X,
% 1.20/1.62 X ), Z, T, X ) ) ],
% 1.20/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X )
% 1.20/1.62 ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T, X,
% 1.20/1.62 X ), Z, T, X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Fact_Ofact__class_Ofact'( Y,
% 1.20/1.62 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Fact_Ofact__class_Ofact'( Y,
% 1.20/1.62 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), Z ) ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), T ) ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.20/1.62 ), X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), Z ) )
% 1.20/1.62 ), hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), Z ) ), =( Y,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.20/1.62 , X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T ) ),
% 1.20/1.62 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), T ) ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( T, 'tc_nat' ), Z ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 X ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( hAPP( 'c_Power_Opower__class_Opower'( Y,
% 1.20/1.62 X ), Z ), X ), T ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ),
% 1.20/1.62 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( hAPP( 'c_Power_Opower__class_Opower'( Y
% 1.20/1.62 , X ), Z ), X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), Z ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), T ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), T ) ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Z, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( hAPP( 'c_Power_Opower__class_Opower'( Y,
% 1.20/1.62 X ), Z ), X ), T ), hAPP( 'c_Power_Opower__class_Opower'( Y, X ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_Suc'( Y ) ), 'tc_nat' )
% 1.20/1.62 , X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.62 Y ), Z ) ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.20/1.62 'c_ATP__Linkup_Osko__Nat__Xnat__diff__split__asm__1__1'( X, Y, Z ),
% 1.20/1.62 'tc_nat' ) ), ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.20/1.62 ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.62 Y ), Z ) ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.20/1.62 'c_ATP__Linkup_Osko__Nat__Xnat__diff__split__1__1'( X, Y, Z ), 'tc_nat' )
% 1.20/1.62 ), ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ =( 'c_Suc'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X )
% 1.20/1.62 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.62 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ ~( 'class_HOL_Oord'( X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'(
% 1.20/1.62 Y ) ), =( 'c_Finite__Set_Osetsum'( Z,
% 1.20/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( T, U, X ), X, Y ),
% 1.20/1.62 'c_Finite__Set_Osetsum'( W, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.62 T, U, X ), X, Y ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1'( T, U, Z, W, X, Y )
% 1.20/1.62 , X ), U ) ) ],
% 1.20/1.62 [ ~( 'class_HOL_Oord'( X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'(
% 1.20/1.62 Y ) ), =( 'c_Finite__Set_Osetsum'( Z,
% 1.20/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( T, U, X ), X, Y ),
% 1.20/1.62 'c_Finite__Set_Osetsum'( W, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.62 T, U, X ), X, Y ) ), hBOOL( hAPP( 'c_lessequals'( T, X ),
% 1.20/1.62 'c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1'( T, U, Z, W, X, Y )
% 1.20/1.62 ) ) ],
% 1.20/1.62 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'(
% 1.20/1.62 Y, 'c_Finite__Set_Osetsum'( Y,
% 1.20/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ), X ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Z, 'tc_nat' ),
% 1.20/1.62 'c_Series_Osko__Series__Xseries__zero__1__1'( Y, Z, X ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), Z ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'c_Suc'( X )
% 1.20/1.62 ), 'c_Suc'( Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.20/1.62 , X ), Y ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.62 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.20/1.62 ), 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ) ), Y ) ) ) ), hBOOL(
% 1.20/1.62 hAPP( X, Z ) ) ],
% 1.20/1.62 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.20/1.62 ), 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ) ), Y ) ) ) ), hBOOL(
% 1.20/1.62 hAPP( X, Z ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'c_Suc'( X ) ), Y ) ), 'c_Suc'(
% 1.20/1.62 Z ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Y ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X )
% 1.20/1.62 , Z ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.62 Y ), Z ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.62 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( X, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y
% 1.20/1.62 , 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X )
% 1.20/1.62 ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.62 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.62 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.62 Y, Z, 'tc_nat' ) ) ) ],
% 1.20/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.20/1.62 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, 'tc_nat' ), X ) ) ), =( X, Z ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.62 'tc_nat' ), X ), Y ), 'tc_nat' ), X ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y
% 1.20/1.62 , 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), X ), Y ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), Y ), X ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( 'c_Finite__Set_Osetsum'( Y,
% 1.20/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.20/1.62 , X ), 'c_Finite__Set_Osetsum'( Y,
% 1.20/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( T, U, 'tc_nat' ), 'tc_nat'
% 1.20/1.62 , X ), X ), 'c_Finite__Set_Osetsum'( Y,
% 1.20/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ), 'tc_nat'
% 1.20/1.62 , X ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), U ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( Z, 'tc_nat' ), T ) ) ) ],
% 1.20/1.62 [ ~( =( 'c_FFT__Mirabelle_Oroot'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_Complex_Ocomplex' ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , Y ), hAPP( 'c_Power_Opower__class_Opower'( Y, X ), Z ) ), X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.62 ), X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ) ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Z, X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.20/1.62 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.62 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.20/1.62 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( 'c_Power_Opower__class_Opower'( Z, X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), Z ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( T, X ), Z ) ) ), =( Y, T ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.62 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.62 'tc_nat' ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.62 'tc_nat' ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), Z ) ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), T ) ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( T, 'tc_nat' ), Z ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), Z ) ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( T, 'tc_nat' ), Z ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 X ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'c_Suc'( Z ) ), T ) ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T ) ) ), Y ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( T, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.20/1.62 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.62 Z, 'c_Suc'( T ), 'tc_nat' ), 'tc_nat', X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.62 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, 'tc_nat' ), Z ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ =( hAPP( 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'(
% 1.20/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ),
% 1.20/1.62 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 'tc_nat' ), X ), Z ) ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.20/1.62 'c_FFT__Mirabelle_Oroot'( Y ), 'tc_Complex_Ocomplex' ), Z ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.62 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.20/1.62 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.62 ), =( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), U ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) ), =( U,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.62 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , Z ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.20/1.62 ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.62 ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'(
% 1.20/1.62 'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X,
% 1.20/1.62 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.20/1.62 , ~( 'c_Series_Osums'( Z, T, X ) ) ],
% 1.20/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'(
% 1.20/1.62 'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X,
% 1.20/1.62 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.20/1.62 , ~( 'c_Series_Osums'( Z, T, X ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.20/1.62 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 1.20/1.62 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.20/1.62 ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.20/1.62 , X ) ), Z ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ],
% 1.20/1.62 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 1.20/1.62 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.20/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.20/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), Y ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ), X
% 1.20/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Z, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.20/1.62 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ), X
% 1.20/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_Power_Opower__class_Opower'( Y, X ),
% 1.20/1.62 Z ), X ), hAPP( 'c_Power_Opower__class_Opower'( Y, X ), T ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.20/1.62 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( T, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( 'c_Power_Opower__class_Opower'( Y, X ), Z ), X ),
% 1.20/1.62 hAPP( 'c_Power_Opower__class_Opower'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ), Y ) ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z
% 1.20/1.62 ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.20/1.62 , X ) ), Z ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), Y ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.20/1.62 ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.20/1.62 Y, X ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.62 X ), Z ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ), Y ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.20/1.62 , X ) ), Z ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X
% 1.20/1.62 ) ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T,
% 1.20/1.62 X, X ), Z, T, X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X
% 1.20/1.62 ) ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T,
% 1.20/1.62 X, X ), Z, T, X ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ) ), 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X,
% 1.20/1.62 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_Suc'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.20/1.62 X ) ) ],
% 1.20/1.62 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), T ) ) ],
% 1.20/1.62 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.20/1.62 X ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.20/1.62 X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.20/1.62 ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z
% 1.20/1.62 ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.20/1.62 ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z
% 1.20/1.62 ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.20/1.62 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OlessThan'(
% 1.20/1.62 'c_Suc'( Z ), 'tc_nat' ), 'tc_nat', X ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.62 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OlessThan'( Z,
% 1.20/1.62 'tc_nat' ), 'tc_nat', X ), hAPP( Y, Z ), X ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.62 Y ), Z ) ) ), ~( hBOOL( hAPP( X,
% 1.20/1.62 'c_ATP__Linkup_Osko__Nat__Xnat__diff__split__asm__1__1'( X, Y, Z ) ) ) )
% 1.20/1.62 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.20/1.62 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.62 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ), Y )
% 1.20/1.62 ) ],
% 1.20/1.62 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.20/1.62 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X
% 1.20/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.62 , X ) ), T ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X
% 1.20/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.62 , X ) ), T ), X ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.62 X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X
% 1.20/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.62 X ), T ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X
% 1.20/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.62 , X ) ), T ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.62 , X ) ), T ), X ), Z ) ) ) ],
% 1.20/1.62 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 'tc_nat' ), X ), Z ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Z ), T, 'tc_nat' )
% 1.20/1.62 , 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), T, 'tc_nat' ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.20/1.62 ) ) ],
% 1.20/1.62 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.62 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.62 'tc_nat' ), X ), Y ), 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.62 Y, Z, 'tc_nat' ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ), 'tc_nat' ), Y ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X, 'tc_nat'
% 1.20/1.62 ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.62 Y ), Z ) ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.20/1.62 'c_ATP__Linkup_Osko__Nat__Xnat__diff__split__1__1'( X, Y, Z ), 'tc_nat' )
% 1.20/1.62 ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), T, 'tc_nat' )
% 1.20/1.62 , 'tc_nat' ), U ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 'tc_nat' ), X ), Z ), T, 'tc_nat' ), 'tc_nat' ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 'tc_nat' ), Y ), Z ), U, 'tc_nat' ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 Y, 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ),
% 1.20/1.62 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ), U, 'tc_nat' ) ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ), Z, 'tc_nat' )
% 1.20/1.62 , 'tc_nat' ), U ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), X )
% 1.20/1.62 ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), T ), U, 'tc_nat' )
% 1.20/1.62 ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ), X, 'tc_nat' ),
% 1.20/1.62 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ), U, 'tc_nat' ) ) ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ),
% 1.20/1.62 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ), U, 'tc_nat' ) ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ), U, 'tc_nat' )
% 1.20/1.62 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), T ) ) ) ],
% 1.20/1.62 [ ~( =( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ), 'tc_nat' ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 'tc_nat' ), X ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.20/1.62 ), Z ), Y ), 'tc_nat' ) ) ), =( Y, T ), =( X, Z ) ],
% 1.20/1.62 [ ~( =( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ), 'tc_nat' ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 'tc_nat' ), X ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.20/1.62 ), Z ), Y ), 'tc_nat' ) ) ), =( Y, T ), =( X, Z ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.20/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.62 , X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.62 , X ) ), T ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ],
% 1.20/1.62 [ =( X, Y ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.20/1.62 'c_Suc'( Y ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' )
% 1.20/1.62 , Y ) ) ],
% 1.20/1.62 [ =( X, Y ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ),
% 1.20/1.62 'c_Suc'( X ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' )
% 1.20/1.62 , X ) ) ],
% 1.20/1.62 [ =( X, Y ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y )
% 1.20/1.62 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( Y
% 1.20/1.62 ) ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), 'tc_nat' ), X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.20/1.62 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.62 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X, 'tc_nat' ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.62 , X ) ), T ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.62 , X ) ), T ), X ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.62 , X ) ), T ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.62 , X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X, 'tc_nat'
% 1.20/1.62 ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.62 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), Z )
% 1.20/1.62 ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 X ), Z ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), Y )
% 1.20/1.62 ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.20/1.62 Z, 'tc_nat' ) ), Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y
% 1.20/1.62 ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.20/1.62 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ) ) ],
% 1.20/1.62 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.20/1.62 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.20/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ) ) ],
% 1.20/1.62 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), X ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), X ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z
% 1.20/1.62 , X ), Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.20/1.62 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.20/1.62 X, 'tc_nat' ) ), X ), Y ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 X ), X ), Y ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.62 X, Y, 'tc_nat' ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.62 X, Y, 'tc_nat' ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.62 Y, X, 'tc_nat' ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.62 X, Y, 'tc_nat' ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X )
% 1.20/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X )
% 1.20/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 1.20/1.62 , Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' )
% 1.20/1.62 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), T ) ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 1.20/1.62 , X ), X ), 'c_HOL_Oplus__class_Oplus'( T, U, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.20/1.62 ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.20/1.62 ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.20/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.20/1.62 ), Y ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X
% 1.20/1.62 ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ), =( Z,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.62 ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.20/1.62 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.20/1.62 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.20/1.62 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.20/1.62 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.20/1.62 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 X ), Y ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.62 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.62 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) )
% 1.20/1.62 ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.20/1.62 , Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) )
% 1.20/1.62 ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.20/1.62 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , Y ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ), X )
% 1.20/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , Y ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ), X )
% 1.20/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.62 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 X ), Z ), U ), X ) ) ), =( T, U ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.62 ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.20/1.62 ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.20/1.62 ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) )
% 1.20/1.62 ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) )
% 1.20/1.62 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) )
% 1.20/1.62 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 X ), X ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 X ), X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z )
% 1.20/1.62 , Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.20/1.62 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z )
% 1.20/1.62 , Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.20/1.62 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ), Z ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.20/1.62 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.20/1.62 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z
% 1.20/1.62 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), =( Z,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), =( Y,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.20/1.62 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Y ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.20/1.62 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.62 X ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.20/1.62 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.20/1.62 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( T, X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.20/1.62 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.20/1.62 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.62 X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.20/1.62 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.20/1.62 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.20/1.62 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.62 X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , T ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.20/1.62 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.20/1.62 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , T ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.20/1.62 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.20/1.62 , Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.20/1.62 , Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.20/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 Y, X ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , Y ), Z ), T, X ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ), W, X ) ) ), =( T,
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ), W, X )
% 1.20/1.62 ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , Y ), Z ), T, X ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ), W, X ) ) ), =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ), T, X )
% 1.20/1.62 , W ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , Y ), Z ), T, X ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ), T, X ), X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.20/1.62 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.20/1.62 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.20/1.62 , X ) ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , Y ), Z ), 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), T ), Y ) ), Z ), U, X ), X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , T ), Z ), U, X ) ) ],
% 1.20/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.62 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), U ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ), X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), T ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), T ) ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Z, X ), T ) ) ), =( Z,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( hAPP( 'c_Power_Opower__class_Opower'( Y
% 1.20/1.62 , X ), Z ), X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), Z ) ), =( Y,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.20/1.62 ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.20/1.62 'class_Power_Opower'( X ) ), =( hAPP( 'c_Power_Opower__class_Opower'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Suc'( Y ) ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( 'c_Power_Opower__class_Opower'( Y, X ), Z ), X ),
% 1.20/1.62 hAPP( 'c_Power_Opower__class_Opower'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), Z ), X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), Z ), X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.20/1.62 ), ~( =( hAPP( 'c_Power_Opower__class_Opower'( Y, X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.62 ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.20/1.62 'c_Finite__Set_Osetsum'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.20/1.62 'tc_bool' ) ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.20/1.62 Y, X ), Z ) ), Y ), hAPP( 'c_Power_Opower__class_Opower'( Y, X ), 'c_Suc'(
% 1.20/1.62 Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), Z ) ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), 'c_Suc'( Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.20/1.62 Y, X ), Z ) ), hAPP( 'c_Power_Opower__class_Opower'( Y, X ), T ) ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Z, T
% 1.20/1.62 , 'tc_nat' ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.20/1.62 Y, X ), Z ) ), Y ) ) ],
% 1.20/1.62 [ ~( 'class_Power_Opower'( X ) ), =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Z, T
% 1.20/1.62 , 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), Z ) ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Finite__Set_Osetsum'( Z, T, U
% 1.20/1.62 , X ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, U ), T, U, X ) ) ],
% 1.20/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Finite__Set_Osetsum'( Z, T, U
% 1.20/1.62 , X ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, U ), T, U, X ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.20/1.62 , X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) )
% 1.20/1.62 ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.20/1.62 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.62 ), X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.20/1.62 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.62 ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_lessequals'( U, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), U ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), 'c_Suc'( Z ) ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.20/1.62 ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.20/1.62 X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.20/1.62 X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.20/1.62 [ =( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ =( 'c_HOL_Oplus__class_Oplus'( X, hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ), 'tc_nat' ), Y ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.62 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), =( Y,
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.62 'tc_nat' ), Y ), X ), X, 'tc_nat' ) ) ],
% 1.20/1.62 [ =( 'c_HOL_Oplus__class_Oplus'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ), Y ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ =( 'c_HOL_Oplus__class_Oplus'( X, hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), Z ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ),
% 1.20/1.62 =( Z, T ) ],
% 1.20/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.20/1.62 hBOOL( hAPP( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.20/1.62 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.20/1.62 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.20/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 X ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), 'c_Suc'( Y ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_Suc'( X ), 'tc_nat' ), Y ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.20/1.62 ) ), 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.20/1.62 ) ), 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.20/1.62 Z, X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.20/1.62 Z, X ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Fact_Ofact__class_Ofact'( X
% 1.20/1.62 , 'tc_nat' ), 'tc_nat' ), 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ ~( hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( X ), 'tc_nat' ), X ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y
% 1.20/1.62 , 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.62 'tc_nat' ), X ), Z ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.20/1.62 , 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.62 ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ),
% 1.20/1.62 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.20/1.62 ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.20/1.62 ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.20/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_Power_Opower__class_Opower'( T, X ),
% 1.20/1.62 Y ), X ), hAPP( 'c_Power_Opower__class_Opower'( T, X ), Z ) ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X
% 1.20/1.62 ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_Power_Opower__class_Opower'( Y, X ),
% 1.20/1.62 Z ), X ), hAPP( 'c_Power_Opower__class_Opower'( Y, X ), T ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.20/1.62 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), T ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_Power_Opower__class_Opower'( T, X ),
% 1.20/1.62 Y ), X ), hAPP( 'c_Power_Opower__class_Opower'( T, X ), Z ) ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X
% 1.20/1.62 ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_Power_Opower__class_Opower'( Y, X ),
% 1.20/1.62 Z ), X ), hAPP( 'c_Power_Opower__class_Opower'( Y, X ), T ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.20/1.62 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.62 X ), T ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.62 X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ) ) ],
% 1.20/1.62 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.62 X, Y, 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.20/1.62 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.62 X, Y, 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ ~( =( hAPP( 'c_Power_Opower__class_Opower'( X, 'tc_nat' ), Y ),
% 1.20/1.62 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 1.20/1.62 'tc_nat' ), Y ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 1.20/1.62 , Y, 'tc_nat' ), 'tc_nat' ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.62 X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.62 ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), Y ) ) ),
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.62 X ), Z ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z
% 1.20/1.62 ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.20/1.62 , Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.20/1.62 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ),
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.62 X ), T ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T )
% 1.20/1.62 , 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), Y ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.20/1.62 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.62 ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.62 ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 X ), X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.62 ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 X ), X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.62 ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 1.20/1.62 , Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' )
% 1.20/1.62 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X,
% 1.20/1.62 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) )
% 1.20/1.62 ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 1.20/1.62 , Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' )
% 1.20/1.62 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.20/1.62 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( T, Y, X ), X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( T, Z, X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.20/1.62 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.20/1.62 Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 1.20/1.62 , X ), X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.20/1.62 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( Z, T, X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.20/1.62 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.20/1.62 Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( T, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 1.20/1.62 , X ), X ), 'c_HOL_Oplus__class_Oplus'( T, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ) ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_Suc'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), Y ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.20/1.62 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.20/1.62 , X ), Y ) ) ],
% 1.20/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.20/1.62 ), Y ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), X ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X
% 1.20/1.62 , 'tc_nat' ), Z ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), X ) ) ],
% 1.20/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 T, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) )
% 1.20/1.62 ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( 'c_lessequals'( U, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.20/1.62 , X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), Z ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X
% 1.20/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 Y, X ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) )
% 1.20/1.62 ) ],
% 1.20/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.20/1.62 ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X )
% 1.20/1.62 , 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.20/1.62 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.20/1.62 , X ) ), Z ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ), Y ) ) ), hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z
% 1.20/1.62 ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T )
% 1.20/1.62 , 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), Y ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.20/1.62 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.20/1.62 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.20/1.62 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.20/1.62 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), Z ) ) ) ],
% 1.20/1.62 [ =( X, Y ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.20/1.62 'c_Suc'( Y ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) )
% 1.20/1.62 ) ],
% 1.20/1.62 [ =( 'c_HOL_Oplus__class_Oplus'( X, hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ), 'tc_nat' ), Y ),
% 1.20/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( X ), 'tc_nat' ), 'c_Suc'( Y ) )
% 1.20/1.62 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_Suc'( X ), 'tc_nat' ), 'c_Suc'( Y ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'(
% 1.20/1.62 'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.20/1.62 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_Series_Osums'( Y
% 1.20/1.62 , T, X ) ) ],
% 1.20/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'(
% 1.20/1.62 'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.20/1.62 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_Series_Osums'( Y
% 1.20/1.62 , T, X ) ) ],
% 1.20/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.20/1.62 , X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z, X ), Y ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( Y, 'tc_nat' ), X ) ) ],
% 1.20/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Power_Opower'( X ) ), =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.20/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.20/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Fact_Ofact__class_Ofact'( Y,
% 1.20/1.62 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.20/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.20/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.20/1.62 Y, X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), X ) ),
% 1.20/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.62 'tc_nat' ), Y ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 X, 'tc_nat' ), Y ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 X, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.62 Y ), Z ) ) ), ~( hBOOL( hAPP( X,
% 1.20/1.62 'c_ATP__Linkup_Osko__Nat__Xnat__diff__split__1__1'( X, Y, Z ) ) ) ), ~(
% 1.20/1.62 hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.62 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X
% 1.20/1.62 ) ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.62 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.20/1.62 'tc_nat' ), X ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.62 Y ), Z ) ) ), ~( hBOOL( hAPP( X,
% 1.20/1.62 'c_ATP__Linkup_Osko__Nat__Xnat__diff__split__asm__1__1'( X, Y, Z ) ) ) )
% 1.20/1.62 , ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.20/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.20/1.62 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.62 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~( =( hAPP( Y,
% 1.20/1.62 'c_Series_Osko__Series__Xseries__zero__1__1'( Y, Z, X ) ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_Series_Osums'( Y,
% 1.20/1.62 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ), X )
% 1.20/1.62 ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.20/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, 'tc_nat' ), Z ), X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y,
% 1.20/1.62 X ), X ), Z ) ) ],
% 1.20/1.62 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.20/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_nat', 'tc_bool' ) ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 1.20/1.62 'c_SetInterval_Oord__class_OlessThan'( X, 'tc_nat' ) ) ],
% 1.20/1.62 [ ~( 'class_HOL_Oord'( X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'(
% 1.20/1.62 Y ) ), ~( =( hAPP( Z,
% 1.20/1.62 'c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1'( T, U, Z, W, X, Y )
% 1.20/1.62 ), hAPP( W, 'c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1'( T, U,
% 1.20/1.62 Z, W, X, Y ) ) ) ), =( 'c_Finite__Set_Osetsum'( Z,
% 1.20/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( T, U, X ), X, Y ),
% 1.20/1.62 'c_Finite__Set_Osetsum'( W, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.62 T, U, X ), X, Y ) ) ],
% 1.20/1.62 [ =( 'c_Finite__Set_Ocard'( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.62 X, Y, 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.62 'tc_nat' ), Y ), X ) ) ],
% 1.20/1.62 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.20/1.62 , 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'v_i', 'tc_nat' ), 'v_n' ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_Finite__Set_Osetsum'( Y,
% 1.20/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T
% 1.20/1.62 ), 'tc_nat' ), 'tc_nat', X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.20/1.62 Z, X ) ), U ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), U ) ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_Transcendental_Osko__Transcendental__Xreal__setsum__nat__ivl__bounded2__1__1'(
% 1.20/1.62 U, Y, Z, X ), 'tc_nat' ), Z ) ) ],
% 1.20/1.62 [ =( hAPP( 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'( X )
% 1.20/1.62 , 'tc_Complex_Ocomplex' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.20/1.62 'tc_Complex_Ocomplex' ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( 'c_Finite__Set_Osetsum'(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ),
% 1.20/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.20/1.62 Y, X ), Z ) ), 'c_HOL_Oone__class_Oone'( X ) ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ) )
% 1.20/1.62 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.20/1.62 ) ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.20/1.62 ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) ) ),
% 1.20/1.62 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.62 ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.62 ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( 'c_Power_Opower__class_Opower'( Y, X ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 X ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.20/1.62 ), =( hAPP( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 X ), X ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.20/1.62 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.20/1.62 'class_Power_Opower'( X ) ), =( hAPP( 'c_Power_Opower__class_Opower'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.20/1.62 Y, 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.20/1.62 'class_Power_Opower'( X ) ), =( hAPP( 'c_Power_Opower__class_Opower'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ) ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.20/1.62 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Z, X ),
% 1.20/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.20/1.62 ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.20/1.62 ],
% 1.20/1.62 [ =( 'c_Finite__Set_Osetsum'( 'c_Power_Opower__class_Opower'( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'( X ),
% 1.20/1.62 'tc_Complex_Ocomplex' ), Y ), 'tc_Complex_Ocomplex' ),
% 1.20/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), X, 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex' ),
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.62 'tc_nat' ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.20/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.20/1.62 Z, X ) ), T ) ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), 'tc_nat' ), T
% 1.20/1.62 , 'tc_nat', X, X ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 1.20/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.20/1.62 Y, X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.20/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.20/1.62 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.20/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ), 'tc_nat'
% 1.20/1.62 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.20/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( U, T, 'tc_nat' ), 'tc_nat'
% 1.20/1.62 , X ) ), ~( hBOOL( hAPP( 'c_lessequals'( U, 'tc_nat' ), T ) ) ), ~( hBOOL(
% 1.20/1.62 hAPP( 'c_lessequals'( Z, 'tc_nat' ), U ) ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'v_i' ), X ), 'tc_nat' ), 'v_n'
% 1.20/1.62 ) ) ],
% 1.20/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'v_i' ), 'tc_nat' ), 'v_n'
% 1.20/1.62 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'v_n' ) )
% 1.20/1.62 ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( 'c_Finite__Set_Osetsum'( Y,
% 1.20/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T
% 1.20/1.62 ), 'tc_nat' ), 'tc_nat', X ), X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.20/1.62 Z, X ) ), U ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), U ) ) ), ~( hBOOL( hAPP(
% 1.20/1.62 'c_lessequals'( hAPP( Y,
% 1.20/1.62 'c_Transcendental_Osko__Transcendental__Xreal__setsum__nat__ivl__bounded2__1__1'(
% 1.20/1.62 U, Y, Z, X ) ), X ), U ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y,
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.62 ) ), =( 'c_Finite__Set_Osetsum'( Y,
% 1.20/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_Suc'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_nat' ), 'tc_nat', X ),
% 1.20/1.62 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ) ]
% 1.20/1.62 ,
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.62 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.20/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.20/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.20/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.20/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.20/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.20/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.20/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.20/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.20/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.20/1.62 Y, X ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.20/1.62 hAPP( 'c_Power_Opower__class_Opower'( Y, X ), Z ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.20/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.62 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 X ), Y ), Z ), X ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.62 hAPP( 'c_Power_Opower__class_Opower'( Y, X ), T ) ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Z, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.62 X ), Y ), Z ), X ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.62 hAPP( 'c_Power_Opower__class_Opower'( Y, X ), T ) ), hAPP(
% 1.20/1.62 'c_Power_Opower__class_Opower'( Z, X ), T ) ) ) ],
% 1.20/1.62 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.20/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.20/1.62 'class_Power_Opower'( X ) ), =( hAPP( 'c_Power_Opower__class_Opower'(
% 1.20/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.62 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.20/1.62 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.20/1.62 ), =( hAPP( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.63 X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.20/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.63 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.20/1.63 =( hAPP( 'c_Power_Opower__class_Opower'( Y, X ), Z ),
% 1.20/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.63 ) ) ],
% 1.20/1.63 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.20/1.63 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.20/1.63 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.20/1.63 ), ~( =( hAPP( 'c_Power_Opower__class_Opower'( Y, X ), Z ),
% 1.20/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.63 ) ) ],
% 1.20/1.63 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.20/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.20/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.20/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ),
% 1.20/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.20/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.20/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.20/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.20/1.63 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.20/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.63 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.63 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.20/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.63 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.63 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.20/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.63 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.63 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.63 X ) ) ],
% 1.20/1.63 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.63 X ) ) ],
% 1.20/1.63 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.20/1.63 , Y ) ],
% 1.20/1.63 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.63 X ) ) ],
% 1.20/1.63 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.63 X ) ), =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ),
% 1.20/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.63 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), X ),
% 1.20/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.63 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.20/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.20/1.63 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.20/1.63 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.20/1.63 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.20/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.20/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.20/1.63 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.20/1.63 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.20/1.63 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.20/1.63 ), ~( =( hAPP( 'c_Power_Opower__class_Opower'( Y, X ),
% 1.20/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.63 ) ) ],
% 1.20/1.63 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ) ), =( Z, T ) ],
% 1.20/1.63 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( X ), T ), T ) ) ), =( Y, Z ) ],
% 1.20/1.63 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.63 'tc_nat' ) ) ],
% 1.20/1.63 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.63 X ) ) ), =( Y, Z ) ],
% 1.20/1.63 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.63 X ) ) ), =( Y, Z ) ],
% 1.20/1.63 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.63 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.20/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.20/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.20/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.20/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.20/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.20/1.63 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.63 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ) ],
% 1.20/1.63 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'v_i', 'tc_nat' ), 'v_n' ) ) ]
% 1.20/1.63 ,
% 1.20/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex'
% 1.20/1.63 ), 'c_Finite__Set_Osetsum'( 'c_Power_Opower__class_Opower'( hAPP(
% 1.20/1.63 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'( 'v_n' ),
% 1.20/1.63 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.63 'tc_nat' ), 'v_i' ), 'v_i' ) ), 'tc_Complex_Ocomplex' ),
% 1.20/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.63 'tc_nat' ), 'v_n', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex' ) ), 'v_a'(
% 1.20/1.63 'v_i' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.63 'tc_Complex_Ocomplex' ), 'c_Nat_Osemiring__1__class_Oof__nat'( 'v_n',
% 1.20/1.63 'tc_Complex_Ocomplex' ) ), 'v_a'( 'v_i' ) ) ) ) ],
% 1.20/1.63 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.20/1.63 'class_Orderings_Opreorder'( Y ) ) ],
% 1.20/1.63 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.20/1.63 'class_Orderings_Oorder'( Y ) ) ],
% 1.20/1.63 [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Obot'(
% 1.20/1.63 Y ) ) ],
% 1.20/1.63 [ 'class_HOL_Oord'( 'tc_fun'( X, Y ) ), ~( 'class_HOL_Oord'( Y ) ) ]
% 1.20/1.63 ,
% 1.20/1.63 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.20/1.63 ],
% 1.20/1.63 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.20/1.63 ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.20/1.63 ],
% 1.20/1.63 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.20/1.63 ,
% 1.20/1.63 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_HOL_Oord'( 'tc_nat' ) ],
% 1.20/1.63 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.20/1.63 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.20/1.63 [ 'class_Orderings_Obot'( 'tc_bool' ) ],
% 1.20/1.63 [ 'class_HOL_Oord'( 'tc_bool' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.20/1.63 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.20/1.63 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.20/1.63 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.20/1.63 ],
% 1.20/1.63 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.20/1.63 ],
% 1.20/1.63 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.20/1.63 ,
% 1.20/1.63 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.20/1.63 ,
% 1.20/1.63 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.20/1.63 ,
% 1.20/1.63 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.20/1.63 ,
% 1.20/1.63 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.20/1.63 ,
% 1.20/1.63 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.20/1.63 ,
% 1.20/1.63 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Nat_Osemiring__char__0'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_HOL_Oord'( 'tc_Int_Oint' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.20/1.63 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.20/1.63 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.20/1.63 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.20/1.63 ],
% 1.20/1.63 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.20/1.63 ],
% 1.20/1.63 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.20/1.63 ],
% 1.20/1.63 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.63 ,
% 1.20/1.63 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.63 ,
% 1.20/1.63 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.63 ,
% 1.20/1.63 [ 'class_RealVector_Oreal__normed__vector'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.63 ,
% 1.20/1.63 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.63 ,
% 1.20/1.63 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.63 ,
% 1.20/1.63 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.63 ,
% 1.20/1.63 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.63 ,
% 1.20/1.63 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.63 ,
% 1.20/1.63 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.63 ,
% 1.20/1.63 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.63 ,
% 1.20/1.63 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'class_RealVector_Oreal__field'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'class_Nat_Osemiring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.63 [ 'c_fequal'( X, X, Y ) ],
% 1.20/1.63 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.20/1.63 ] .
% 1.20/1.63
% 1.20/1.63
% 1.20/1.63 percentage equality = 0.188569, percentage horn = 0.819000
% 1.20/1.63 This is a problem with some equality
% 1.20/1.63
% 1.20/1.63
% 1.20/1.63
% 1.20/1.63 Options Used:
% 1.20/1.63
% 1.20/1.63 useres = 1
% 1.20/1.63 useparamod = 1
% 1.20/1.63 useeqrefl = 1
% 1.20/1.63 useeqfact = 1
% 1.20/1.63 usefactor = 1
% 1.24/1.63 usesimpsplitting = 0
% 1.24/1.63 usesimpdemod = 5
% 1.24/1.63 usesimpres = 3
% 1.24/1.63
% 1.24/1.63 resimpinuse = 1000
% 1.24/1.63 resimpclauses = 20000
% 1.24/1.63 substype = eqrewr
% 1.24/1.63 backwardsubs = 1
% 1.24/1.63 selectoldest = 5
% 1.24/1.63
% 1.24/1.63 litorderings [0] = split
% 1.24/1.63 litorderings [1] = extend the termordering, first sorting on arguments
% 1.24/1.63
% 1.24/1.63 termordering = kbo
% 1.24/1.63
% 1.24/1.63 litapriori = 0
% 1.24/1.63 termapriori = 1
% 1.24/1.63 litaposteriori = 0
% 1.24/1.63 termaposteriori = 0
% 1.24/1.63 demodaposteriori = 0
% 1.24/1.63 ordereqreflfact = 0
% 1.24/1.63
% 1.24/1.63 litselect = negord
% 1.24/1.63
% 1.24/1.63 maxweight = 15
% 1.24/1.63 maxdepth = 30000
% 1.24/1.63 maxlength = 115
% 1.24/1.63 maxnrvars = 195
% 1.24/1.63 excuselevel = 1
% 1.24/1.63 increasemaxweight = 1
% 1.24/1.63
% 1.24/1.63 maxselected = 10000000
% 1.24/1.63 maxnrclauses = 10000000
% 1.24/1.63
% 1.24/1.63 showgenerated = 0
% 1.24/1.63 showkept = 0
% 1.24/1.63 showselected = 0
% 1.24/1.63 showdeleted = 0
% 1.24/1.63 showresimp = 1
% 1.24/1.63 showstatus = 2000
% 1.24/1.63
% 1.24/1.63 prologoutput = 1
% 1.24/1.63 nrgoals = 5000000
% 1.24/1.63 totalproof = 1
% 1.24/1.63
% 1.24/1.63 Symbols occurring in the translation:
% 1.24/1.63
% 1.24/1.63 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.24/1.63 . [1, 2] (w:1, o:137, a:1, s:1, b:0),
% 1.24/1.63 ! [4, 1] (w:0, o:63, a:1, s:1, b:0),
% 1.24/1.63 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.24/1.63 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.24/1.63 'tc_nat' [42, 0] (w:1, o:17, a:1, s:1, b:0),
% 1.24/1.63 'c_HOL_Oplus__class_Oplus' [43, 3] (w:1, o:173, a:1, s:1, b:0),
% 1.24/1.63 'class_OrderedGroup_Oab__semigroup__add' [45, 1] (w:1, o:69, a:1, s:1
% 1.24/1.63 , b:0),
% 1.24/1.63 'class_Ring__and__Field_Ocomm__semiring__1' [49, 1] (w:1, o:70, a:1
% 1.24/1.63 , s:1, b:0),
% 1.24/1.63 'c_HOL_Ozero__class_Ozero' [51, 1] (w:1, o:71, a:1, s:1, b:0),
% 1.24/1.63 'c_HOL_Oord__class_Oless' [52, 2] (w:1, o:162, a:1, s:1, b:0),
% 1.24/1.63 hAPP [54, 2] (w:1, o:163, a:1, s:1, b:0),
% 1.24/1.63 hBOOL [55, 1] (w:1, o:72, a:1, s:1, b:0),
% 1.24/1.63 'c_lessequals' [57, 2] (w:1, o:164, a:1, s:1, b:0),
% 1.24/1.63 'c_COMBB' [65, 5] (w:1, o:182, a:1, s:1, b:0),
% 1.24/1.63 'c_COMBC' [67, 5] (w:1, o:183, a:1, s:1, b:0),
% 1.24/1.63 'class_Orderings_Opreorder' [68, 1] (w:1, o:74, a:1, s:1, b:0),
% 1.24/1.63 'class_Orderings_Olinorder' [69, 1] (w:1, o:75, a:1, s:1, b:0),
% 1.24/1.63 'c_HOL_Ominus__class_Ominus' [70, 1] (w:1, o:76, a:1, s:1, b:0),
% 1.24/1.63 'c_Suc' [71, 1] (w:1, o:77, a:1, s:1, b:0),
% 1.24/1.63 'c_Fact_Ofact__class_Ofact' [72, 2] (w:1, o:165, a:1, s:1, b:0),
% 1.24/1.63 'c_HOL_Otimes__class_Otimes' [73, 1] (w:1, o:78, a:1, s:1, b:0),
% 1.24/1.63 'class_Ring__and__Field_Ofield' [74, 1] (w:1, o:79, a:1, s:1, b:0),
% 1.24/1.63 'c_HOL_Oinverse__class_Odivide' [75, 1] (w:1, o:80, a:1, s:1, b:0),
% 1.24/1.63 'c_HOL_Oone__class_Oone' [76, 1] (w:1, o:81, a:1, s:1, b:0),
% 1.24/1.63 'class_Ring__and__Field_Odivision__by__zero' [77, 1] (w:1, o:83, a:1
% 1.24/1.63 , s:1, b:0),
% 1.24/1.63 'class_Ring__and__Field_Oordered__field' [78, 1] (w:1, o:86, a:1, s:1
% 1.24/1.63 , b:0),
% 1.24/1.63 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [79, 1]
% 1.24/1.63 (w:1, o:87, a:1, s:1, b:0),
% 1.24/1.63 'class_OrderedGroup_Ocomm__monoid__add' [80, 1] (w:1, o:88, a:1, s:1
% 1.24/1.63 , b:0),
% 1.24/1.63 'class_Ring__and__Field_Osemiring' [81, 1] (w:1, o:93, a:1, s:1, b:0)
% 1.24/1.63 ,
% 1.24/1.63 'class_Int_Onumber' [82, 1] (w:1, o:95, a:1, s:1, b:0),
% 1.24/1.63 'c_Int_Onumber__class_Onumber__of' [84, 2] (w:1, o:167, a:1, s:1, b:0
% 1.24/1.63 ),
% 1.24/1.63 'c_HOL_Oinverse__class_Oinverse' [85, 2] (w:1, o:166, a:1, s:1, b:0)
% 1.24/1.63 ,
% 1.24/1.63 'class_OrderedGroup_Oab__group__add' [86, 1] (w:1, o:96, a:1, s:1, b:
% 1.24/1.63 0),
% 1.24/1.63 'class_Orderings_Oorder' [87, 1] (w:1, o:73, a:1, s:1, b:0),
% 1.24/1.63 'class_OrderedGroup_Opordered__comm__monoid__add' [89, 1] (w:1, o:97
% 1.24/1.63 , a:1, s:1, b:0),
% 1.24/1.63 'c_Nat_Osemiring__1__class_Oof__nat' [90, 2] (w:1, o:168, a:1, s:1
% 1.24/1.63 , b:0),
% 1.24/1.63 'class_Ring__and__Field_Odivision__ring' [91, 1] (w:1, o:98, a:1, s:1
% 1.24/1.63 , b:0),
% 1.24/1.63 'class_Ring__and__Field_Oordered__semidom' [92, 1] (w:1, o:100, a:1
% 1.24/1.63 , s:1, b:0),
% 1.24/1.63 'c_Power_Opower__class_Opower' [93, 2] (w:1, o:169, a:1, s:1, b:0),
% 1.24/1.63 'class_Int_Onumber__ring' [94, 1] (w:1, o:101, a:1, s:1, b:0),
% 1.24/1.63 'class_Orderings_Obot' [96, 1] (w:1, o:102, a:1, s:1, b:0),
% 1.24/1.63 'c_Orderings_Obot__class_Obot' [97, 1] (w:1, o:103, a:1, s:1, b:0),
% 1.24/1.63 'class_Ring__and__Field_Oordered__idom' [98, 1] (w:1, o:104, a:1, s:1
% 1.24/1.63 , b:0),
% 1.24/1.63 'class_OrderedGroup_Olordered__ab__group__add' [99, 1] (w:1, o:105
% 9.33/9.77 , a:1, s:1, b:0),
% 9.33/9.77 'c_SetInterval_Oord__class_OlessThan' [100, 2] (w:1, o:170, a:1, s:1
% 9.33/9.77 , b:0),
% 9.33/9.77 'tc_bool' [101, 0] (w:1, o:42, a:1, s:1, b:0),
% 9.33/9.77 'tc_fun' [102, 2] (w:1, o:171, a:1, s:1, b:0),
% 9.33/9.77 'class_Int_Oring__char__0' [103, 1] (w:1, o:106, a:1, s:1, b:0),
% 9.33/9.77 'c_SetInterval_Oord__class_OatLeastLessThan' [104, 3] (w:1, o:174, a:
% 9.33/9.77 1, s:1, b:0),
% 9.33/9.77 'c_Finite__Set_Ocard' [105, 2] (w:1, o:172, a:1, s:1, b:0),
% 9.33/9.77 'c_ATP__Linkup_Osko__Nat__Xnat__diff__split__1__1' [106, 3] (w:1, o:
% 9.33/9.77 175, a:1, s:1, b:0),
% 9.33/9.77 'class_RealVector_Oreal__normed__field' [107, 1] (w:1, o:107, a:1, s:
% 9.33/9.77 1, b:0),
% 9.33/9.77 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [109, 1]
% 9.33/9.77 (w:1, o:108, a:1, s:1, b:0),
% 9.33/9.77 'class_Ring__and__Field_Ozero__neq__one' [110, 1] (w:1, o:109, a:1
% 9.33/9.77 , s:1, b:0),
% 9.33/9.77 'class_Ring__and__Field_Oidom' [111, 1] (w:1, o:110, a:1, s:1, b:0),
% 9.33/9.77
% 9.33/9.77 'class_OrderedGroup_Omonoid__add' [112, 1] (w:1, o:111, a:1, s:1, b:0
% 9.33/9.77 ),
% 9.33/9.77 'class_Ring__and__Field_Oordered__semiring__strict' [113, 1] (w:1, o:
% 9.33/9.77 112, a:1, s:1, b:0),
% 9.33/9.77 'v_n' [114, 0] (w:1, o:43, a:1, s:1, b:0),
% 9.33/9.77 'class_OrderedGroup_Opordered__ab__semigroup__add' [115, 1] (w:1, o:
% 9.33/9.77 113, a:1, s:1, b:0),
% 9.33/9.77 'c_ATP__Linkup_Osko__Nat__Xnat__diff__split__asm__1__1' [116, 3] (w:1
% 9.33/9.77 , o:176, a:1, s:1, b:0),
% 9.33/9.77 'c_Finite__Set_Osetsum' [119, 4] (w:1, o:180, a:1, s:1, b:0),
% 9.33/9.77 'class_Ring__and__Field_Osemiring__1' [120, 1] (w:1, o:115, a:1, s:1
% 9.33/9.77 , b:0),
% 9.33/9.77 'class_Ring__and__Field_Oordered__ring__strict' [121, 1] (w:1, o:99
% 9.33/9.77 , a:1, s:1, b:0),
% 9.33/9.77 'class_Ring__and__Field_Oordered__semiring' [122, 1] (w:1, o:116, a:1
% 9.33/9.77 , s:1, b:0),
% 9.33/9.77 'class_Ring__and__Field_Ocomm__semiring' [123, 1] (w:1, o:82, a:1, s:
% 9.33/9.77 1, b:0),
% 9.33/9.77 'class_RealVector_Oreal__normed__algebra' [124, 1] (w:1, o:117, a:1
% 9.33/9.77 , s:1, b:0),
% 9.33/9.77 'class_OrderedGroup_Omonoid__mult' [128, 1] (w:1, o:118, a:1, s:1, b:
% 9.33/9.77 0),
% 9.33/9.77 'class_OrderedGroup_Ocomm__monoid__mult' [129, 1] (w:1, o:119, a:1
% 9.33/9.77 , s:1, b:0),
% 9.33/9.77 'class_Ring__and__Field_Opordered__ring' [131, 1] (w:1, o:121, a:1
% 9.33/9.77 , s:1, b:0),
% 9.33/9.77 'class_RealVector_Oreal__field' [132, 1] (w:1, o:122, a:1, s:1, b:0)
% 9.33/9.77 ,
% 9.33/9.77 'c_Series_Osums' [135, 3] (w:1, o:177, a:1, s:1, b:0),
% 9.33/9.77 'class_OrderedGroup_Ocancel__ab__semigroup__add' [137, 1] (w:1, o:123
% 9.33/9.77 , a:1, s:1, b:0),
% 9.33/9.77 'class_OrderedGroup_Ocancel__semigroup__add' [138, 1] (w:1, o:124, a:
% 9.33/9.77 1, s:1, b:0),
% 9.33/9.77 'class_OrderedGroup_Opordered__ab__group__add' [140, 1] (w:1, o:125
% 9.33/9.77 , a:1, s:1, b:0),
% 9.33/9.77 'class_OrderedGroup_Ogroup__add' [143, 1] (w:1, o:126, a:1, s:1, b:0)
% 9.33/9.77 ,
% 9.33/9.77 'class_Ring__and__Field_Osemiring__0' [145, 1] (w:1, o:114, a:1, s:1
% 9.33/9.77 , b:0),
% 9.33/9.77 'class_HOL_Oord' [150, 1] (w:1, o:94, a:1, s:1, b:0),
% 9.33/9.77 'c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1' [151, 6] (w:1
% 9.33/9.77 , o:184, a:1, s:1, b:0),
% 9.33/9.77 'class_RealVector_Oreal__normed__vector' [152, 1] (w:1, o:127, a:1
% 9.33/9.77 , s:1, b:0),
% 9.33/9.77 'c_Series_Osko__Series__Xseries__zero__1__1' [153, 3] (w:1, o:178, a:
% 9.33/9.77 1, s:1, b:0),
% 9.33/9.77 'c_FFT__Mirabelle_Oroot' [154, 1] (w:1, o:128, a:1, s:1, b:0),
% 9.33/9.77 'tc_Complex_Ocomplex' [155, 0] (w:1, o:53, a:1, s:1, b:0),
% 9.33/9.77 'class_Power_Opower' [156, 1] (w:1, o:131, a:1, s:1, b:0),
% 9.33/9.77 'class_Ring__and__Field_Opordered__cancel__semiring' [158, 1] (w:1
% 9.33/9.77 , o:132, a:1, s:1, b:0),
% 9.33/9.77 'class_Ring__and__Field_Opordered__semiring' [159, 1] (w:1, o:133, a:
% 9.33/9.77 1, s:1, b:0),
% 9.33/9.77 'class_Ring__and__Field_Omult__mono' [160, 1] (w:1, o:134, a:1, s:1
% 9.33/9.77 , b:0),
% 9.33/9.77 'class_Ring__and__Field_Omult__mono1' [161, 1] (w:1, o:135, a:1, s:1
% 9.33/9.77 , b:0),
% 9.33/9.77 'class_Ring__and__Field_Oordered__comm__semiring__strict' [162, 1]
% 9.33/9.77 (w:1, o:120, a:1, s:1, b:0),
% 9.33/9.77 'class_Ring__and__Field_Oring' [163, 1] (w:1, o:89, a:1, s:1, b:0),
% 9.33/9.77 'class_Ring__and__Field_Ono__zero__divisors' [164, 1] (w:1, o:85, a:1
% 9.33/9.77 , s:1, b:0),
% 9.33/9.77 'class_Ring__and__Field_Omult__zero' [165, 1] (w:1, o:84, a:1, s:1
% 9.33/9.77 , b:0),
% 9.33/9.77 'class_Nat_Osemiring__char__0' [166, 1] (w:1, o:68, a:1, s:1, b:0),
% 9.33/9.77 'v_i' [167, 0] (w:1, o:55, a:1, s:1, b:0),
% 61.55/61.95
% 61.55/61.95 'c_Transcendental_Osko__Transcendental__Xreal__setsum__nat__ivl__bounded2__1__1'
% 61.55/61.95 [169, 4] (w:1, o:181, a:1, s:1, b:0),
% 61.55/61.95 'class_Ring__and__Field_Oring__1' [170, 1] (w:1, o:90, a:1, s:1, b:0)
% 61.55/61.95 ,
% 61.55/61.95 'class_Ring__and__Field_Oring__no__zero__divisors' [171, 1] (w:1, o:
% 61.55/61.95 91, a:1, s:1, b:0),
% 61.55/61.95 'class_OrderedGroup_Oab__semigroup__mult' [176, 1] (w:1, o:129, a:1
% 61.55/61.95 , s:1, b:0),
% 61.55/61.95 'class_OrderedGroup_Oab__semigroup__idem__mult' [177, 1] (w:1, o:130
% 61.55/61.95 , a:1, s:1, b:0),
% 61.55/61.95 'class_Ring__and__Field_Oring__1__no__zero__divisors' [178, 1] (w:1
% 61.55/61.95 , o:92, a:1, s:1, b:0),
% 61.55/61.95 'v_a' [179, 1] (w:1, o:136, a:1, s:1, b:0),
% 61.55/61.95 'tc_Int_Oint' [182, 0] (w:1, o:61, a:1, s:1, b:0),
% 61.55/61.95 'c_fequal' [183, 3] (w:1, o:179, a:1, s:1, b:0).
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Starting Search:
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 4935
% 61.55/61.95 Kept: 2064
% 61.55/61.95 Inuse: 157
% 61.55/61.95 Deleted: 3
% 61.55/61.95 Deletedinuse: 0
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 13836
% 61.55/61.95 Kept: 5319
% 61.55/61.95 Inuse: 339
% 61.55/61.95 Deleted: 19
% 61.55/61.95 Deletedinuse: 0
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 19500
% 61.55/61.95 Kept: 7641
% 61.55/61.95 Inuse: 437
% 61.55/61.95 Deleted: 19
% 61.55/61.95 Deletedinuse: 0
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 25145
% 61.55/61.95 Kept: 9890
% 61.55/61.95 Inuse: 495
% 61.55/61.95 Deleted: 29
% 61.55/61.95 Deletedinuse: 3
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 32029
% 61.55/61.95 Kept: 11941
% 61.55/61.95 Inuse: 520
% 61.55/61.95 Deleted: 29
% 61.55/61.95 Deletedinuse: 3
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 41039
% 61.55/61.95 Kept: 15286
% 61.55/61.95 Inuse: 595
% 61.55/61.95 Deleted: 30
% 61.55/61.95 Deletedinuse: 4
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 50985
% 61.55/61.95 Kept: 17684
% 61.55/61.95 Inuse: 615
% 61.55/61.95 Deleted: 31
% 61.55/61.95 Deletedinuse: 5
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 58354
% 61.55/61.95 Kept: 20194
% 61.55/61.95 Inuse: 673
% 61.55/61.95 Deleted: 38
% 61.55/61.95 Deletedinuse: 10
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95 Resimplifying clauses:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 63841
% 61.55/61.95 Kept: 22202
% 61.55/61.95 Inuse: 700
% 61.55/61.95 Deleted: 466
% 61.55/61.95 Deletedinuse: 10
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 70569
% 61.55/61.95 Kept: 24547
% 61.55/61.95 Inuse: 713
% 61.55/61.95 Deleted: 466
% 61.55/61.95 Deletedinuse: 10
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 76818
% 61.55/61.95 Kept: 26610
% 61.55/61.95 Inuse: 723
% 61.55/61.95 Deleted: 466
% 61.55/61.95 Deletedinuse: 10
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 84405
% 61.55/61.95 Kept: 28828
% 61.55/61.95 Inuse: 773
% 61.55/61.95 Deleted: 466
% 61.55/61.95 Deletedinuse: 10
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 91213
% 61.55/61.95 Kept: 30880
% 61.55/61.95 Inuse: 808
% 61.55/61.95 Deleted: 469
% 61.55/61.95 Deletedinuse: 13
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 97653
% 61.55/61.95 Kept: 32918
% 61.55/61.95 Inuse: 853
% 61.55/61.95 Deleted: 469
% 61.55/61.95 Deletedinuse: 13
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 104762
% 61.55/61.95 Kept: 36309
% 61.55/61.95 Inuse: 863
% 61.55/61.95 Deleted: 469
% 61.55/61.95 Deletedinuse: 13
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 139146
% 61.55/61.95 Kept: 38758
% 61.55/61.95 Inuse: 873
% 61.55/61.95 Deleted: 469
% 61.55/61.95 Deletedinuse: 13
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95 Resimplifying clauses:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 146453
% 61.55/61.95 Kept: 41675
% 61.55/61.95 Inuse: 883
% 61.55/61.95 Deleted: 672
% 61.55/61.95 Deletedinuse: 13
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 163717
% 61.55/61.95 Kept: 45103
% 61.55/61.95 Inuse: 938
% 61.55/61.95 Deleted: 672
% 61.55/61.95 Deletedinuse: 13
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 176173
% 61.55/61.95 Kept: 47955
% 61.55/61.95 Inuse: 944
% 61.55/61.95 Deleted: 672
% 61.55/61.95 Deletedinuse: 13
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 184059
% 61.55/61.95 Kept: 49979
% 61.55/61.95 Inuse: 963
% 61.55/61.95 Deleted: 672
% 61.55/61.95 Deletedinuse: 13
% 61.55/61.95
% 61.55/61.95 Resimplifying inuse:
% 61.55/61.95 Done
% 61.55/61.95
% 61.55/61.95
% 61.55/61.95 Intermediate Status:
% 61.55/61.95 Generated: 196838
% 136.30/136.75 Kept: 52195
% 136.30/136.75 Inuse: 983
% 136.30/136.75 Deleted: 672
% 136.30/136.75 Deletedinuse: 13
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 215088
% 136.30/136.75 Kept: 55051
% 136.30/136.75 Inuse: 993
% 136.30/136.75 Deleted: 672
% 136.30/136.75 Deletedinuse: 13
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 234015
% 136.30/136.75 Kept: 57921
% 136.30/136.75 Inuse: 1003
% 136.30/136.75 Deleted: 672
% 136.30/136.75 Deletedinuse: 13
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 243481
% 136.30/136.75 Kept: 60138
% 136.30/136.75 Inuse: 1033
% 136.30/136.75 Deleted: 672
% 136.30/136.75 Deletedinuse: 13
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75 Resimplifying clauses:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 252349
% 136.30/136.75 Kept: 62333
% 136.30/136.75 Inuse: 1063
% 136.30/136.75 Deleted: 1108
% 136.30/136.75 Deletedinuse: 13
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 261457
% 136.30/136.75 Kept: 64525
% 136.30/136.75 Inuse: 1093
% 136.30/136.75 Deleted: 1108
% 136.30/136.75 Deletedinuse: 13
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 291322
% 136.30/136.75 Kept: 69465
% 136.30/136.75 Inuse: 1108
% 136.30/136.75 Deleted: 1108
% 136.30/136.75 Deletedinuse: 13
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 300031
% 136.30/136.75 Kept: 71765
% 136.30/136.75 Inuse: 1123
% 136.30/136.75 Deleted: 1108
% 136.30/136.75 Deletedinuse: 13
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 309983
% 136.30/136.75 Kept: 74056
% 136.30/136.75 Inuse: 1148
% 136.30/136.75 Deleted: 1108
% 136.30/136.75 Deletedinuse: 13
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 318721
% 136.30/136.75 Kept: 76148
% 136.30/136.75 Inuse: 1173
% 136.30/136.75 Deleted: 1108
% 136.30/136.75 Deletedinuse: 13
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 342203
% 136.30/136.75 Kept: 79687
% 136.30/136.75 Inuse: 1183
% 136.30/136.75 Deleted: 1108
% 136.30/136.75 Deletedinuse: 13
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75 Resimplifying clauses:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 352371
% 136.30/136.75 Kept: 82044
% 136.30/136.75 Inuse: 1198
% 136.30/136.75 Deleted: 1332
% 136.30/136.75 Deletedinuse: 14
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 367228
% 136.30/136.75 Kept: 85166
% 136.30/136.75 Inuse: 1203
% 136.30/136.75 Deleted: 1332
% 136.30/136.75 Deletedinuse: 14
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 382455
% 136.30/136.75 Kept: 88275
% 136.30/136.75 Inuse: 1208
% 136.30/136.75 Deleted: 1332
% 136.30/136.75 Deletedinuse: 14
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 395081
% 136.30/136.75 Kept: 91656
% 136.30/136.75 Inuse: 1213
% 136.30/136.75 Deleted: 1332
% 136.30/136.75 Deletedinuse: 14
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 407807
% 136.30/136.75 Kept: 94926
% 136.30/136.75 Inuse: 1218
% 136.30/136.75 Deleted: 1332
% 136.30/136.75 Deletedinuse: 14
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 420490
% 136.30/136.75 Kept: 98290
% 136.30/136.75 Inuse: 1223
% 136.30/136.75 Deleted: 1332
% 136.30/136.75 Deletedinuse: 14
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 450733
% 136.30/136.75 Kept: 104834
% 136.30/136.75 Inuse: 1238
% 136.30/136.75 Deleted: 1332
% 136.30/136.75 Deletedinuse: 14
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75 Resimplifying clauses:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 485464
% 136.30/136.75 Kept: 110272
% 136.30/136.75 Inuse: 1253
% 136.30/136.75 Deleted: 1394
% 136.30/136.75 Deletedinuse: 14
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 495467
% 136.30/136.75 Kept: 113140
% 136.30/136.75 Inuse: 1268
% 136.30/136.75 Deleted: 1394
% 136.30/136.75 Deletedinuse: 14
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 502289
% 136.30/136.75 Kept: 115203
% 136.30/136.75 Inuse: 1278
% 136.30/136.75 Deleted: 1394
% 136.30/136.75 Deletedinuse: 14
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 509209
% 136.30/136.75 Kept: 117240
% 136.30/136.75 Inuse: 1288
% 136.30/136.75 Deleted: 1394
% 136.30/136.75 Deletedinuse: 14
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 521170
% 136.30/136.75 Kept: 119925
% 136.30/136.75 Inuse: 1303
% 136.30/136.75 Deleted: 1394
% 136.30/136.75 Deletedinuse: 14
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 530846
% 136.30/136.75 Kept: 122266
% 136.30/136.75 Inuse: 1308
% 136.30/136.75 Deleted: 1394
% 136.30/136.75 Deletedinuse: 14
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75
% 136.30/136.75 Intermediate Status:
% 136.30/136.75 Generated: 565127
% 136.30/136.75 Kept: 126599
% 136.30/136.75 Inuse: 1318
% 136.30/136.75 Deleted: 1394
% 136.30/136.75 Deletedinuse: 14
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75 Resimplifying clauses:
% 136.30/136.75 Done
% 136.30/136.75
% 136.30/136.75 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 578365
% 224.55/225.00 Kept: 129585
% 224.55/225.00 Inuse: 1333
% 224.55/225.00 Deleted: 1579
% 224.55/225.00 Deletedinuse: 14
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 591475
% 224.55/225.00 Kept: 132862
% 224.55/225.00 Inuse: 1343
% 224.55/225.00 Deleted: 1579
% 224.55/225.00 Deletedinuse: 14
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 600506
% 224.55/225.00 Kept: 135134
% 224.55/225.00 Inuse: 1348
% 224.55/225.00 Deleted: 1579
% 224.55/225.00 Deletedinuse: 14
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 609675
% 224.55/225.00 Kept: 137415
% 224.55/225.00 Inuse: 1353
% 224.55/225.00 Deleted: 1579
% 224.55/225.00 Deletedinuse: 14
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 619133
% 224.55/225.00 Kept: 139729
% 224.55/225.00 Inuse: 1363
% 224.55/225.00 Deleted: 1579
% 224.55/225.00 Deletedinuse: 14
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 625116
% 224.55/225.00 Kept: 141789
% 224.55/225.00 Inuse: 1373
% 224.55/225.00 Deleted: 1579
% 224.55/225.00 Deletedinuse: 14
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 633311
% 224.55/225.00 Kept: 144356
% 224.55/225.00 Inuse: 1388
% 224.55/225.00 Deleted: 1579
% 224.55/225.00 Deletedinuse: 14
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 642069
% 224.55/225.00 Kept: 146962
% 224.55/225.00 Inuse: 1403
% 224.55/225.00 Deleted: 1579
% 224.55/225.00 Deletedinuse: 14
% 224.55/225.00
% 224.55/225.00 Resimplifying clauses:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 651955
% 224.55/225.00 Kept: 148977
% 224.55/225.00 Inuse: 1413
% 224.55/225.00 Deleted: 1763
% 224.55/225.00 Deletedinuse: 14
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 661207
% 224.55/225.00 Kept: 151751
% 224.55/225.00 Inuse: 1428
% 224.55/225.00 Deleted: 1763
% 224.55/225.00 Deletedinuse: 14
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 670333
% 224.55/225.00 Kept: 154387
% 224.55/225.00 Inuse: 1443
% 224.55/225.00 Deleted: 1763
% 224.55/225.00 Deletedinuse: 14
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 681554
% 224.55/225.00 Kept: 157232
% 224.55/225.00 Inuse: 1448
% 224.55/225.00 Deleted: 1763
% 224.55/225.00 Deletedinuse: 14
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 693171
% 224.55/225.00 Kept: 160104
% 224.55/225.00 Inuse: 1453
% 224.55/225.00 Deleted: 1763
% 224.55/225.00 Deletedinuse: 14
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 704361
% 224.55/225.00 Kept: 163042
% 224.55/225.00 Inuse: 1458
% 224.55/225.00 Deleted: 1763
% 224.55/225.00 Deletedinuse: 14
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 715086
% 224.55/225.00 Kept: 166033
% 224.55/225.00 Inuse: 1463
% 224.55/225.00 Deleted: 1763
% 224.55/225.00 Deletedinuse: 14
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00 Resimplifying clauses:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 725895
% 224.55/225.00 Kept: 169165
% 224.55/225.00 Inuse: 1473
% 224.55/225.00 Deleted: 1919
% 224.55/225.00 Deletedinuse: 14
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 780138
% 224.55/225.00 Kept: 176131
% 224.55/225.00 Inuse: 1478
% 224.55/225.00 Deleted: 1919
% 224.55/225.00 Deletedinuse: 14
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 789466
% 224.55/225.00 Kept: 178135
% 224.55/225.00 Inuse: 1491
% 224.55/225.00 Deleted: 1919
% 224.55/225.00 Deletedinuse: 14
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 804959
% 224.55/225.00 Kept: 180429
% 224.55/225.00 Inuse: 1513
% 224.55/225.00 Deleted: 1923
% 224.55/225.00 Deletedinuse: 18
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 813498
% 224.55/225.00 Kept: 182528
% 224.55/225.00 Inuse: 1524
% 224.55/225.00 Deleted: 1923
% 224.55/225.00 Deletedinuse: 18
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 826914
% 224.55/225.00 Kept: 184586
% 224.55/225.00 Inuse: 1552
% 224.55/225.00 Deleted: 1946
% 224.55/225.00 Deletedinuse: 40
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 834513
% 224.55/225.00 Kept: 186601
% 224.55/225.00 Inuse: 1562
% 224.55/225.00 Deleted: 1947
% 224.55/225.00 Deletedinuse: 41
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00 Resimplifying clauses:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 870507
% 224.55/225.00 Kept: 190235
% 224.55/225.00 Inuse: 1567
% 224.55/225.00 Deleted: 34258
% 224.55/225.00 Deletedinuse: 41
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 877623
% 224.55/225.00 Kept: 192593
% 224.55/225.00 Inuse: 1577
% 224.55/225.00 Deleted: 34258
% 224.55/225.00 Deletedinuse: 41
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00 Resimplifying inuse:
% 224.55/225.00 Done
% 224.55/225.00
% 224.55/225.00
% 224.55/225.00 Intermediate Status:
% 224.55/225.00 Generated: 885414
% 224.55/225.00 Kept: 194743
% 224.55/225.00 Inuse: 1587
% 224.55/225.00 Deleted: 34258
% 224.55/225.00 Deletedinuse: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------