TSTP Solution File: SWV636-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV636-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.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 16:27:19 EDT 2022
% Result : Unknown 6.07s 6.51s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV636-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Tue Jun 14 17:41:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.14/1.51 *** allocated 10000 integers for termspace/termends
% 1.14/1.51 *** allocated 10000 integers for clauses
% 1.14/1.51 *** allocated 10000 integers for justifications
% 1.14/1.51 *** allocated 15000 integers for termspace/termends
% 1.14/1.51 *** allocated 22500 integers for termspace/termends
% 1.14/1.51 *** allocated 33750 integers for termspace/termends
% 1.14/1.51 Bliksem 1.12
% 1.14/1.51
% 1.14/1.51
% 1.14/1.51 Automatic Strategy Selection
% 1.14/1.51
% 1.14/1.51 Clauses:
% 1.14/1.51 [
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.14/1.51 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.51 ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.14/1.51 ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.14/1.51 ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.14/1.51 ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.14/1.51 ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.14/1.51 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.14/1.51 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.14/1.51 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.14/1.51 , ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.14/1.51 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.51 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.14/1.51 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.14/1.51 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.14/1.51 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.14/1.51 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.51 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.14/1.51 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.51 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.51 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.14/1.51 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.14/1.51 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.14/1.51 ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.14/1.51 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.14/1.51 ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.14/1.51 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.14/1.51 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.14/1.51 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.14/1.51 ) ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.14/1.51 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.14/1.51 ) ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.14/1.51 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.14/1.51 , X ) ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.14/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.14/1.51 , X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 Y, T, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.14/1.51 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 Y, T, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.14/1.51 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.14/1.51 X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 Z, T, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.14/1.51 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 Z, T, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.14/1.51 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.14/1.51 X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.14/1.51 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.14/1.51 ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.14/1.51 ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.14/1.51 ],
% 1.14/1.51 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.14/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.14/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.14/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.14/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.14/1.51 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.14/1.51 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.14/1.51 , X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.14/1.51 ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.51 ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.51 , X ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.14/1.51 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.14/1.51 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.14/1.51 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.14/1.51 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 1.14/1.51 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.14/1.51 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 1.14/1.51 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), Y,
% 1.14/1.51 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 1.14/1.51 , X ), Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y, X )
% 1.14/1.51 , X ), Z ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.14/1.51 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.14/1.51 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OMin', 'tc_Int_Oint' ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OMin',
% 1.14/1.51 'tc_Int_Oint' ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OMin',
% 1.14/1.51 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OMin',
% 1.14/1.51 'tc_Int_Oint' ) ) ],
% 1.14/1.51 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.14/1.51 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.14/1.51 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 1.14/1.51 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.14/1.51 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.14/1.51 , 'c_Power_Opower__class_Opower'( Y, Z, X ) ), ~(
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), T
% 1.14/1.51 , X ), 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.14/1.51 X ), Z, X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.14/1.51 ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.14/1.51 ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.14/1.51 ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.14/1.51 ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.14/1.51 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.14/1.51 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.14/1.51 Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X )
% 1.14/1.51 , 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.14/1.51 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.14/1.51 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.14/1.51 ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.14/1.51 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.14/1.51 ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.14/1.51 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.14/1.51 ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.14/1.51 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.14/1.51 ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.14/1.51 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.14/1.51 ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.14/1.51 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.14/1.51 ) ) ],
% 1.14/1.51 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.14/1.51 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.14/1.51 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.14/1.51 ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.14/1.51 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.14/1.51 ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.14/1.51 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.14/1.51 ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.14/1.51 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.14/1.51 , T, X ), X ), T, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.14/1.51 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 1.14/1.51 [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.14/1.51 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'(
% 1.14/1.51 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.14/1.51 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.51 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.14/1.51 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.14/1.51 , X ), Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.14/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Y, T, X ),
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 1.14/1.51 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Odiv'(
% 1.14/1.51 X, 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.14/1.51 ), 'tc_nat' ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' )
% 1.14/1.51 ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.14/1.51 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.14/1.51 X, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.14/1.51 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.14/1.51 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.14/1.51 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.14/1.51 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 1.14/1.51 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.51 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.14/1.51 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.51 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.14/1.51 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.14/1.51 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.14/1.51 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.14/1.51 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.14/1.51 , T, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.14/1.51 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.14/1.51 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.51 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.14/1.51 ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 1.14/1.51 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( T, X ), X ), X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.14/1.51 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.14/1.51 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.14/1.51 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y, X ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 1.14/1.51 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.14/1.51 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 1.14/1.51 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), =( Y, X ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ],
% 1.14/1.51 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.14/1.51 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 1.14/1.51 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.14/1.51 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.14/1.51 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.14/1.51 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.14/1.51 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.14/1.51 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.14/1.51 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.14/1.51 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.14/1.51 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.14/1.51 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.14/1.51 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.14/1.51 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.14/1.51 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.14/1.51 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.14/1.51 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.14/1.51 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.14/1.51 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.14/1.51 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ),
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) )
% 1.14/1.51 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.14/1.51 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.51 ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( T, 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), X
% 1.14/1.51 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Z, 'c_Divides_Odiv__class_Odiv'( Y, T, X ), X
% 1.14/1.51 ) ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.14/1.51 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Z,
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), T, X ) ), =( T,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.14/1.51 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), Z, X ) ), =( Z,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.51 ), X ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.51 X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.51 X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~( 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_Divides_Osemiring__div'( X )
% 1.14/1.51 ), ~( =( 'c_Divides_Odiv__class_Omod'(
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.51 Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.14/1.51 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_Divides_Osemiring__div'( X )
% 1.14/1.51 ), =( 'c_Divides_Odiv__class_Omod'( 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.51 Y, X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.51 Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 1.14/1.51 , X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 1.14/1.51 , X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.14/1.51 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.14/1.51 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 1.14/1.51 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 1.14/1.51 X ), Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 1.14/1.51 , X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.14/1.51 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.14/1.51 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.14/1.51 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.14/1.51 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.14/1.51 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.14/1.51 , T, X ), X ), T, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.14/1.51 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.14/1.51 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.14/1.51 ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.14/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.14/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.14/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.14/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.14/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.14/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.14/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.14/1.51 , X ), Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.14/1.51 , X ), Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.14/1.51 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.14/1.51 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.14/1.51 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 1.14/1.51 , 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 1.14/1.51 , X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.14/1.51 , Y, X ), X ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.14/1.51 , Z, X ), X ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.14/1.51 , Z, X ), X ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.14/1.51 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.14/1.51 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.14/1.51 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.14/1.51 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.14/1.51 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.14/1.51 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.14/1.51 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.14/1.51 , T, X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.51 Y, T, X ), Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.14/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oone__class_Oone'( X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.51 ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 1.14/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Z, Y, X ),
% 1.14/1.51 'c_HOL_Oone__class_Oone'( X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.51 ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.14/1.51 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.14/1.51 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), X
% 1.14/1.51 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), Z
% 1.14/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.51 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ),
% 1.14/1.51 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.14/1.51 ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.14/1.51 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.14/1.51 ), X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.14/1.51 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Z, Y, X
% 1.14/1.51 ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.14/1.51 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.14/1.51 ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( T ), X ),
% 1.14/1.51 'c_Power_Opower__class_Opower'( Z, 'c_Suc'( T ), X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_Power_Opower__class_Opower'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.51 ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), X ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.14/1.51 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.14/1.51 'c_Power_Opower__class_Opower'( T, 'c_Suc'( Z ), X ) ) ), =( Y, T ), ~(
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.14/1.51 Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z
% 1.14/1.51 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.14/1.51 ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.14/1.51 ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.14/1.51 'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.14/1.51 ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.14/1.51 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.14/1.51 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oabs__class_Oabs'(
% 1.14/1.51 Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.14/1.51 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.14/1.51 ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.14/1.51 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.14/1.51 X ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.14/1.51 ],
% 1.14/1.51 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), Y, X ),
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.14/1.51 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.51 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.14/1.51 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( T, X ), X ) ), ~(
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.14/1.51 ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.14/1.51 ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.14/1.51 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.14/1.51 X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.14/1.51 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.14/1.51 ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.14/1.51 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.14/1.51 X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.14/1.51 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.14/1.51 ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.14/1.51 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Odiv'( Y, Z,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( T, U, X ), X ),
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( U, T, X ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.14/1.51 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 1.14/1.51 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.14/1.51 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.14/1.51 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.14/1.51 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'(
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' )
% 1.14/1.51 , 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.14/1.51 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.14/1.51 T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X ) ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.14/1.51 ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.14/1.51 ) ) ],
% 1.14/1.51 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y,
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z, X ),
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z, X ),
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Y ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( Z, Y, X ), X ),
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Z, Y, X ), X ), Z ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.14/1.51 ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Odiv'(
% 1.14/1.51 Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.14/1.51 'c_HOL_Ouminus__class_Ouminus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.14/1.51 X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Odiv'(
% 1.14/1.51 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.14/1.51 'c_HOL_Ouminus__class_Ouminus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.14/1.51 X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.14/1.51 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( X, Z, 'tc_nat'
% 1.14/1.51 ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ),
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ), 'tc_nat' ), Z, 'tc_nat' )
% 1.14/1.51 , 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' )
% 1.14/1.51 , 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.14/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.14/1.51 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.14/1.51 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' )
% 1.14/1.51 , 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.14/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.14/1.51 Y, 'tc_nat' ), 'tc_nat' ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.14/1.51 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.14/1.51 Y, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.14/1.51 'tc_nat' ) ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.14/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ) ],
% 1.14/1.51 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), 'c_Suc'( 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.14/1.51 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.14/1.51 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 1.14/1.51 X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, T
% 1.14/1.51 , X ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, Z
% 1.14/1.51 , X ), 'c_Divides_Odiv__class_Odiv'( T, Z, X ), X ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.14/1.51 'c_lessequals'( Y, Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.14/1.51 'c_lessequals'( Y, Z, X ) ) ],
% 1.14/1.51 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ],
% 1.14/1.51 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 1.14/1.51 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.14/1.51 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.14/1.51 X ) ) ), =( Z, T ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.14/1.51 X ) ) ), =( Z, T ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.14/1.51 X ) ) ), =( Y, T ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.51 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.51 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.51 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ],
% 1.14/1.51 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.14/1.51 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.14/1.51 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.14/1.51 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.51 X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.14/1.51 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 1.14/1.51 [ =( 'c_Suc'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Odiv'(
% 1.14/1.51 X, 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.14/1.51 ), 'tc_nat' ) ), X ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' )
% 1.14/1.51 ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.14/1.51 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.51 'tc_nat' ) ), Y, 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat'
% 1.14/1.51 ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.51 'tc_nat' ) ), Y, 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.14/1.51 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OPls', 'tc_Int_Oint' )
% 1.14/1.51 ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.14/1.51 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 1.14/1.51 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 1.14/1.51 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), T, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y, X )
% 1.14/1.51 , X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ), X ), T, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Z, T, X ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 'tc_Int_Oint' ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit0'( X ),
% 1.14/1.51 'tc_Int_Oint' ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit0'( X ),
% 1.14/1.51 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X,
% 1.14/1.51 'tc_Int_Oint' ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 'tc_Int_Oint' ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit1'( X ),
% 1.14/1.51 'tc_Int_Oint' ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit1'( X ),
% 1.14/1.51 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X,
% 1.14/1.51 'tc_Int_Oint' ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.14/1.51 X ) ) ],
% 1.14/1.51 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.14/1.51 X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.14/1.51 X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.51 ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.51 ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.51 ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.51 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ),
% 1.14/1.51 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.14/1.51 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.14/1.51 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.14/1.51 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.51 'tc_nat' ), 'tc_nat' ) ],
% 1.14/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.51 'tc_nat' ), 'tc_nat' ) ],
% 1.14/1.51 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.14/1.51 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.14/1.51 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.14/1.51 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.51 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.51 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.14/1.51 ), 'tc_nat' ), X ) ],
% 1.14/1.51 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.14/1.51 , X, 'tc_nat' ), X ) ],
% 1.14/1.51 [ =( 'c_Int_OBit1'( 'c_Int_OMin' ), 'c_Int_OMin' ) ],
% 1.14/1.51 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OMin' ) ), =( X, 'c_Int_OMin' ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( =( 'c_Int_OMin', 'c_Int_OBit1'( X ) ) ), =( 'c_Int_OMin', X ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.14/1.51 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.14/1.51 'tc_Int_Oint' ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.14/1.51 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.14/1.51 'tc_Int_Oint' ) ) ],
% 1.14/1.51 [ =( 'c_Int_OMin', 'c_Int_OBit1'( 'c_Int_OMin' ) ) ],
% 1.14/1.51 [ ~( =( 'c_Int_OPls', 'c_Int_OMin' ) ) ],
% 1.14/1.51 [ ~( =( 'c_Int_OMin', 'c_Int_OPls' ) ) ],
% 1.14/1.51 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OPls',
% 1.14/1.51 'tc_Int_Oint' ) ) ],
% 1.14/1.51 [ ~( =( 'c_Int_OMin', 'c_Int_OBit0'( X ) ) ) ],
% 1.14/1.51 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OMin' ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.14/1.51 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.14/1.51 'tc_Int_Oint' ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.14/1.51 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.14/1.51 'tc_Int_Oint' ) ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ),
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.14/1.51 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ),
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ),
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.14/1.51 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ),
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.14/1.51 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.14/1.51 'c_Int_OPls' ) ), 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.14/1.51 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.14/1.51 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.14/1.51 , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.14/1.51 'c_Int_OPls' ) ), 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.14/1.51 , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.14/1.51 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.14/1.51 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.14/1.51 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.14/1.51 , 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.14/1.51 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.14/1.51 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.14/1.51 , 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.51 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.14/1.51 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.14/1.51 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.14/1.51 Z, T, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 1.14/1.51 , 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X
% 1.14/1.51 ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.14/1.51 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.14/1.51 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.14/1.51 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.51 , 'tc_nat' ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.14/1.51 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 1.14/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.14/1.51 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.14/1.51 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 1.14/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.14/1.51 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), Z ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Z, Y, X ), X ), Z ) ],
% 1.14/1.51 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.14/1.51 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.14/1.51 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 1.14/1.51 X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.14/1.51 , X ), Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.14/1.51 , X ), Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.14/1.51 Z, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.14/1.51 Z, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.14/1.51 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.14/1.51 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.14/1.51 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.14/1.51 Y, X ), Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.51 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.14/1.51 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.14/1.51 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ), Z ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.51 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.14/1.51 , X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.14/1.51 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 1.14/1.51 ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.14/1.51 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.14/1.51 Z, X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.14/1.51 Y, Z, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.14/1.51 , Z ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.51 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.14/1.51 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.51 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.14/1.51 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.14/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.51 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat'
% 1.14/1.51 ), 'tc_nat' ) ],
% 1.14/1.51 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat' ) ), 'tc_nat' ) )
% 1.14/1.51 ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.14/1.51 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.14/1.51 ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.14/1.51 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.14/1.51 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.14/1.51 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.14/1.51 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.14/1.51 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.14/1.51 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.14/1.51 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.14/1.51 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.14/1.51 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 X, T, 'tc_nat' ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.14/1.51 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 1.14/1.51 ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.14/1.51 ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 1.14/1.51 Y, 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 1.14/1.51 ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.14/1.51 ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 1.14/1.51 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( Y, X,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.14/1.51 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'(
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.14/1.51 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 1.14/1.51 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 1.14/1.51 , T ), =( X, Z ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.51 ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.14/1.51 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.51 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.14/1.51 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.14/1.51 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.14/1.51 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 1.14/1.51 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 1.14/1.51 Z, X ) ) ],
% 1.14/1.51 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Power_Opower__class_Opower'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.14/1.51 T, X ), 'c_Divides_Odiv__class_Odiv'( 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.51 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), Y,
% 1.14/1.51 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 Y, X, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.14/1.51 , Y, 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'( Y,
% 1.14/1.51 X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.14/1.51 Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.14/1.51 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.14/1.51 ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.14/1.51 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.14/1.51 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.14/1.51 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_Int_Oint' ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.14/1.51 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.14/1.51 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.14/1.51 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.14/1.51 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OMin',
% 1.14/1.51 'tc_Int_Oint' ) ) ],
% 1.14/1.51 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.51 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( T,
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Y, U, 'tc_nat' ), 'tc_nat' ) ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 1.14/1.51 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), 'c_Suc'( 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.14/1.51 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.14/1.51 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.14/1.51 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.14/1.51 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.14/1.51 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OMin',
% 1.14/1.51 'tc_Int_Oint' ) ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.14/1.51 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 1.14/1.51 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.51 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 1.14/1.51 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.14/1.51 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.14/1.51 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.14/1.51 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.14/1.51 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.14/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 1.14/1.51 , X ), X ), Y ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.14/1.51 Y, X ), X ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.14/1.51 'c_lessequals'( Z, Y, X ) ],
% 1.14/1.51 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.51 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.14/1.51 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.51 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.14/1.51 'c_Power_Opower__class_Opower'( 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.51 'c_Int_OMin', X ), Y, X ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.14/1.51 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), Y, X ),
% 1.14/1.51 'c_HOL_Oone__class_Oone'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y
% 1.14/1.51 , 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.51 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), Y, X ),
% 1.14/1.51 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.14/1.51 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.14/1.51 , 'tc_nat' ), 'tc_nat' ), 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.51 X ), X ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Z,
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.51 , 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.51 X ), 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ), X ), ~(
% 1.14/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.51 , 'tc_nat' ), 'tc_nat' ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ), X ), ~(
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.51 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.14/1.51 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ =( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.14/1.51 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z
% 1.14/1.51 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' )
% 1.14/1.51 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.14/1.51 , Z, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.14/1.51 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( 'c_Divides_Odiv__class_Odiv'( Y
% 1.14/1.51 , X, 'tc_nat' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.14/1.51 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ),
% 1.14/1.51 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.14/1.51 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.14/1.51 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.14/1.51 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.14/1.51 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.14/1.51 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.51 X, Y, 'tc_nat' ) ), X, 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) )
% 1.14/1.51 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 1.14/1.51 'tc_nat' ) ) ],
% 1.14/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.14/1.51 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.14/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.51 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X
% 1.14/1.51 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.51 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.14/1.51 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.14/1.51 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.14/1.51 , X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.14/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.14/1.51 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.14/1.51 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.14/1.51 , X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.14/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.14/1.51 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.51 X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.14/1.51 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.14/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 1.14/1.51 ,
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.51 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.14/1.51 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.14/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.14/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.14/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.14/1.51 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.14/1.51 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.14/1.51 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 1.14/1.51 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 1.14/1.51 , T ), =( X, Z ) ],
% 1.14/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 1.14/1.51 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X,
% 1.14/1.51 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 1.14/1.51 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.14/1.51 'tc_nat' ) ) ],
% 1.14/1.51 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 1.14/1.51 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.14/1.51 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.14/1.51 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.14/1.51 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.14/1.51 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.14/1.51 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 1.14/1.51 ],
% 1.14/1.51 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.14/1.51 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.14/1.51 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.14/1.51 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.14/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.14/1.51 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.51 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.14/1.51 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z,
% 1.14/1.51 Y, 'tc_nat' ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.14/1.52 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 1.14/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.14/1.52 'tc_nat' ), Z, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z
% 1.14/1.52 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 1.14/1.52 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.52 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.14/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oone__class_Oone'(
% 1.14/1.52 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.52 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'(
% 1.14/1.52 'tc_nat' ), X, 'tc_nat' ) ],
% 1.14/1.52 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'(
% 1.14/1.52 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ],
% 1.14/1.52 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.14/1.52 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.14/1.52 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.14/1.52 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.14/1.52 [ ~( =( 'c_Complex_Oii', 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex'
% 1.14/1.52 ) ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.52 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.14/1.52 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.52 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~(
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.14/1.52 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.14/1.52 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.14/1.52 ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.14/1.52 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.14/1.52 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.52 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.14/1.52 ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.14/1.52 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.14/1.52 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.14/1.52 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.14/1.52 ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.14/1.52 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.14/1.52 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.14/1.52 ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.14/1.52 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.14/1.52 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.52 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.14/1.52 ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.14/1.52 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.14/1.52 ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.14/1.52 ), X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.14/1.52 , X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.14/1.52 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' )
% 1.14/1.52 ), 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.14/1.52 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.14/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.14/1.52 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.14/1.52 Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.14/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.52 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.52 , T, X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.14/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.52 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.52 , T, X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.14/1.52 ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.14/1.52 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ),
% 1.14/1.52 ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X
% 1.14/1.52 ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.14/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.14/1.52 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.14/1.52 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X
% 1.14/1.52 ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.14/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.14/1.52 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.14/1.52 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.52 , Z, X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.14/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.14/1.52 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.52 , Z, X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.14/1.52 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.14/1.52 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.14/1.52 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.14/1.52 , Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.14/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.52 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 Y, T, X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.14/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.52 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 Y, T, X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.14/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.14/1.52 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.14/1.52 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.14/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.14/1.52 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.14/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.14/1.52 X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 X ), T, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.14/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.14/1.52 Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.14/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.14/1.52 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.14/1.52 X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.14/1.52 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.14/1.52 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.14/1.52 Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.14/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.14/1.52 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.14/1.52 Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.14/1.52 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.14/1.52 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 1.14/1.52 X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.14/1.52 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.14/1.52 , T, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.14/1.52 , Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.14/1.52 , T, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.14/1.52 , Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.14/1.52 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.14/1.52 , T, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.14/1.52 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.14/1.52 , Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 1.14/1.52 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.14/1.52 ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.14/1.52 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 X ), T, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 1.14/1.52 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.14/1.52 ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.14/1.52 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.14/1.52 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.14/1.52 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.14/1.52 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.14/1.52 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.14/1.52 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.14/1.52 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.14/1.52 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.14/1.52 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.14/1.52 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( T, X )
% 1.14/1.52 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.14/1.52 , Z, X ), Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , X ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.14/1.52 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.14/1.52 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.52 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 1.14/1.52 , X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.52 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 1.14/1.52 , X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.14/1.52 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.14/1.52 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ), Z ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.14/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.14/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ],
% 1.14/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.52 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.52 , X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.52 , X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.14/1.52 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.52 , X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.14/1.52 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.52 , X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.14/1.52 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.14/1.52 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.14/1.52 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.14/1.52 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.14/1.52 , Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.14/1.52 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.14/1.52 , T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.14/1.52 ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.14/1.52 , Z, X ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.14/1.52 ), ~( 'c_lessequals'( T, Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.14/1.52 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.14/1.52 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.14/1.52 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.14/1.52 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.14/1.52 , X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.14/1.52 , X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.14/1.52 , X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.14/1.52 , X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.14/1.52 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.14/1.52 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.14/1.52 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.14/1.52 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.14/1.52 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.14/1.52 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.14/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.52 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.14/1.52 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.52 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.14/1.52 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 1.14/1.52 , X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.14/1.52 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.14/1.52 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.52 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 1.14/1.52 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.52 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 1.14/1.52 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.52 ), =( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.14/1.52 , U, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( U,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.14/1.52 , U, X ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.14/1.52 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.14/1.52 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.14/1.52 ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.14/1.52 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.52 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.14/1.52 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.14/1.52 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.14/1.52 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.14/1.52 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.14/1.52 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.14/1.52 , X ), X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.14/1.52 ), X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 Y, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), T, X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , X ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.14/1.52 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.14/1.52 ), X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), T, X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.52 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), T, X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.14/1.52 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.52 , X ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.14/1.52 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.14/1.52 ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.14/1.52 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.14/1.52 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.14/1.52 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.14/1.52 ), X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.14/1.52 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 X ), T, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 1.14/1.52 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.14/1.52 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.14/1.52 ), X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 Y, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), T, X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.14/1.52 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.14/1.52 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'( Z,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.14/1.52 , X ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.14/1.52 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.52 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.14/1.52 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.14/1.52 , X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.14/1.52 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.14/1.52 ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.14/1.52 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.52 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.14/1.52 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 1.14/1.52 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 1.14/1.52 ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_Int_Oint' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.14/1.52 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.14/1.52 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.14/1.52 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.14/1.52 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.14/1.52 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.14/1.52 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.14/1.52 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.14/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.52 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.14/1.52 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.14/1.52 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , X ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.14/1.52 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ) ), =( Z,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.14/1.52 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.14/1.52 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.14/1.52 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.14/1.52 , T, X ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.14/1.52 ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.14/1.52 ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.14/1.52 ), X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.14/1.52 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.14/1.52 ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.14/1.52 ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.14/1.52 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.14/1.52 ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.14/1.52 ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y, X ), ~( 'c_lessequals'( Z,
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), =( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.14/1.52 Z, 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.14/1.52 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.14/1.52 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.14/1.52 Z, T, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.52 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Z, Y, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.14/1.52 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.14/1.52 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.14/1.52 ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.14/1.52 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.14/1.52 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.14/1.52 ) ],
% 1.14/1.52 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.14/1.52 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.14/1.52 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.14/1.52 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.14/1.52 ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ),
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.14/1.52 ), X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), Y, X ),
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 Y, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ),
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ),
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.14/1.52 , X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.14/1.52 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ),
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OMin', X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.14/1.52 ), Y ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.14/1.52 ), Y ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Z,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), X )
% 1.14/1.52 ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ),
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ),
% 1.14/1.52 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.14/1.52 ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.14/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Power_Opower__class_Opower'(
% 1.14/1.52 Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.14/1.52 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.14/1.52 , ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.14/1.52 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' )
% 1.14/1.52 ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 1.14/1.52 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.14/1.52 ) ), X, 'tc_nat' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.14/1.52 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.14/1.52 ) ), X, 'tc_nat' ) ) ],
% 1.14/1.52 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 1.14/1.52 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.14/1.52 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.14/1.52 'tc_nat' ) ) ],
% 1.14/1.52 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.14/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 1.14/1.52 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.14/1.52 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.14/1.52 , Z, 'tc_nat' ) ) ],
% 1.14/1.52 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.14/1.52 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.52 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.14/1.52 'tc_nat' ), X, 'tc_nat' ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.14/1.52 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.14/1.52 'tc_nat' ), Y, 'tc_nat' ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 1.14/1.52 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.14/1.52 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.14/1.52 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.14/1.52 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.14/1.52 'tc_nat' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.14/1.52 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 1.14/1.52 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.52 'c_Suc'( 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' )
% 1.14/1.52 ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), 'c_Suc'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), Y, 'tc_nat' )
% 1.14/1.52 ), X ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.14/1.52 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.14/1.52 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.14/1.52 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.14/1.52 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.14/1.52 , T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.14/1.52 , T, X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.14/1.52 , T, X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.14/1.52 , T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), T, X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.14/1.52 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.14/1.52 ), X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.14/1.52 ), X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.14/1.52 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.14/1.52 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T
% 1.14/1.52 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.14/1.52 ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.14/1.52 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.14/1.52 , Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.14/1.52 , Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.14/1.52 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.14/1.52 ), X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.14/1.52 ), X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.14/1.52 ), X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.14/1.52 ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.14/1.52 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T
% 1.14/1.52 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.14/1.52 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T
% 1.14/1.52 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.14/1.52 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.14/1.52 ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.14/1.52 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 T, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.14/1.52 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) )
% 1.14/1.52 ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.14/1.52 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) )
% 1.14/1.52 ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_OPls'
% 1.14/1.52 , Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.14/1.52 ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.14/1.52 ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z
% 1.14/1.52 ), X ), 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), X ) ), ~(
% 1.14/1.52 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.14/1.52 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.14/1.52 ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.14/1.52 , X ), X ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) )
% 1.14/1.52 ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , 'tc_nat' ), X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.14/1.52 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , 'tc_nat' ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.14/1.52 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , 'tc_nat' ), 'tc_nat' ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.14/1.52 X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Z
% 1.14/1.52 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.14/1.52 , T, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.14/1.52 X ) ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 1.14/1.52 , X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.14/1.52 ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X
% 1.14/1.52 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X
% 1.14/1.52 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.14/1.52 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.14/1.52 ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.14/1.52 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.14/1.52 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.14/1.52 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.14/1.52 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.14/1.52 Z, T, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.14/1.52 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.14/1.52 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.14/1.52 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.14/1.52 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.14/1.52 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.14/1.52 ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.14/1.52 ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.14/1.52 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.14/1.52 ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.14/1.52 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'( Y
% 1.14/1.52 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ), Y ) ],
% 1.14/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), Y, X ), Y ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.14/1.52 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.14/1.52 Y, T, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.14/1.52 ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.52 'c_Suc'( Z ), X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.14/1.52 Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.14/1.52 ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, T, X ), X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.14/1.52 'tc_nat' ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.14/1.52 ), X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.14/1.52 Y, X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.52 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.14/1.52 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.14/1.52 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.14/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.14/1.52 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.14/1.52 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.14/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'(
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), Y, X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.14/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.14/1.52 ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.14/1.52 , X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.14/1.52 'tc_Int_Oint' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.14/1.52 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.14/1.52 'tc_Int_Oint' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.14/1.52 'tc_Int_Oint' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.14/1.52 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.14/1.52 'tc_Int_Oint' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.14/1.52 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.14/1.52 'tc_Int_Oint' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.14/1.52 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.14/1.52 'tc_Int_Oint' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.14/1.52 'tc_Int_Oint' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.14/1.52 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X,
% 1.14/1.52 'tc_Int_Oint' ) ) ],
% 1.14/1.52 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.14/1.52 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 1.14/1.52 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.14/1.52 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.14/1.52 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.14/1.52 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.14/1.52 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.14/1.52 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.14/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' )
% 1.14/1.52 , 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.14/1.52 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.14/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' )
% 1.14/1.52 ) ],
% 1.14/1.52 [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ), ~(
% 1.14/1.52 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.14/1.52 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X, X,
% 1.14/1.52 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.14/1.52 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.14/1.52 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.14/1.52 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.14/1.52 ) ],
% 1.14/1.52 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', 'tc_nat' ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.52 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.14/1.52 , Y, 'tc_nat' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.14/1.52 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.14/1.52 'c_Suc'( X ), 'tc_nat' ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.14/1.52 'c_Suc'( X ), 'tc_nat' ) ],
% 1.14/1.52 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.14/1.52 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.14/1.52 ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.14/1.52 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X
% 1.14/1.52 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.52 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.14/1.52 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.14/1.52 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.14/1.52 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) )
% 1.14/1.52 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.14/1.52 , 'tc_nat' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.14/1.52 'tc_nat' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.14/1.52 'tc_nat' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.14/1.52 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.14/1.52 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.14/1.52 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.14/1.52 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z
% 1.14/1.52 , X ), 'c_Power_Opower__class_Opower'( Y, Z, X ) ), ~(
% 1.14/1.52 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.14/1.52 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'(
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ),
% 1.14/1.52 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 1.14/1.52 ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z
% 1.14/1.52 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_Power_Opower__class_Opower'( Y
% 1.14/1.52 , Z, X ), X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.14/1.52 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), =( Z,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.14/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 1.14/1.52 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.14/1.52 ) ],
% 1.14/1.52 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.14/1.52 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.14/1.52 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.14/1.52 'tc_nat' ), 'tc_nat' ) ],
% 1.14/1.52 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.14/1.52 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.52 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T )
% 1.14/1.52 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.52 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.14/1.52 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.14/1.52 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 1.14/1.52 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.14/1.52 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.14/1.52 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.14/1.52 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.14/1.52 ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 1.14/1.52 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 1.14/1.52 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 1.14/1.52 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 1.14/1.52 'tc_nat' ) ) ],
% 1.14/1.52 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.52 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.14/1.52 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.14/1.52 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.14/1.52 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , 'tc_nat' ), 'tc_nat' ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.14/1.52 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.14/1.52 T, Z, X ) ) ), =( Y, T ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.52 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.14/1.52 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.14/1.52 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'( 'c_Suc'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( X
% 1.14/1.52 , 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat'
% 1.14/1.52 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.14/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( X
% 1.14/1.52 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.14/1.52 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.14/1.52 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.14/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.14/1.52 , 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.14/1.52 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.14/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 1.14/1.52 , 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.14/1.52 X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.14/1.52 'tc_nat' ), X, 'tc_nat' ) ],
% 1.14/1.52 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.14/1.52 X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 1.14/1.52 'tc_nat' ), X, 'tc_nat' ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.14/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.14/1.52 'tc_Int_Oint' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint' ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.14/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y,
% 1.14/1.52 'tc_Int_Oint' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.14/1.52 'tc_nat' ), X ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.14/1.52 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.14/1.52 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.14/1.52 , 'tc_nat' ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.14/1.52 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.14/1.52 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.14/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), X ), Y, X ), 'c_HOL_Oplus__class_Oplus'( Y, Y, X ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 Y, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), X ), X ), 'c_HOL_Oplus__class_Oplus'( Y, Y, X ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), X ) ) ],
% 1.14/1.52 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.14/1.52 [ =( 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.14/1.52 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_Power_Opower__class_Opower'( Y
% 1.14/1.52 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ],
% 1.14/1.52 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ), 'tc_nat' ) ],
% 1.14/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( X, X, 'tc_nat' ) ) ],
% 1.14/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' )
% 1.14/1.52 , 'c_HOL_Oplus__class_Oplus'( X, X, 'tc_nat' ) ) ],
% 1.14/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.14/1.52 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.14/1.52 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.14/1.52 ) ), 'c_Complex_Oii' ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), X ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.14/1.52 ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.14/1.52 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.14/1.52 ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.14/1.52 ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.14/1.52 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ), =( Y
% 1.14/1.52 , Z ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.14/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.52 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.14/1.52 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.52 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.14/1.52 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.14/1.52 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.14/1.52 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.14/1.52 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.14/1.52 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.14/1.52 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.14/1.52 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.14/1.52 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.14/1.52 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), X ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), X ), =( Z,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), X ), =( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.14/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), X ), Y, X ), Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' )
% 1.14/1.52 , X ), X ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ), X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ) ), X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.14/1.52 Y, Z, X ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ) ), X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ) ) ],
% 1.14/1.52 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.14/1.52 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.14/1.52 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.14/1.52 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.14/1.52 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.14/1.52 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' )
% 1.14/1.52 ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), Y, 'tc_nat' )
% 1.14/1.52 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), X ), 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), Y, 'tc_nat' ) ), X ),
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.14/1.52 , X ), X ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.14/1.52 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.14/1.52 X ), T, X ) ) ],
% 1.14/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.14/1.52 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.14/1.52 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.52 T, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.14/1.52 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.14/1.52 X ), T, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.14/1.52 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.14/1.52 T, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.14/1.52 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.14/1.52 X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.14/1.52 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.14/1.52 T, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.14/1.52 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.14/1.52 ) ],
% 1.14/1.52 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.14/1.52 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), Y, 'tc_nat' ), X ),
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.14/1.52 Y, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.52 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.52 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Z,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ), X ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.14/1.52 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.14/1.52 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.14/1.52 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.14/1.52 , Y, X ) ) ],
% 1.14/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.14/1.52 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.14/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.14/1.52 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.52 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.14/1.52 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.14/1.52 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.14/1.52 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X
% 1.14/1.52 ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.14/1.52 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.14/1.52 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.14/1.52 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.14/1.52 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 1.14/1.52 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.14/1.52 X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.14/1.52 , Z, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.14/1.52 ), =( Z, Y ) ],
% 1.14/1.52 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.14/1.52 ) ],
% 1.14/1.52 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.14/1.52 ) ],
% 1.14/1.52 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.14/1.52 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.14/1.52 X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.14/1.52 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.14/1.52 X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.14/1.52 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.14/1.52 X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.14/1.52 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.14/1.52 X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 Y, Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 Y, Z, X ) ) ],
% 1.14/1.52 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.14/1.52 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ],
% 1.14/1.52 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.14/1.52 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.14/1.52 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 1.14/1.52 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.14/1.52 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.14/1.52 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.14/1.52 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.14/1.52 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.14/1.52 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.14/1.52 , 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ), X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.14/1.52 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.14/1.52 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.14/1.52 ), 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.14/1.52 ), 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.14/1.52 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.14/1.52 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.14/1.52 X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.14/1.52 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.14/1.52 [ =( 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' )
% 1.14/1.52 ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 1.14/1.52 'tc_Complex_Ocomplex' ), 'c_Power_Opower__class_Opower'(
% 1.14/1.52 'c_FFT__Mirabelle_Oroot'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.14/1.52 'tc_nat' ), 'tc_Complex_Ocomplex' ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.14/1.52 X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.14/1.52 ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z
% 1.14/1.52 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'(
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ), Z, X
% 1.14/1.52 ), 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 1.14/1.52 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.14/1.52 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 1.14/1.52 Y, Z, X ), X ) ) ],
% 1.14/1.52 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.14/1.52 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.14/1.52 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.14/1.52 X ), Y ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.14/1.52 X ), Y ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.14/1.52 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.14/1.52 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.14/1.52 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( =( X, 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.14/1.52 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.14/1.52 'tc_nat' ), X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.52 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.14/1.52 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.14/1.52 , X ) ) ],
% 1.14/1.52 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.14/1.52 , Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.14/1.52 , Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ) ) ],
% 1.14/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.14/1.52 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.14/1.52 Y, T, X ) ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X
% 1.14/1.52 ), Y, X ) ), =( Z, T ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.14/1.52 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.14/1.52 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.14/1.52 X ), X ) ) ],
% 1.14/1.52 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.14/1.52 ,
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.14/1.52 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.14/1.52 X ), T, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.14/1.52 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.14/1.52 X ), T, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.14/1.52 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.14/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.52 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.14/1.52 , Y, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.14/1.52 , T, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.14/1.52 , T, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.14/1.52 , Y, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.14/1.52 Y, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.52 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 1.14/1.52 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), T, X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.14/1.52 ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.14/1.52 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.14/1.52 ],
% 1.14/1.52 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( Y,
% 1.14/1.52 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.14/1.52 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.14/1.52 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.14/1.52 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.14/1.52 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.14/1.52 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.14/1.52 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.14/1.52 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.14/1.52 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.14/1.52 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.14/1.52 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.14/1.52 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.14/1.52 , Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.14/1.52 , X ) ) ), =( Y, Z ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.14/1.52 , X ) ) ), =( Y, Z ) ],
% 1.14/1.52 [ =( 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'( X ), X,
% 1.14/1.52 'tc_Complex_Ocomplex' ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex'
% 1.14/1.52 ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.14/1.52 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 Z, Y, X ) ) ],
% 1.14/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.52 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.14/1.52 , X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.14/1.52 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.14/1.52 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.14/1.52 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.14/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.14/1.52 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.14/1.52 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 1.14/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.14/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.14/1.53 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.53 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.53 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.53 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.14/1.53 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.53 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.14/1.53 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.14/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.14/1.53 , Z, X ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), Y
% 1.14/1.53 , X ), Y ) ],
% 1.14/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.53 Y, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.14/1.53 , X ), Y ) ],
% 1.14/1.53 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.14/1.53 ), 'tc_nat' ) ) ],
% 1.14/1.53 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.14/1.53 ],
% 1.14/1.53 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.14/1.53 ],
% 1.14/1.53 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.14/1.53 ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.14/1.53 ],
% 1.14/1.53 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.14/1.53 , X, 'tc_nat' ), X ) ],
% 1.14/1.53 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.14/1.53 ), 'tc_nat' ), X ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.14/1.53 ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.14/1.53 ],
% 1.14/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.14/1.53 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' )
% 1.14/1.53 , X ), 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.53 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ), X ) ) ],
% 1.14/1.53 [ =( 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'(
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_Complex_Ocomplex' ),
% 1.14/1.53 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'( Y ), Z,
% 1.14/1.53 'tc_Complex_Ocomplex' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.14/1.53 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.53 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.14/1.53 , T, X ), 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.53 Z, T, 'tc_nat' ), X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.14/1.53 , Y, X ) ) ],
% 1.14/1.53 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.14/1.53 , Y, X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.14/1.53 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.14/1.53 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.14/1.53 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.14/1.53 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.14/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ],
% 1.14/1.53 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.14/1.53 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.14/1.53 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.14/1.53 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.14/1.53 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.53 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.14/1.53 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.14/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.14/1.53 'tc_nat' ) ) ],
% 1.14/1.53 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.14/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.14/1.53 'tc_nat' ) ) ],
% 1.14/1.53 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.14/1.53 'tc_nat' ) ), =( Y, Z ) ],
% 1.14/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.14/1.53 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 1.14/1.53 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.14/1.53 ) ) ],
% 1.14/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.14/1.53 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.14/1.53 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 1.14/1.53 ) ) ],
% 1.14/1.53 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.14/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.53 'c_Int_OBit1'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y
% 1.14/1.53 , X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.53 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.14/1.53 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.14/1.53 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.14/1.53 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.14/1.53 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.14/1.53 , Y, X ) ) ],
% 1.14/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.14/1.53 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.53 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 1.14/1.53 ],
% 1.14/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.14/1.53 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.53 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 1.14/1.53 ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.14/1.53 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.14/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.14/1.53 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ), X ),
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.14/1.53 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.53 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.53 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.14/1.53 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.14/1.53 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.14/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.14/1.53 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.14/1.53 X ), T, X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.14/1.53 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.14/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.14/1.53 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.14/1.53 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.14/1.53 'tc_nat' ) ) ],
% 1.14/1.53 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.14/1.53 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.14/1.53 'tc_nat' ) ) ],
% 1.14/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.14/1.53 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.14/1.53 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.14/1.53 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.14/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.14/1.53 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.14/1.53 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.14/1.53 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.14/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.14/1.53 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.14/1.53 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.14/1.53 'tc_nat' ) ) ],
% 1.14/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.14/1.53 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.14/1.53 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.14/1.53 'tc_nat' ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.14/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), =(
% 1.14/1.53 Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.14/1.53 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.14/1.53 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.14/1.53 ), ~( =( 'c_Power_Opower__class_Opower'( Y,
% 1.14/1.53 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.14/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.14/1.53 ) ) ],
% 1.14/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.14/1.53 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.14/1.53 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.14/1.53 ), Y ) ],
% 1.14/1.53 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.14/1.53 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.14/1.53 ) ) ],
% 1.14/1.53 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.14/1.53 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.14/1.53 ) ) ],
% 1.14/1.53 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.14/1.53 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.14/1.53 ), Y ) ],
% 1.14/1.53 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.14/1.53 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.14/1.53 ), Y ) ],
% 1.14/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.14/1.53 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.14/1.53 , X ) ) ],
% 1.14/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.14/1.53 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.14/1.53 , X ) ) ],
% 1.14/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.14/1.53 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.14/1.53 , X ) ) ],
% 1.14/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.14/1.53 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.14/1.53 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.14/1.53 , X ) ) ],
% 1.14/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.14/1.53 'v_n', 'tc_nat' ) ],
% 1.14/1.53 [ ~( =( 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'(
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( 'v_n', 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.14/1.53 , 'v_n', 'tc_Complex_Ocomplex' ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.14/1.53 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex'
% 1.14/1.53 ) ) ) ],
% 1.14/1.53 [ =( 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'(
% 1.14/1.53 'c_HOL_Otimes__class_Otimes'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.14/1.53 , 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.14/1.53 'tc_nat' ), 'tc_Complex_Ocomplex' ), 'c_Power_Opower__class_Opower'(
% 1.14/1.53 'c_FFT__Mirabelle_Oroot'( 'c_Int_Onumber__class_Onumber__of'(
% 1.14/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 1.14/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_Complex_Ocomplex' ) ), ~(
% 1.14/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.14/1.53 'tc_nat' ) ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.14/1.53 ],
% 1.14/1.53 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.14/1.53 ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.14/1.53 ],
% 1.14/1.53 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.14/1.53 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.14/1.53 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.14/1.53 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.14/1.53 ],
% 1.14/1.53 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.14/1.53 ],
% 1.14/1.53 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Odvd'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.14/1.53 'tc_Complex_Ocomplex' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.14/1.53 'tc_Complex_Ocomplex' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.14/1.53 'tc_Complex_Ocomplex' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.14/1.53 ],
% 1.14/1.53 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.14/1.53 ],
% 1.14/1.53 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.14/1.53 ],
% 1.14/1.53 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.14/1.53 ,
% 1.14/1.53 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.14/1.53 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.14/1.53 [ 'class_Ring__and__Field_Odvd'( 'tc_Complex_Ocomplex' ) ],
% 1.14/1.53 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.14/1.53 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.14/1.53 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.14/1.53 [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ]
% 1.14/1.53 ] .
% 1.14/1.53
% 1.14/1.53
% 1.14/1.53 percentage equality = 0.228012, percentage horn = 0.849510
% 1.14/1.53 This is a problem with some equality
% 1.14/1.53
% 1.14/1.53
% 1.14/1.53
% 1.14/1.53 Options Used:
% 1.14/1.53
% 1.14/1.53 useres = 1
% 1.14/1.53 useparamod = 1
% 1.14/1.53 useeqrefl = 1
% 1.14/1.53 useeqfact = 1
% 1.14/1.53 usefactor = 1
% 1.14/1.53 usesimpsplitting = 0
% 1.14/1.53 usesimpdemod = 5
% 1.14/1.53 usesimpres = 3
% 1.14/1.53
% 1.14/1.53 resimpinuse = 1000
% 1.14/1.53 resimpclauses = 20000
% 1.14/1.53 substype = eqrewr
% 1.14/1.53 backwardsubs = 1
% 1.14/1.53 selectoldest = 5
% 1.14/1.53
% 1.14/1.53 litorderings [0] = split
% 1.14/1.53 litorderings [1] = extend the termordering, first sorting on arguments
% 1.14/1.53
% 1.14/1.53 termordering = kbo
% 1.14/1.53
% 1.14/1.53 litapriori = 0
% 1.14/1.53 termapriori = 1
% 1.14/1.53 litaposteriori = 0
% 1.14/1.53 termaposteriori = 0
% 1.14/1.53 demodaposteriori = 0
% 1.14/1.53 ordereqreflfact = 0
% 1.14/1.53
% 1.14/1.53 litselect = negord
% 1.14/1.53
% 1.14/1.53 maxweight = 15
% 1.14/1.53 maxdepth = 30000
% 1.14/1.53 maxlength = 115
% 1.14/1.53 maxnrvars = 195
% 1.14/1.53 excuselevel = 1
% 1.14/1.53 increasemaxweight = 1
% 1.14/1.53
% 1.14/1.53 maxselected = 10000000
% 1.14/1.53 maxnrclauses = 10000000
% 1.34/1.76
% 1.34/1.76 showgenerated = 0
% 1.34/1.76 showkept = 0
% 1.34/1.76 showselected = 0
% 1.34/1.76 showdeleted = 0
% 1.34/1.76 showresimp = 1
% 1.34/1.76 showstatus = 2000
% 1.34/1.76
% 1.34/1.76 prologoutput = 1
% 1.34/1.76 nrgoals = 5000000
% 1.34/1.76 totalproof = 1
% 1.34/1.76
% 1.34/1.76 Symbols occurring in the translation:
% 1.34/1.76
% 1.34/1.76 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.34/1.76 . [1, 2] (w:1, o:127, a:1, s:1, b:0),
% 1.34/1.76 ! [4, 1] (w:0, o:52, a:1, s:1, b:0),
% 1.34/1.76 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.34/1.76 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.34/1.76 'class_Ring__and__Field_Oidom' [40, 1] (w:1, o:57, a:1, s:1, b:0),
% 1.34/1.76 'class_Int_Onumber__ring' [41, 1] (w:1, o:58, a:1, s:1, b:0),
% 1.34/1.76 'c_HOL_Ozero__class_Ozero' [43, 1] (w:1, o:59, a:1, s:1, b:0),
% 1.34/1.76 'c_HOL_Oplus__class_Oplus' [44, 3] (w:1, o:157, a:1, s:1, b:0),
% 1.34/1.76 'class_Ring__and__Field_Ocomm__semiring__1' [45, 1] (w:1, o:61, a:1
% 1.34/1.76 , s:1, b:0),
% 1.34/1.76 'class_OrderedGroup_Ocomm__monoid__add' [46, 1] (w:1, o:62, a:1, s:1
% 1.34/1.76 , b:0),
% 1.34/1.76 'class_Ring__and__Field_Oordered__field' [48, 1] (w:1, o:65, a:1, s:1
% 1.34/1.76 , b:0),
% 1.34/1.76 'c_HOL_Oinverse__class_Odivide' [50, 3] (w:1, o:158, a:1, s:1, b:0),
% 1.34/1.76
% 1.34/1.76 'c_lessequals' [53, 3] (w:1, o:159, a:1, s:1, b:0),
% 1.34/1.76 'c_HOL_Oord__class_Oless' [54, 3] (w:1, o:156, a:1, s:1, b:0),
% 1.34/1.76 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [55, 1]
% 1.34/1.76 (w:1, o:67, a:1, s:1, b:0),
% 1.34/1.76 'class_OrderedGroup_Opordered__comm__monoid__add' [58, 1] (w:1, o:68
% 1.34/1.76 , a:1, s:1, b:0),
% 1.34/1.76 'class_Ring__and__Field_Odivision__by__zero' [59, 1] (w:1, o:70, a:1
% 1.34/1.76 , s:1, b:0),
% 1.34/1.76 'c_HOL_Oabs__class_Oabs' [60, 2] (w:1, o:152, a:1, s:1, b:0),
% 1.34/1.76 'class_Orderings_Oorder' [61, 1] (w:1, o:71, a:1, s:1, b:0),
% 1.34/1.76 'class_Orderings_Opreorder' [62, 1] (w:1, o:72, a:1, s:1, b:0),
% 1.34/1.76 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [63, 1]
% 1.34/1.76 (w:1, o:73, a:1, s:1, b:0),
% 1.34/1.76 'class_OrderedGroup_Omonoid__add' [65, 1] (w:1, o:76, a:1, s:1, b:0)
% 1.34/1.76 ,
% 1.34/1.76 'class_RealVector_Oreal__normed__field' [66, 1] (w:1, o:77, a:1, s:1
% 1.34/1.76 , b:0),
% 1.34/1.76 'class_Ring__and__Field_Ofield' [67, 1] (w:1, o:78, a:1, s:1, b:0),
% 1.34/1.76 'class_OrderedGroup_Opordered__ab__group__add__abs' [68, 1] (w:1, o:
% 1.34/1.76 79, a:1, s:1, b:0),
% 1.34/1.76 'class_OrderedGroup_Olordered__ab__group__add' [69, 1] (w:1, o:74, a:
% 1.34/1.76 1, s:1, b:0),
% 1.34/1.76 'class_Divides_Osemiring__div' [70, 1] (w:1, o:81, a:1, s:1, b:0),
% 1.34/1.76 'c_Divides_Odiv__class_Omod' [71, 3] (w:1, o:160, a:1, s:1, b:0),
% 1.34/1.76 'c_Divides_Odiv__class_Odiv' [72, 3] (w:1, o:161, a:1, s:1, b:0),
% 1.34/1.76 'c_Ring__and__Field_Odvd__class_Odvd' [73, 3] (w:1, o:162, a:1, s:1
% 1.34/1.76 , b:0),
% 1.34/1.76 'tc_nat' [74, 0] (w:1, o:25, a:1, s:1, b:0),
% 1.34/1.76 'c_HOL_Otimes__class_Otimes' [78, 3] (w:1, o:163, a:1, s:1, b:0),
% 1.34/1.76 'c_Suc' [80, 1] (w:1, o:82, a:1, s:1, b:0),
% 1.34/1.76 'c_Parity_Oeven__odd__class_Oeven' [81, 2] (w:1, o:153, a:1, s:1, b:0
% 1.34/1.76 ),
% 1.34/1.76 'c_Int_OMin' [82, 0] (w:1, o:35, a:1, s:1, b:0),
% 1.34/1.76 'tc_Int_Oint' [83, 0] (w:1, o:36, a:1, s:1, b:0),
% 1.34/1.76 'c_Int_OBit1' [84, 1] (w:1, o:85, a:1, s:1, b:0),
% 1.34/1.76 'class_Ring__and__Field_Oordered__idom' [85, 1] (w:1, o:86, a:1, s:1
% 1.34/1.76 , b:0),
% 1.34/1.76 'c_Power_Opower__class_Opower' [86, 3] (w:1, o:164, a:1, s:1, b:0),
% 1.34/1.76 'class_OrderedGroup_Oab__semigroup__add' [87, 1] (w:1, o:87, a:1, s:1
% 1.34/1.76 , b:0),
% 1.34/1.76 'class_OrderedGroup_Oab__group__add' [88, 1] (w:1, o:88, a:1, s:1, b:
% 1.34/1.76 0),
% 1.34/1.76 'c_HOL_Oone__class_Oone' [89, 1] (w:1, o:83, a:1, s:1, b:0),
% 1.34/1.76 'class_Ring__and__Field_Olordered__ring' [90, 1] (w:1, o:89, a:1, s:1
% 1.34/1.76 , b:0),
% 1.34/1.76 'class_OrderedGroup_Olordered__ab__group__add__abs' [92, 1] (w:1, o:
% 1.34/1.76 75, a:1, s:1, b:0),
% 1.34/1.76 'class_Orderings_Olinorder' [93, 1] (w:1, o:90, a:1, s:1, b:0),
% 1.34/1.76 'class_Ring__and__Field_Opordered__ring__abs' [94, 1] (w:1, o:96, a:1
% 1.34/1.76 , s:1, b:0),
% 1.34/1.76 'class_Ring__and__Field_Oordered__ring__strict' [95, 1] (w:1, o:91
% 1.34/1.76 , a:1, s:1, b:0),
% 1.34/1.76 'class_Int_Onumber' [96, 1] (w:1, o:97, a:1, s:1, b:0),
% 1.34/1.76 'c_Int_Onumber__class_Onumber__of' [97, 2] (w:1, o:155, a:1, s:1, b:0
% 1.34/1.76 ),
% 1.34/1.76 'class_Ring__and__Field_Ocomm__semiring' [100, 1] (w:1, o:69, a:1, s:
% 1.34/1.76 1, b:0),
% 1.34/1.76 'class_RealVector_Oreal__normed__algebra' [101, 1] (w:1, o:98, a:1
% 6.07/6.50 , s:1, b:0),
% 6.07/6.50 'class_Ring__and__Field_Odvd' [103, 1] (w:1, o:99, a:1, s:1, b:0),
% 6.07/6.50 'class_Ring__and__Field_Osemiring' [104, 1] (w:1, o:104, a:1, s:1, b:
% 6.07/6.50 0),
% 6.07/6.50 'class_Ring__and__Field_Oordered__semidom' [106, 1] (w:1, o:92, a:1
% 6.07/6.50 , s:1, b:0),
% 6.07/6.50 'class_OrderedGroup_Omonoid__mult' [107, 1] (w:1, o:105, a:1, s:1, b:
% 6.07/6.50 0),
% 6.07/6.50 'c_HOL_Ouminus__class_Ouminus' [108, 2] (w:1, o:154, a:1, s:1, b:0),
% 6.07/6.50
% 6.07/6.50 'class_OrderedGroup_Opordered__ab__semigroup__add' [109, 1] (w:1, o:
% 6.07/6.50 106, a:1, s:1, b:0),
% 6.07/6.50 'class_Divides_Oring__div' [110, 1] (w:1, o:80, a:1, s:1, b:0),
% 6.07/6.50 'class_OrderedGroup_Ocancel__ab__semigroup__add' [111, 1] (w:1, o:107
% 6.07/6.50 , a:1, s:1, b:0),
% 6.07/6.50 'class_OrderedGroup_Ocancel__semigroup__add' [112, 1] (w:1, o:108, a:
% 6.07/6.50 1, s:1, b:0),
% 6.07/6.50 'c_Int_OPls' [114, 0] (w:1, o:40, a:1, s:1, b:0),
% 6.07/6.50 'c_Int_OBit0' [115, 1] (w:1, o:84, a:1, s:1, b:0),
% 6.07/6.50 'class_OrderedGroup_Ogroup__add' [122, 1] (w:1, o:109, a:1, s:1, b:0)
% 6.07/6.50 ,
% 6.07/6.50 'class_Ring__and__Field_Ocomm__ring__1' [123, 1] (w:1, o:60, a:1, s:1
% 6.07/6.50 , b:0),
% 6.07/6.50 'class_OrderedGroup_Opordered__ab__group__add' [124, 1] (w:1, o:110
% 6.07/6.50 , a:1, s:1, b:0),
% 6.07/6.50 'class_Ring__and__Field_Oabs__if' [130, 1] (w:1, o:111, a:1, s:1, b:0
% 6.07/6.50 ),
% 6.07/6.50 'c_Complex_Oii' [131, 0] (w:1, o:46, a:1, s:1, b:0),
% 6.07/6.50 'tc_Complex_Ocomplex' [132, 0] (w:1, o:47, a:1, s:1, b:0),
% 6.07/6.50 'class_Ring__and__Field_Oordered__semiring__strict' [133, 1] (w:1, o:
% 6.07/6.50 93, a:1, s:1, b:0),
% 6.07/6.50 'class_Ring__and__Field_Oordered__semiring' [134, 1] (w:1, o:94, a:1
% 6.07/6.50 , s:1, b:0),
% 6.07/6.50 'class_Ring__and__Field_Omult__mono1' [135, 1] (w:1, o:112, a:1, s:1
% 6.07/6.50 , b:0),
% 6.07/6.50 'class_Ring__and__Field_Omult__mono' [136, 1] (w:1, o:113, a:1, s:1
% 6.07/6.50 , b:0),
% 6.07/6.50 'class_Ring__and__Field_Opordered__ring' [137, 1] (w:1, o:114, a:1
% 6.07/6.50 , s:1, b:0),
% 6.07/6.50 'class_Ring__and__Field_Opordered__cancel__semiring' [138, 1] (w:1
% 6.07/6.50 , o:115, a:1, s:1, b:0),
% 6.07/6.50 'class_Ring__and__Field_Opordered__semiring' [139, 1] (w:1, o:116, a:
% 6.07/6.51 1, s:1, b:0),
% 6.07/6.51 'class_Ring__and__Field_Osemiring__0' [140, 1] (w:1, o:117, a:1, s:1
% 6.07/6.51 , b:0),
% 6.07/6.51 'class_Power_Opower' [141, 1] (w:1, o:121, a:1, s:1, b:0),
% 6.07/6.51 'class_OrderedGroup_Oordered__ab__group__add' [142, 1] (w:1, o:66, a:
% 6.07/6.51 1, s:1, b:0),
% 6.07/6.51 'c_FFT__Mirabelle_Oroot' [144, 1] (w:1, o:122, a:1, s:1, b:0),
% 6.07/6.51 'class_OrderedGroup_Oab__semigroup__mult' [149, 1] (w:1, o:118, a:1
% 6.07/6.51 , s:1, b:0),
% 6.07/6.51 'class_OrderedGroup_Ocomm__monoid__mult' [150, 1] (w:1, o:119, a:1
% 6.07/6.51 , s:1, b:0),
% 6.07/6.51 'class_OrderedGroup_Oab__semigroup__idem__mult' [151, 1] (w:1, o:120
% 6.07/6.51 , a:1, s:1, b:0),
% 6.07/6.51 'class_Ring__and__Field_Ozero__neq__one' [152, 1] (w:1, o:123, a:1
% 6.07/6.51 , s:1, b:0),
% 6.07/6.51 'class_Ring__and__Field_Ono__zero__divisors' [153, 1] (w:1, o:64, a:1
% 6.07/6.51 , s:1, b:0),
% 6.07/6.51 'class_Ring__and__Field_Omult__zero' [154, 1] (w:1, o:63, a:1, s:1
% 6.07/6.51 , b:0),
% 6.07/6.51 'class_Ring__and__Field_Oring__1__no__zero__divisors' [155, 1] (w:1
% 6.07/6.51 , o:100, a:1, s:1, b:0),
% 6.07/6.51 'class_Ring__and__Field_Oring' [156, 1] (w:1, o:101, a:1, s:1, b:0),
% 6.07/6.51
% 6.07/6.51 'class_Ring__and__Field_Oring__1' [158, 1] (w:1, o:102, a:1, s:1, b:0
% 6.07/6.51 ),
% 6.07/6.51 'class_Ring__and__Field_Oring__no__zero__divisors' [159, 1] (w:1, o:
% 6.07/6.51 103, a:1, s:1, b:0),
% 6.07/6.51 'class_Ring__and__Field_Osemiring__1' [160, 1] (w:1, o:124, a:1, s:1
% 6.07/6.51 , b:0),
% 6.07/6.51 'class_Lattices_Oboolean__algebra' [161, 1] (w:1, o:125, a:1, s:1, b:
% 6.07/6.51 0),
% 6.07/6.51 'class_Int_Oring__char__0' [162, 1] (w:1, o:126, a:1, s:1, b:0),
% 6.07/6.51 'class_Ring__and__Field_Oordered__comm__semiring__strict' [163, 1]
% 6.07/6.51 (w:1, o:95, a:1, s:1, b:0),
% 6.07/6.51 'v_n' [164, 0] (w:1, o:51, a:1, s:1, b:0).
% 6.07/6.51
% 6.07/6.51
% 6.07/6.51 Starting Search:
% 6.07/6.51
% 6.07/6.51 Resimplifying inuse:
% 6.07/6.51 Done
% 6.07/6.51
% 6.07/6.51
% 6.07/6.51 Intermediate Status:
% 6.07/6.51 Generated: 4013
% 6.07/6.51 Kept: 2028
% 6.07/6.51 Inuse: 170
% 6.07/6.51 Deleted: 1
% 6.07/6.51 Deletedinuse: 0
% 6.07/6.51
% 6.07/6.51 Resimplifying inuse:
% 6.07/6.51 Done
% 6.07/6.51
% 6.07/6.51 Resimplifying inuse:
% 6.07/6.51 Done
% 6.07/6.51
% 6.07/6.51
% 6.07/6.51 Intermediate Status:
% 6.07/6.51 Generated: 8677
% 6.07/6.51 Kept: 4073
% 6.07/6.51 Inuse: 279
% 6.07/6.51 Deleted: 2
% 6.07/6.51 Deletedinuse: 0
% 6.07/6.51
% 6.07/6.51 Resimplifying inuse:
% 6.07/6.51 Done
% 6.07/6.51
% 6.07/6.51 Resimplifying inuse:
% 6.07/6.51 Done
% 6.07/6.51
% 6.07/6.51
% 6.07/6.51 Intermediate Status:
% 6.07/6.51 Generated: Segmentation fault (core dumped)
% 6.07/6.51 Bliksem ended
%------------------------------------------------------------------------------