TSTP Solution File: SWV716-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV716-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.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 16:28:01 EDT 2022
% Result : Timeout 300.07s 300.52s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV716-1 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.14 % Command : bliksem %s
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % DateTime : Tue Jun 14 23:17:34 EDT 2022
% 0.14/0.36 % CPUTime :
% 1.25/1.65 *** allocated 10000 integers for termspace/termends
% 1.25/1.65 *** allocated 10000 integers for clauses
% 1.25/1.65 *** allocated 10000 integers for justifications
% 1.25/1.65 *** allocated 15000 integers for termspace/termends
% 1.25/1.65 *** allocated 22500 integers for termspace/termends
% 1.25/1.65 *** allocated 33750 integers for termspace/termends
% 1.25/1.65 *** allocated 50625 integers for termspace/termends
% 1.25/1.65 Bliksem 1.12
% 1.25/1.65
% 1.25/1.65
% 1.25/1.65 Automatic Strategy Selection
% 1.25/1.65
% 1.25/1.65 Clauses:
% 1.25/1.65 [
% 1.25/1.65 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.65 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.25/1.65 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.65 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.25/1.65 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.25/1.65 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.25/1.65 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.25/1.65 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.25/1.65 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.65 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.25/1.65 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.65 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.25/1.65 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 1.25/1.65 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc',
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.25/1.65 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.65 X ), Z ), Y ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.65 X ), Y ), Z ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.65 X ), Z ), Y ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.65 X ), Y ), Z ), X ) ) ],
% 1.25/1.65 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.65 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.25/1.65 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.25/1.65 ,
% 1.25/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.25/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.25/1.65 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.25/1.65 , 'tc_nat' ) ) ],
% 1.25/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.25/1.65 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.25/1.65 , 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.25/1.65 ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.25/1.65 , X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 1.25/1.65 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.65 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.65 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.25/1.65 ,
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.65 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.65 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.25/1.65 ,
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.65 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.25/1.65 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.25/1.65 ,
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.65 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.25/1.65 ,
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.65 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.25/1.65 ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.65 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.65 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.65 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.25/1.65 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.25/1.65 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.25/1.65 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.25/1.65 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.25/1.65 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.25/1.65 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.65 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.65 , Y ), T ), Z, X ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.65 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.65 , Y ), Z ), T, X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.65 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.65 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'( Y
% 1.25/1.65 , T, X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.25/1.65 Z, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.65 X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.65 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.65 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 'tc_nat' ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.65 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.25/1.65 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.65 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.25/1.65 ,
% 1.25/1.65 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.25/1.65 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.25/1.65 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.25/1.65 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.25/1.65 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.25/1.65 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ),
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), ~(
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.25/1.65 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ],
% 1.25/1.65 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ],
% 1.25/1.65 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.25/1.65 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.25/1.65 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP(
% 1.25/1.65 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.25/1.65 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.25/1.65 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ],
% 1.25/1.65 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.25/1.65 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.25/1.65 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.25/1.65 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.65 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.25/1.65 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.25/1.65 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.25/1.65 X ) ) ) ],
% 1.25/1.65 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 1.25/1.65 Y, Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.25/1.65 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.25/1.65 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.25/1.65 X ) ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.25/1.65 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.25/1.65 X ) ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.25/1.65 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.25/1.65 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.25/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.25/1.65 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.25/1.65 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.25/1.65 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.25/1.65 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.25/1.65 , V0, U, V1 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.25/1.65 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.25/1.65 , V0, U, V1 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.25/1.65 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.25/1.65 X, T, U, Y, W, V0 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.25/1.65 X, T, U, Z, W, V0 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.25/1.65 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.25/1.65 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.25/1.65 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.25/1.65 T, X, U, Y, W, V0 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.25/1.65 T, X, U, Z, W, V0 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.25/1.65 T, X, U, W, Y, V0 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.25/1.65 T, X, U, W, Z, V0 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.25/1.65 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.25/1.65 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.25/1.65 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.25/1.65 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.25/1.65 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.25/1.65 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.25/1.65 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.25/1.65 , V0, V1, V2 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.25/1.65 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.25/1.65 W, V0, V1, V2 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.25/1.65 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.25/1.65 , V0, V1, V2 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.25/1.65 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.25/1.65 W, V0, V1, V2 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.25/1.65 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.25/1.65 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.25/1.65 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.25/1.65 W, V0, V1, V2 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.25/1.65 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.25/1.65 W, V0, V1, V2 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.25/1.65 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.25/1.65 , V0, V1, V2 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.25/1.65 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.25/1.65 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.25/1.65 , V0, V1, V2 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.25/1.65 X, T, U, Y, W, V0 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.25/1.65 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.25/1.65 , V0, V1, V2 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.25/1.65 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.25/1.65 T, X, U, Y, W, V0 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.25/1.65 T, X, U, W, Y, V0 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.25/1.65 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.25/1.65 , V0, V1, V2 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.25/1.65 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.25/1.65 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.25/1.65 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.25/1.65 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.25/1.65 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.25/1.65 'c_lessequals'( Y, Z, X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.25/1.65 'c_lessequals'( Y, Z, X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.25/1.65 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.25/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.25/1.65 ) ],
% 1.25/1.65 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.25/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.25/1.65 ) ],
% 1.25/1.65 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.25/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.25/1.65 ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.25/1.65 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.25/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.25/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.25/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.25/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.25/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.65 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.65 [ ~( =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.25/1.65 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.25/1.65 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.25/1.65 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.65 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.25/1.65 ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.65 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.65 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.25/1.65 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.25/1.65 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.65 X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.65 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.65 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.65 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.25/1.65 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.25/1.65 , hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.25/1.65 ) ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ), X ),
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.25/1.65 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', 'tc_nat' ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.25/1.65 Z ), X ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.65 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.25/1.65 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ),
% 1.25/1.65 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.25/1.65 Z, 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.25/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.25/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.25/1.65 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.25/1.65 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.25/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.25/1.65 Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc',
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ),
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.65 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ),
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.65 'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.25/1.65 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.25/1.65 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.65 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.25/1.65 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.65 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.25/1.65 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.25/1.65 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.25/1.65 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.25/1.65 ,
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.25/1.65 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.25/1.65 ,
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.25/1.65 ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.25/1.65 ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.25/1.65 ],
% 1.25/1.65 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.65 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.25/1.65 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ), ~(
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.25/1.65 'tc_nat' ) ) ],
% 1.25/1.65 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.25/1.65 'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.25/1.65 'tc_nat' ) ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.25/1.65 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.65 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.25/1.65 ,
% 1.25/1.65 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.25/1.65 , Z ) ), Z ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.25/1.65 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.25/1.65 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.65 X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.25/1.65 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.65 X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.65 X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.65 X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.65 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.65 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.25/1.65 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.65 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.25/1.65 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.65 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.65 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.25/1.65 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.25/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.25/1.65 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.65 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.25/1.65 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.25/1.65 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.25/1.65 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.25/1.65 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.25/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.25/1.65 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.25/1.65 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.65 'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z,
% 1.25/1.65 'tc_nat' ) ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.65 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.25/1.65 , ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.65 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.25/1.65 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.65 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.25/1.65 , ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.65 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.25/1.65 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.25/1.65 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.25/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.25/1.65 'c_lessequals'( Y, T, X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.25/1.65 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.25/1.65 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.25/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.25/1.65 'c_lessequals'( Z, T, X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.25/1.65 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.25/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.25/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.25/1.65 'c_lessequals'( Y, T, X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.25/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.25/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.25/1.65 'c_lessequals'( Z, T, X ) ) ],
% 1.25/1.65 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.25/1.65 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ),
% 1.25/1.65 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.25/1.65 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.25/1.65 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.25/1.65 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ),
% 1.25/1.65 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.65 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.65 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( T, X ), X ) )
% 1.25/1.65 , ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.25/1.65 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.25/1.65 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.25/1.65 , Y, 'tc_nat' ) ) ],
% 1.25/1.65 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), =( Y, X ),
% 1.25/1.65 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ],
% 1.25/1.65 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.25/1.65 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.25/1.65 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.25/1.65 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.25/1.65 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.25/1.65 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.25/1.65 , X ) ) ), =( Y, Z ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.25/1.65 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.25/1.65 , X ) ) ), =( Y, Z ) ],
% 1.25/1.65 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 1.25/1.65 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( T, X ) ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), Z, X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.25/1.65 ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.25/1.65 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.25/1.65 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.25/1.65 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ), ~( 'c_lessequals'( Z
% 1.25/1.65 , Y, 'tc_nat' ) ) ],
% 1.25/1.65 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.65 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), Y ) ), ~(
% 1.25/1.65 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 1.25/1.65 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( 'c_Suc',
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.25/1.65 ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.65 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.65 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.25/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.25/1.65 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.65 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.25/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.25/1.65 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.25/1.65 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.25/1.65 ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.25/1.65 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.25/1.65 ,
% 1.25/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.25/1.65 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.25/1.65 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.25/1.65 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.25/1.65 ,
% 1.25/1.65 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.25/1.65 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.25/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.25/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.65 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ),
% 1.25/1.65 'c_Complex_Oii' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.65 'tc_Complex_Ocomplex' ), 'c_Complex_Oii' ), X ) ),
% 1.25/1.65 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_Complex_Ocomplex' ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.25/1.65 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.25/1.65 ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.25/1.65 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.25/1.65 ) ],
% 1.25/1.65 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.25/1.65 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.25/1.65 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.25/1.65 ) ],
% 1.25/1.65 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.25/1.65 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.25/1.65 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.25/1.65 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.25/1.65 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.25/1.65 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.65 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.65 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.65 , 'tc_nat' ), 'tc_nat' ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.65 , 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.65 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.65 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.25/1.65 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y,
% 1.25/1.65 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.65 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.65 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.25/1.65 ), X ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.65 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.25/1.65 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.65 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.25/1.65 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.25/1.65 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.25/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.25/1.65 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.25/1.65 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.25/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.25/1.65 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oabs__class_Oabs'(
% 1.25/1.65 Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.25/1.65 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.25/1.65 ), Y ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 1.25/1.65 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.25/1.65 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.25/1.65 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 1.25/1.65 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.65 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 1.25/1.65 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.25/1.65 , hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), X ), ~(
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.25/1.65 , X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.25/1.65 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 1.25/1.65 ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.25/1.65 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OPls', 'tc_Int_Oint' )
% 1.25/1.65 ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 1.25/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.25/1.65 'c_HOL_Ominus__class_Ominus'( Y, T, X ), X ) ), 'c_HOL_Oabs__class_Oabs'(
% 1.25/1.65 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ) ), X ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.25/1.65 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.25/1.65 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.65 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.25/1.65 ,
% 1.25/1.65 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 1.25/1.65 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 1.25/1.65 'tc_nat' ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.25/1.65 ) ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.25/1.65 ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.65 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.65 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.25/1.65 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.25/1.65 ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.65 X ) ) ],
% 1.25/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 'tc_Int_Oint' ), ~(
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit0'( X ),
% 1.25/1.65 'tc_Int_Oint' ) ) ],
% 1.25/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit0'( X ),
% 1.25/1.65 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X,
% 1.25/1.65 'tc_Int_Oint' ) ) ],
% 1.25/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 'tc_Int_Oint' ), ~(
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit1'( X ),
% 1.25/1.65 'tc_Int_Oint' ) ) ],
% 1.25/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit1'( X ),
% 1.25/1.65 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X,
% 1.25/1.65 'tc_Int_Oint' ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.25/1.65 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.65 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y
% 1.25/1.65 , 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z,
% 1.25/1.65 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.25/1.65 ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.65 ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.65 ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.65 ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.65 ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.65 ), X ) ) ],
% 1.25/1.65 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.25/1.65 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.25/1.65 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.25/1.65 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.25/1.65 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 1.25/1.65 X ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.25/1.65 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.25/1.65 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.25/1.65 ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.65 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.25/1.65 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.65 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.25/1.65 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.25/1.65 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.65 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.25/1.65 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.25/1.65 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.25/1.65 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.25/1.65 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 1.25/1.65 'tc_nat' ), ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.65 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.25/1.65 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.25/1.65 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 1.25/1.65 X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.65 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.25/1.65 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.25/1.65 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.65 'tc_nat' ), 'tc_nat' ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.65 ) ) ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.65 ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.25/1.65 ,
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.25/1.65 , 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ), X ),
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.25/1.65 , Y ), Z ), X ) ) ],
% 1.25/1.65 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.25/1.65 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~(
% 1.25/1.65 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.25/1.65 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc',
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ), Z
% 1.25/1.65 ), 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.65 ), Y ), Z ), X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.65 Z, X ) ) ],
% 1.25/1.65 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.65 'tc_nat' ) ) ) ],
% 1.25/1.65 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_Int_Oint' ) ) ],
% 1.25/1.65 [ ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.25/1.65 ), Y ), X ), 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), X, 'tc_nat' ), Y ) ]
% 1.25/1.65 ,
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.25/1.65 ,
% 1.25/1.65 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.25/1.65 , X ), Y ), 'tc_nat' ) ],
% 1.25/1.65 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.25/1.65 , X ), Y ), 'tc_nat' ) ],
% 1.25/1.65 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.25/1.65 , Y ), X ), 'tc_nat' ) ],
% 1.25/1.65 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.25/1.65 , X ), Y ), 'tc_nat' ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.25/1.65 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.65 X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.25/1.65 ,
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.65 , X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.25/1.65 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.25/1.65 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.25/1.65 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.25/1.65 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.25/1.65 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.25/1.65 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.25/1.65 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.65 , X ) ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.65 'c_Power_Opower__class_Opower'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.65 X ), X ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.65 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Y ), X ), ~(
% 1.25/1.65 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.25/1.65 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ), ~( 'c_lessequals'(
% 1.25/1.65 X, Y, 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y, hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y,
% 1.25/1.65 X, 'tc_nat' ) ), X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.65 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ),
% 1.25/1.65 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.65 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat'
% 1.25/1.65 ) ) ],
% 1.25/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.25/1.65 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ),
% 1.25/1.65 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.65 'tc_nat' ), X ), Y ), Z, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 1.25/1.65 ) ) ],
% 1.25/1.65 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OMin',
% 1.25/1.65 'tc_Int_Oint' ) ) ],
% 1.25/1.65 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.25/1.65 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 1.25/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.25/1.65 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.25/1.65 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.25/1.65 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.25/1.65 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.25/1.65 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.65 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.25/1.65 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.25/1.65 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.25/1.65 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y
% 1.25/1.65 , Z, X ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X
% 1.25/1.65 ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.25/1.65 ) ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.25/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ),
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.25/1.65 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 1.25/1.65 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' )
% 1.25/1.65 , 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.25/1.65 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.25/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.25/1.65 'tc_nat' ) ) ],
% 1.25/1.65 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.25/1.65 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.25/1.65 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 1.25/1.65 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.25/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.65 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.25/1.65 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.25/1.65 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.25/1.65 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 1.25/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.25/1.65 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X
% 1.25/1.66 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.25/1.66 Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X
% 1.25/1.66 ) ],
% 1.25/1.66 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'tc_nat' ),
% 1.25/1.66 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.25/1.66 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.25/1.66 , X ), Z, X ) ) ],
% 1.25/1.66 [ 'c_lessequals'( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ),
% 1.25/1.66 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.25/1.66 X, Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.25/1.66 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.66 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.25/1.66 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.25/1.66 ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.66 ), X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), X,
% 1.25/1.66 'tc_nat' ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.25/1.66 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.25/1.66 X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X
% 1.25/1.66 ), X ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.25/1.66 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.25/1.66 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.66 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.25/1.66 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.66 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.25/1.66 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 X ), Y ), Z ) ), T ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.25/1.66 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.25/1.66 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 X ), Y ), Z ) ), T ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.25/1.66 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.66 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.25/1.66 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.25/1.66 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.66 ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.25/1.66 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X ) ],
% 1.25/1.66 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.25/1.66 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.25/1.66 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.25/1.66 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.25/1.66 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.66 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.25/1.66 , X ) ), T, X ) ) ],
% 1.25/1.66 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.66 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.25/1.66 ), Z ), T, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.25/1.66 ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.25/1.66 ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.25/1.66 ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.25/1.66 ), X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.25/1.66 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.66 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.25/1.66 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.25/1.66 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.25/1.66 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.25/1.66 ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.25/1.66 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.66 X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.25/1.66 'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.25/1.66 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.25/1.66 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Y,
% 1.25/1.66 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.25/1.66 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.25/1.66 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.25/1.66 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.25/1.66 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.66 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.66 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.25/1.66 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 1.25/1.66 ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.25/1.66 Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), ~(
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.25/1.66 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.25/1.66 , 'tc_nat' ), 'tc_nat' ), 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.66 X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.25/1.66 X ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X,
% 1.25/1.66 'tc_nat' ) ],
% 1.25/1.66 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), Z, 'tc_nat' ), 'tc_nat'
% 1.25/1.66 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( =( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) )
% 1.25/1.66 , Y ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat'
% 1.25/1.66 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.66 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.25/1.66 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.25/1.66 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.25/1.66 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.25/1.66 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OMin',
% 1.25/1.66 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OMin',
% 1.25/1.66 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OMin', 'tc_Int_Oint' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OMin',
% 1.25/1.66 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.25/1.66 ), 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 'tc_nat' ) ],
% 1.25/1.66 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.25/1.66 , Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.25/1.66 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.25/1.66 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y,
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 1.25/1.66 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.25/1.66 , 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.25/1.66 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.25/1.66 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ],
% 1.25/1.66 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.66 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.25/1.66 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.66 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.25/1.66 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.25/1.66 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.25/1.66 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.25/1.66 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.25/1.66 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.25/1.66 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.25/1.66 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.66 Y ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.25/1.66 Y ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.66 Y ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.25/1.66 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.25/1.66 Y ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.25/1.66 Y ) ],
% 1.25/1.66 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.25/1.66 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.25/1.66 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.66 Y ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.25/1.66 Y ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.25/1.66 ), Y ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.25/1.66 ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.25/1.66 ) ) ],
% 1.25/1.66 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.25/1.66 ), Y ) ],
% 1.25/1.66 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OMin',
% 1.25/1.66 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.25/1.66 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.66 'tc_nat' ) ) ) ],
% 1.25/1.66 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.25/1.66 , Y ) ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.25/1.66 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.25/1.66 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 1.25/1.66 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.66 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.25/1.66 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.25/1.66 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.25/1.66 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.25/1.66 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.25/1.66 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.25/1.66 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.66 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.66 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.25/1.66 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Z ), Y ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ),
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.66 X, 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 'tc_nat' ), X ), 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ), Y,
% 1.25/1.66 'tc_nat' ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.25/1.66 ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.25/1.66 ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.25/1.66 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.25/1.66 Y, X ), X ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.25/1.66 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.25/1.66 Y, X ) ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.25/1.66 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.25/1.66 Z, X ) ) ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.25/1.66 'c_lessequals'( Z, Y, X ) ],
% 1.25/1.66 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.66 'c_Int_OMin', X ) ), Y ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.66 'c_Int_OMin', X ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.25/1.66 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.66 , 'tc_nat' ), 'tc_nat' ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.25/1.66 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.66 , 'tc_nat' ), 'tc_nat' ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), =( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), Y, X ),
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.25/1.66 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.25/1.66 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.25/1.66 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.25/1.66 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.25/1.66 ~( hBOOL( hAPP( X, T ) ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), hAPP( 'c_Suc', T ) ),
% 1.25/1.66 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 'tc_nat' ), Z ), T ), Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.66 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( 'c_Suc',
% 1.25/1.66 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ), 'tc_nat' ) ],
% 1.25/1.66 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), Z ) ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.25/1.66 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.25/1.66 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc',
% 1.25/1.66 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.25/1.66 'tc_nat' ), Y, 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 1.25/1.66 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.25/1.66 , Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.25/1.66 , T, 'tc_nat' ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ) ), ~( 'c_lessequals'(
% 1.25/1.66 T, Z, 'tc_nat' ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.25/1.66 , T, 'tc_nat' ) ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ), =( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ) ), T ), U, 'tc_nat'
% 1.25/1.66 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z
% 1.25/1.66 ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ), 'tc_nat' ) ),
% 1.25/1.66 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.25/1.66 ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.25/1.66 ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ) ), Y ) ), Z ), U, 'tc_nat'
% 1.25/1.66 ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), T ) ), U ), 'tc_nat' )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T
% 1.25/1.66 ) ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ), 'tc_nat' ) ),
% 1.25/1.66 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.25/1.66 ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.25/1.66 ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ) ), Y ) ), U ), 'tc_nat' )
% 1.25/1.66 ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.25/1.66 [ =( 'c_FFT__Mirabelle_OIFFT'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.25/1.66 ), X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.25/1.66 ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.25/1.66 ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) )
% 1.25/1.66 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 1.25/1.66 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 1.25/1.66 ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.25/1.66 ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.25/1.66 ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.25/1.66 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.25/1.66 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.25/1.66 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.25/1.66 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X
% 1.25/1.66 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( T, Y, X ), X ), Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.25/1.66 , X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.66 , X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.66 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.25/1.66 ), Y ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.25/1.66 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.25/1.66 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.25/1.66 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.66 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.25/1.66 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.66 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.25/1.66 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.66 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.25/1.66 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.66 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.25/1.66 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.25/1.66 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.25/1.66 ) ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.25/1.66 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.25/1.66 ) ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.25/1.66 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.25/1.66 , X ) ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.25/1.66 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.25/1.66 , X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.25/1.66 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.25/1.66 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.66 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.25/1.66 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.25/1.66 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.25/1.66 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.25/1.66 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.66 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.25/1.66 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.25/1.66 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.25/1.66 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.66 T, X ) ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.25/1.66 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.25/1.66 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.25/1.66 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.25/1.66 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.25/1.66 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.25/1.66 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.25/1.66 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 Z, Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.25/1.66 , X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.25/1.66 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.25/1.66 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.25/1.66 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.25/1.66 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.25/1.66 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.25/1.66 , X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.25/1.66 , X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.25/1.66 , X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.25/1.66 , X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.25/1.66 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.25/1.66 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.25/1.66 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.25/1.66 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.25/1.66 ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.25/1.66 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.25/1.66 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.66 T, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.66 X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.25/1.66 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.66 T, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.25/1.66 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.25/1.66 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.25/1.66 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.25/1.66 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.25/1.66 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.25/1.66 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.66 ), X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.66 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.66 , Z ), T ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Z, T, X ), Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.66 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.25/1.66 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.25/1.66 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.66 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.25/1.66 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.25/1.66 ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.66 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.66 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.25/1.66 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.25/1.66 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.25/1.66 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.25/1.66 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.25/1.66 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.25/1.66 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.25/1.66 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.25/1.66 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.25/1.66 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.25/1.66 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.66 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( Y, X ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.25/1.66 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.25/1.66 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.25/1.66 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.25/1.66 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.25/1.66 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.66 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.25/1.66 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.25/1.66 ), 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.25/1.66 ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.25/1.66 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.25/1.66 , X ) ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.25/1.66 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.25/1.66 , X ) ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.25/1.66 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.25/1.66 ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.25/1.66 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.25/1.66 ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.25/1.66 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.25/1.66 ) ) ],
% 1.25/1.66 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.25/1.66 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.25/1.66 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.25/1.66 ) ) ],
% 1.25/1.66 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.25/1.66 ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.25/1.66 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.25/1.66 , X ) ), T ) ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.25/1.66 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.25/1.66 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.66 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X
% 1.25/1.66 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), 'c_HOL_Ominus__class_Ominus'( Y, T, X ) ),
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, T, X
% 1.25/1.66 ) ), U ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( T, Y, X
% 1.25/1.66 ) ), Z ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ) ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X
% 1.25/1.66 ) ), Z ) ), T ), W ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X
% 1.25/1.66 ) ), Z ) ), W ) ) ],
% 1.25/1.66 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.25/1.66 Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ), Y )
% 1.25/1.66 ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.25/1.66 Y ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.25/1.66 ) ), Z ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.25/1.66 , X ), X ), Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.66 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.25/1.66 ), X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.66 , X ), X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.25/1.66 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.66 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.66 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.25/1.66 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.66 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.25/1.66 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.25/1.66 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.25/1.66 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.66 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.66 , X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.66 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.66 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.25/1.66 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.66 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.25/1.66 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.25/1.66 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.25/1.66 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.25/1.66 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.66 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.66 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.66 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.66 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.25/1.66 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.25/1.66 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.66 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.25/1.66 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.66 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.25/1.66 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.25/1.66 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.66 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.66 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.66 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.25/1.66 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.25/1.66 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.66 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.66 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.66 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.66 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.25/1.66 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.25/1.66 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.25/1.66 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.25/1.66 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.66 , X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.66 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.25/1.66 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.66 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.25/1.66 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.25/1.66 , X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.25/1.66 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.25/1.66 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.25/1.66 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.25/1.66 , X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.25/1.66 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.25/1.66 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.25/1.66 ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.25/1.66 ), 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ), Z ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.66 ), Y ), Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.25/1.66 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.25/1.66 , X ) ), Z ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.66 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.66 ), =( 'c_HOL_Oinverse__class_Odivide'( Y, U, X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.66 'c_Int_OPls', X ) ), Y ) ],
% 1.25/1.66 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.66 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.25/1.66 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.66 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.25/1.66 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.66 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.66 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.25/1.66 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.25/1.66 X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.25/1.66 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.66 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.25/1.66 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.25/1.66 ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.25/1.66 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.66 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.25/1.66 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.25/1.66 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.66 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.25/1.66 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.25/1.66 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.25/1.66 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.25/1.66 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.25/1.66 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.25/1.66 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.25/1.66 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.25/1.66 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.25/1.66 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.25/1.66 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.66 hAPP( 'c_Suc', Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.25/1.66 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.25/1.66 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.25/1.66 ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.66 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.66 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.66 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y,
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ],
% 1.25/1.66 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.66 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.66 ), Y ), T ), Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.25/1.66 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.25/1.66 ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.25/1.66 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.25/1.66 ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.25/1.66 ) ],
% 1.25/1.66 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.66 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.25/1.66 T, X ) ), T, X ) ) ],
% 1.25/1.66 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.66 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.25/1.66 ) ), Z ), T, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.25/1.66 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.25/1.66 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.66 'c_Int_OMin', X ) ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ),
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( T, hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.25/1.66 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X
% 1.25/1.66 ) ), U ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), T ), U ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ), W, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.25/1.66 ) ), T ) ), U ), W, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 X ), Y ), T ) ), U ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.25/1.66 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.25/1.66 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.25/1.66 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.25/1.66 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.25/1.66 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.25/1.66 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.25/1.66 X ) ) ],
% 1.25/1.66 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.25/1.66 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.25/1.66 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.25/1.66 X ), Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.25/1.66 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.25/1.66 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.25/1.66 , T, X ), X ), T, X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X ), X ) )
% 1.25/1.66 ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.25/1.66 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.25/1.66 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.66 ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.66 ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.25/1.66 ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.66 ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.25/1.66 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.25/1.66 ), Z ), Y ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.66 ) ), =( Y, Z ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.66 ) ), =( Y, Z ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.25/1.66 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.66 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ),
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'(
% 1.25/1.66 Y, T, X ) ), 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.66 , Y ), Z ), Z, X ), Y ) ],
% 1.25/1.66 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.25/1.66 X ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), =( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.25/1.66 Z, 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.66 'tc_nat' ) ), X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.25/1.66 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.25/1.66 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.25/1.66 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.25/1.66 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ),
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ),
% 1.25/1.66 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.25/1.66 'c_HOL_Oone__class_Oone'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.66 'c_Int_OMin', X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.25/1.66 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.25/1.66 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.25/1.66 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.66 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.25/1.66 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.25/1.66 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.25/1.66 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.25/1.66 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.66 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.25/1.66 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.66 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.66 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.25/1.66 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.25/1.66 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.25/1.66 ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.25/1.66 ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.25/1.66 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.25/1.66 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.25/1.66 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.25/1.66 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.25/1.66 ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.25/1.66 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.25/1.66 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ),
% 1.25/1.66 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.25/1.66 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.25/1.66 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.25/1.66 ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.66 ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.25/1.66 , T, X ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), T, X ) ), =( T,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.25/1.66 ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Z, X ) ), =( Z,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 'c_lessequals'(
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 'c_lessequals'(
% 1.25/1.66 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ), ~(
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.25/1.66 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.66 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.25/1.66 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.66 'c_Int_OMin', X ) ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.66 'c_Int_OMin', X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.25/1.66 'c_HOL_Oone__class_Oone'( X ), X ) ), Y ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.25/1.66 'c_HOL_Oone__class_Oone'( X ), X ) ), 'c_Parity_Oeven__odd__class_Oeven'(
% 1.25/1.66 Y, 'tc_nat' ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.25/1.66 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.25/1.66 ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.25/1.66 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T,
% 1.25/1.66 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.25/1.66 'c_HOL_Oone__class_Oone'( X ), X ) ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.25/1.66 ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.66 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ),
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.25/1.66 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.25/1.66 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.25/1.66 [ =( 'c_Int_OBit1'( 'c_Int_OMin' ), 'c_Int_OMin' ) ],
% 1.25/1.66 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OMin' ) ), =( X, 'c_Int_OMin' ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( =( 'c_Int_OMin', 'c_Int_OBit1'( X ) ) ), =( 'c_Int_OMin', X ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.25/1.66 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.25/1.66 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.25/1.66 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.25/1.66 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ =( 'c_Int_OMin', 'c_Int_OBit1'( 'c_Int_OMin' ) ) ],
% 1.25/1.66 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', X
% 1.25/1.66 ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_lessequals'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.25/1.66 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'(
% 1.25/1.66 X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'c_lessequals'( hAPP( 'c_Suc', X ), X, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', X
% 1.25/1.66 ), Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_lessequals'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.25/1.66 X, Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.25/1.66 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.25/1.66 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.66 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.66 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.25/1.66 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.25/1.66 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 X, hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.25/1.66 ), 'tc_nat' ) ) ],
% 1.25/1.66 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.66 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 1.25/1.66 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 1.25/1.66 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 1.25/1.66 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.25/1.66 hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 1.25/1.66 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.66 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 1.25/1.66 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.25/1.66 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.25/1.66 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.25/1.66 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.25/1.66 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.25/1.66 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X,
% 1.25/1.66 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.25/1.66 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.25/1.66 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.25/1.66 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.25/1.66 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.25/1.66 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.25/1.66 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.25/1.66 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.25/1.66 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.66 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.25/1.66 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.25/1.66 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.25/1.66 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.66 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.25/1.66 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 1.25/1.66 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.25/1.66 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.25/1.66 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ), =( Z,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.66 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.25/1.66 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.66 ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.25/1.66 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.25/1.66 ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.25/1.66 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), 'c_HOL_Ominus__class_Ominus'( T
% 1.25/1.66 , Z, 'tc_nat' ) ) ), 'c_lessequals'( T, Z, 'tc_nat' ), =( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.66 hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ), 'tc_nat' ), ~( 'c_lessequals'( Y,
% 1.25/1.66 Z, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y )
% 1.25/1.66 , 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.25/1.66 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.25/1.66 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.25/1.66 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.25/1.66 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, hAPP(
% 1.25/1.66 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.25/1.66 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.25/1.66 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.25/1.66 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.25/1.66 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.25/1.66 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ),
% 1.25/1.66 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ) ],
% 1.25/1.66 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.25/1.66 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.25/1.66 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.25/1.66 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.25/1.66 , Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.25/1.66 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.25/1.66 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.25/1.66 , X, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.25/1.66 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.25/1.66 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.25/1.66 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.66 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.25/1.66 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.25/1.66 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.25/1.66 , X, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.25/1.66 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.66 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.25/1.66 ), 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.25/1.66 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.66 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.25/1.66 ), 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.25/1.66 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.25/1.66 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.25/1.66 'tc_nat' ) ), =( Y, Z ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.25/1.66 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.25/1.66 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.25/1.66 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.25/1.66 hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~(
% 1.25/1.66 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.25/1.66 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 1.25/1.66 ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.25/1.66 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.25/1.66 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 1.25/1.66 , 'tc_nat' ) ) ],
% 1.25/1.66 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.25/1.66 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.25/1.66 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 1.25/1.66 ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.25/1.66 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.25/1.66 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.25/1.66 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 1.25/1.66 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.25/1.66 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.25/1.66 ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.25/1.66 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.25/1.66 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X,
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ) ) ],
% 1.25/1.66 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~(
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.25/1.66 'tc_nat' ), 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.25/1.66 'tc_nat' ), 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.25/1.66 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.25/1.66 'tc_nat' ) ) ],
% 1.25/1.66 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.25/1.66 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.25/1.66 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), hAPP(
% 1.25/1.66 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), hAPP( 'c_Suc',
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.25/1.66 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), hAPP(
% 1.25/1.66 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), hAPP( 'c_Suc',
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.25/1.66 [ ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y )
% 1.25/1.66 , hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, hAPP(
% 1.25/1.66 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.25/1.66 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.25/1.66 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.25/1.66 'tc_nat' ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP(
% 1.25/1.66 hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 'tc_nat' ) )
% 1.25/1.66 ],
% 1.25/1.66 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.25/1.66 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.66 'tc_nat' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ),
% 1.25/1.66 X ), 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.66 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.66 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ),
% 1.25/1.66 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.66 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.25/1.66 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.25/1.66 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.25/1.66 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.25/1.66 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.25/1.66 , 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ), T ) ), U ), W, X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ), W, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.66 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), U ) ), W ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.25/1.66 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.25/1.66 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.66 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.66 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.25/1.66 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.25/1.66 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.66 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.25/1.66 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.25/1.66 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.25/1.66 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.25/1.66 , X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.25/1.66 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.66 ), T ), Z ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.25/1.66 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.25/1.66 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.25/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.66 ), T ), Z ), X ) ) ],
% 1.25/1.66 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.25/1.66 'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), X ), Y ) ) ) ],
% 1.25/1.66 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.25/1.66 X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), X ), Y ) ) ) ],
% 1.25/1.66 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.25/1.66 X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.25/1.66 'c_Suc', Y ) ) ) ],
% 1.25/1.66 [ =( X, hAPP( 'c_Suc', Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.25/1.66 'c_lessequals'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.25/1.66 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.25/1.66 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.25/1.66 V0, V1 ) ) ],
% 1.25/1.66 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.25/1.66 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.25/1.66 V0, V1 ) ) ],
% 1.25/1.66 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.25/1.66 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W
% 1.25/1.66 , V0, V1 ) ) ],
% 1.25/1.66 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.25/1.66 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W
% 1.25/1.66 , V0, V1 ) ) ],
% 1.25/1.66 [ 'c_Fun_Oinj__on'( 'c_Suc', X, 'tc_nat', 'tc_nat' ) ],
% 1.25/1.66 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.25/1.66 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =(
% 1.25/1.66 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), 'c_lessequals'( Y,
% 1.25/1.66 X, 'tc_nat' ) ],
% 1.25/1.66 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP(
% 1.25/1.66 'c_Suc', Y ), X, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_lessequals'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', X ), 'tc_nat' ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ),
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.25/1.66 [ ~( =( 'c_Int_OPls', 'c_Int_OMin' ) ) ],
% 1.25/1.66 [ ~( =( 'c_Int_OMin', 'c_Int_OPls' ) ) ],
% 1.25/1.66 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OPls',
% 1.25/1.66 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.25/1.66 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.25/1.66 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.66 hAPP( 'c_Suc', T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z
% 1.25/1.66 ), hAPP( 'c_Suc', T ) ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.25/1.66 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ) )
% 1.25/1.66 , =( Y, T ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) )
% 1.25/1.66 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.25/1.66 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.66 ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.25/1.66 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.66 ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.25/1.66 , Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( Y, X ) ), Z ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.25/1.66 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.25/1.66 ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.25/1.66 , Z ), Y ), 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.25/1.66 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.25/1.66 ],
% 1.25/1.66 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.25/1.66 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.25/1.66 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.25/1.66 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.25/1.66 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.25/1.66 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.25/1.66 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.66 X, T, 'tc_nat' ) ],
% 1.25/1.66 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.25/1.66 ), 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.25/1.66 ), 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.25/1.66 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.25/1.66 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.25/1.66 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.25/1.66 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.25/1.66 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.25/1.66 'tc_nat' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.25/1.66 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( =( 'c_Int_OMin', 'c_Int_OBit0'( X ) ) ) ],
% 1.25/1.66 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OMin' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.25/1.66 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.25/1.66 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.25/1.66 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.25/1.66 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ),
% 1.25/1.66 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.25/1.66 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ), ~(
% 1.25/1.66 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.66 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.25/1.66 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.25/1.66 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.25/1.66 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.66 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.25/1.66 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.25/1.66 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.25/1.66 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.25/1.66 ,
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.25/1.66 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.25/1.66 Y, X ), Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.25/1.66 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.25/1.66 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ],
% 1.25/1.66 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.25/1.66 Z, X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.25/1.66 Y, Z, X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.25/1.66 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.25/1.66 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.25/1.66 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.25/1.66 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.25/1.66 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.25/1.66 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.25/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.25/1.66 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.66 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.25/1.66 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.25/1.66 [ =( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.25/1.66 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 'tc_nat' ), Z ), hAPP( 'c_Suc', X ) ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), Y,
% 1.25/1.67 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.67 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.25/1.67 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.25/1.67 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.67 'tc_nat' ) ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( 'c_Suc',
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.25/1.67 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 1.25/1.67 ), 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', Z ), Y, 'tc_nat' ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.25/1.67 ), X, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc',
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.25/1.67 ), X, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc',
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), 'tc_nat' ) ],
% 1.25/1.67 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ) ), 'tc_nat' ) ) ],
% 1.25/1.67 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ),
% 1.25/1.67 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.25/1.67 'tc_nat' ) ) ],
% 1.25/1.67 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 1.25/1.67 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.25/1.67 'tc_nat' ) ) ],
% 1.25/1.67 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.25/1.67 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.25/1.67 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.25/1.67 , 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.67 'tc_nat' ), X, 'tc_nat' ) ],
% 1.25/1.67 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.25/1.67 , 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.67 'tc_nat' ), Y, 'tc_nat' ) ],
% 1.25/1.67 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.25/1.67 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.25/1.67 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.25/1.67 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.25/1.67 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z )
% 1.25/1.67 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ),
% 1.25/1.67 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.25/1.67 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X )
% 1.25/1.67 , Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ),
% 1.25/1.67 'tc_nat' ) ) ],
% 1.25/1.67 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc',
% 1.25/1.67 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.25/1.67 'tc_nat' ), Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.25/1.67 'tc_nat' ) ) ],
% 1.25/1.67 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( 'c_Suc',
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.67 'tc_nat' ), X ), Z ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 1.25/1.67 Z, Y, 'tc_nat' ) ) ],
% 1.25/1.67 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc',
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z, 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ), ~(
% 1.25/1.67 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.25/1.67 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.25/1.67 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.25/1.67 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.25/1.67 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.25/1.67 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.67 'tc_nat' ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.67 'tc_nat' ) ) ],
% 1.25/1.67 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.25/1.67 , Z ) ],
% 1.25/1.67 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.25/1.67 , Z ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.25/1.67 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.67 , Y ), T ), Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.25/1.67 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.67 , Y ), T ), Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.67 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.25/1.67 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.25/1.67 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.25/1.67 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.25/1.67 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.25/1.67 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.25/1.67 , ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.67 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.25/1.67 , 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.25/1.67 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.25/1.67 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.25/1.67 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.25/1.67 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 X ), Y ), T ), Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.67 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.25/1.67 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.25/1.67 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.25/1.67 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.25/1.67 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.25/1.67 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.25/1.67 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.25/1.67 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.25/1.67 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.25/1.67 'c_HOL_Oone__class_Oone'( X ) ), X ), Z, X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.25/1.67 'c_HOL_Oone__class_Oone'( X ) ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 Y, Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.25/1.67 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.25/1.67 ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.25/1.67 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.25/1.67 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.25/1.67 ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.25/1.67 ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.25/1.67 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.25/1.67 ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.25/1.67 ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.25/1.67 'c_HOL_Oone__class_Oone'( X ), X ) ), Z ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.25/1.67 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.25/1.67 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.25/1.67 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.25/1.67 , X ) ), T ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.25/1.67 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.25/1.67 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.25/1.67 , 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.25/1.67 , X ) ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.25/1.67 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.25/1.67 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.67 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.25/1.67 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.25/1.67 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.25/1.67 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.67 ) ],
% 1.25/1.67 [ ~( 'class_RealVector_Oreal__field'( X ) ), =(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), W, X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 X ), Y ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.25/1.67 Z, U, X ), W, X ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, T, X )
% 1.25/1.67 , W, X ) ), U ) ) ) ],
% 1.25/1.67 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.67 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.67 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.25/1.67 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.25/1.67 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.25/1.67 ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.67 X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.67 X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.25/1.67 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' )
% 1.25/1.67 ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.25/1.67 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.25/1.67 , ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.25/1.67 ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), X ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.67 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.25/1.67 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc',
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.67 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.25/1.67 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.67 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.25/1.67 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.67 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), U ), Z ) ), X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.25/1.67 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), U ), X ) ), Z ) ), =( Y,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.67 [ =( hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X, hAPP( 'c_Suc',
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.25/1.67 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, hAPP(
% 1.25/1.67 'c_Suc', Y ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.25/1.67 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( X
% 1.25/1.67 , 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat'
% 1.25/1.67 ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.25/1.67 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.25/1.67 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.67 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 'tc_nat' ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.25/1.67 'tc_nat' ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.67 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.25/1.67 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.67 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.25/1.67 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.25/1.67 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.67 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.67 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.67 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.67 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.25/1.67 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.67 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.67 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.25/1.67 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.67 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.67 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.67 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.67 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.25/1.67 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.67 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.25/1.67 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.67 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.25/1.67 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.67 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.67 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.67 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.25/1.67 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T
% 1.25/1.67 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.67 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.25/1.67 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.25/1.67 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.25/1.67 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.67 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.67 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.67 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.25/1.67 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.67 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.67 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.25/1.67 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.67 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.67 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.67 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.67 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.67 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.67 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.25/1.67 ), Y ), hAPP( 'c_Suc', Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.25/1.67 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.25/1.67 , Y, X ) ) ],
% 1.25/1.67 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.25/1.67 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.67 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.25/1.67 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.25/1.67 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.25/1.67 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.25/1.67 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.25/1.67 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.25/1.67 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.25/1.67 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.25/1.67 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.25/1.67 ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) )
% 1.25/1.67 , 'tc_nat' ) ],
% 1.25/1.67 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T )
% 1.25/1.67 , 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.25/1.67 , Z, 'tc_nat' ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.25/1.67 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.25/1.67 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.25/1.67 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.25/1.67 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.25/1.67 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.25/1.67 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.67 'tc_nat' ) ), Y ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.67 'tc_nat' ) ) ) ],
% 1.25/1.67 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.25/1.67 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.25/1.67 ), X ), X ), 'tc_nat' ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 1.25/1.67 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.25/1.67 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.25/1.67 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 1.25/1.67 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.25/1.67 ), X ), Z ), 'tc_nat' ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.25/1.67 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( Y, 'c_Divides_Odiv__class_Omod'( Y, X,
% 1.25/1.67 'tc_nat' ), 'tc_nat' ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( X, 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.25/1.67 'tc_nat' ), 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ),
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.25/1.67 ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.25/1.67 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ) ), Y ) ), U ), 'tc_nat' )
% 1.25/1.67 ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.25/1.67 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), T ) ), U ), 'tc_nat' )
% 1.25/1.67 , ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), X ),
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ), 'tc_nat' ) ),
% 1.25/1.67 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ),
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.25/1.67 ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ) ), Y ) ), Z ), U, 'tc_nat'
% 1.25/1.67 ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ) ), T ), U, 'tc_nat'
% 1.25/1.67 ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.25/1.67 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), T ),
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ), 'tc_nat' ) ),
% 1.25/1.67 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.25/1.67 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y
% 1.25/1.67 , X, 'tc_nat' ) ), Z ) ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.67 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z
% 1.25/1.67 ) ), T ) ) ],
% 1.25/1.67 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ),
% 1.25/1.67 'tc_nat' ) ) ],
% 1.25/1.67 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.67 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ) ), Y ) ), U ), 'tc_nat' )
% 1.25/1.67 ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.25/1.67 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.67 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ) ), Y ) ), Z ), U, 'tc_nat'
% 1.25/1.67 ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.25/1.67 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~(
% 1.25/1.67 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z, hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( T
% 1.25/1.67 , X, 'tc_nat' ) ), Y ) ), U ) ) ],
% 1.25/1.67 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~(
% 1.25/1.67 'c_lessequals'( T, X, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X
% 1.25/1.67 , T, 'tc_nat' ) ), Y ) ), Z ), U ) ],
% 1.25/1.67 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y
% 1.25/1.67 , X, 'tc_nat' ) ), Z ) ), T ) ) ) ],
% 1.25/1.67 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 1.25/1.67 hBOOL( hAPP( X, Z ) ) ],
% 1.25/1.67 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 1.25/1.67 hBOOL( hAPP( X, Z ) ) ],
% 1.25/1.67 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 1.25/1.67 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 1.25/1.67 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.25/1.67 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.25/1.67 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.67 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.67 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.25/1.67 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.25/1.67 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.25/1.67 ],
% 1.25/1.67 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.25/1.67 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 1.25/1.67 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.25/1.67 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.25/1.67 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.25/1.67 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.25/1.67 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ) ],
% 1.25/1.67 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.25/1.67 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.25/1.67 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.25/1.67 , 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat'
% 1.25/1.67 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.25/1.67 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.25/1.67 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.25/1.67 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 1.25/1.67 'tc_nat' ) ],
% 1.25/1.67 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.25/1.67 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.25/1.67 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.25/1.67 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.25/1.67 ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ),
% 1.25/1.67 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.67 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.25/1.67 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.25/1.67 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.25/1.67 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ),
% 1.25/1.67 'c_Complex_Oii' ), 'c_Complex_Oii' ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.25/1.67 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex'
% 1.25/1.67 ) ) ],
% 1.25/1.67 [ ~( =( 'c_Complex_Oii', 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex'
% 1.25/1.67 ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.67 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.25/1.67 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.25/1.67 , X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.25/1.67 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.67 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.25/1.67 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.25/1.67 X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.25/1.67 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.25/1.67 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.67 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.25/1.67 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.67 ), Y ), T ), Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.25/1.67 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.25/1.67 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 X ), T ), Z ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.25/1.67 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.25/1.67 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.25/1.67 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.25/1.67 Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.25/1.67 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.25/1.67 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.25/1.67 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.25/1.67 ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.25/1.67 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( Y
% 1.25/1.67 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.25/1.67 ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.25/1.67 ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) )
% 1.25/1.67 ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.67 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.25/1.67 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) )
% 1.25/1.67 ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_OPls'
% 1.25/1.67 , Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.25/1.67 ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.25/1.67 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( Z
% 1.25/1.67 , T, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.25/1.67 X ), Y, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.25/1.67 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.25/1.67 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.25/1.67 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.25/1.67 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.67 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.25/1.67 ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.25/1.67 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.25/1.67 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.25/1.67 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.25/1.67 ), X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.67 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.67 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.25/1.67 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.67 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.25/1.67 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.67 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.25/1.67 ), X ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.67 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.25/1.67 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.25/1.67 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.25/1.67 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.25/1.67 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.25/1.67 ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.25/1.67 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.25/1.67 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.67 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.25/1.67 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.25/1.67 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.25/1.67 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.25/1.67 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.25/1.67 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.25/1.67 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.25/1.67 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.67 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.25/1.67 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.25/1.67 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.25/1.67 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.25/1.67 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.25/1.67 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.25/1.67 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ominus__class_Ominus'(
% 1.25/1.67 hAPP( 'c_Suc', Z ), T, 'tc_nat' ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.25/1.67 , T, 'tc_nat' ) ) ), Y ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ) ],
% 1.25/1.67 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.25/1.67 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc'
% 1.25/1.67 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.25/1.67 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.25/1.67 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.25/1.67 , X, Z, U, W, V0 ) ) ],
% 1.25/1.67 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.25/1.67 'c_Suc', X ), Y, 'tc_nat' ), 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.25/1.67 hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ), 'c_Fact_Ofact__class_Ofact'(
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 'tc_nat' ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.25/1.67 , 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 'tc_nat' ), X ), Y ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 'tc_nat' ), X ), Z ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.25/1.67 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( Y ) ), Z ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.25/1.67 'tc_nat' ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.25/1.67 , 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.25/1.67 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ), X ),
% 1.25/1.67 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'(
% 1.25/1.67 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.25/1.67 'tc_nat' ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.25/1.67 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y,
% 1.25/1.67 'tc_Int_Oint' ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.67 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint' ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.67 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.25/1.67 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.25/1.67 'tc_Int_Oint' ) ) ],
% 1.25/1.67 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.25/1.67 , Y ) ) ],
% 1.25/1.67 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.67 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.25/1.67 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.25/1.67 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.67 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.25/1.67 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.25/1.67 ) ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.25/1.67 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.25/1.67 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) )
% 1.25/1.67 ) ],
% 1.25/1.67 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.25/1.67 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.67 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.25/1.67 ) ],
% 1.25/1.67 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.25/1.67 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.25/1.67 , Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.25/1.67 ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.25/1.67 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.25/1.67 'tc_nat' ), X ), X ) ) ],
% 1.25/1.67 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ) ],
% 1.25/1.67 [ 'c_Fun_Oinj__on'( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), X, 'tc_nat', 'tc_nat' ) ],
% 1.25/1.67 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.25/1.67 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.25/1.67 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.25/1.67 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.25/1.67 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.67 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.25/1.67 ) ), 'c_Complex_Oii' ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), X ), X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.25/1.67 ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.25/1.67 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.25/1.67 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 X, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.25/1.67 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.25/1.67 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.25/1.67 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'tc_nat' ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.25/1.67 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.25/1.67 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.67 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), X ), X ) ],
% 1.25/1.67 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.25/1.67 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.67 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.25/1.67 'c_HOL_Oone__class_Oone'( X ), X ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.25/1.67 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.25/1.67 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.25/1.67 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ) ), =( X,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.25/1.67 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.25/1.67 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.67 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.25/1.67 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.25/1.67 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_Fun_Oinj__on'( 'c_COMBB'( 'c_Suc', hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), X,
% 1.25/1.67 'tc_nat', 'tc_nat' ) ],
% 1.25/1.67 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.25/1.67 X ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.67 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ), X ) )
% 1.25/1.67 ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.25/1.67 ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.25/1.67 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.25/1.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.67 'c_Int_OMin', X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.25/1.67 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.67 'c_Int_OMin', X ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.25/1.67 'c_HOL_Oone__class_Oone'( X ), X ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.25/1.67 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.25/1.67 ) ],
% 1.25/1.67 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.25/1.67 [ =( 'c_FFT__Mirabelle_OIDFT'( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), X, Y ), hAPP(
% 1.25/1.67 'c_FFT__Mirabelle_OIFFT'( 'v_ka____', X ), Y ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.25/1.67 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.25/1.67 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ) )
% 1.25/1.67 ],
% 1.25/1.67 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.25/1.67 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.25/1.67 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.25/1.67 ), Y ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.67 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.25/1.67 ), Y ) ],
% 1.25/1.67 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.25/1.67 'tc_nat' ), hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.25/1.67 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.25/1.67 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ) ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.25/1.67 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.25/1.67 , 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.25/1.67 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.25/1.67 'c_FFT__Mirabelle_Oroot'( X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 'tc_nat' ), Y ), Z ) ) ) ],
% 1.25/1.67 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.25/1.67 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.25/1.67 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.25/1.67 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 1.25/1.67 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.25/1.67 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.25/1.67 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.25/1.67 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.25/1.67 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y
% 1.25/1.67 ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 1.25/1.67 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 1.25/1.67 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.25/1.67 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ),
% 1.25/1.67 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.25/1.67 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.25/1.67 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.25/1.67 ) ],
% 1.25/1.67 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.25/1.67 , X ) ) ],
% 1.25/1.67 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.25/1.67 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.25/1.67 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.25/1.67 , Y, X ) ) ],
% 1.25/1.67 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.25/1.67 , Y, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.25/1.67 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.25/1.67 , T ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.25/1.67 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.25/1.67 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.25/1.67 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.25/1.67 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.25/1.67 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.25/1.67 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.25/1.67 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.25/1.67 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.25/1.67 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.25/1.67 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.25/1.67 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.25/1.67 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.25/1.67 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.25/1.67 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.25/1.67 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.25/1.67 'c_Suc', X ), Y, 'tc_nat' ), hAPP( 'c_Suc', Z ), 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.25/1.67 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.25/1.67 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.25/1.67 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ), Y, 'tc_nat'
% 1.25/1.67 ) ) ],
% 1.25/1.67 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.25/1.67 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.25/1.67 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.25/1.67 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.25/1.67 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.25/1.67 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.25/1.67 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( 'v_i____', hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( 'c_Suc', 'v_ka____' ) ), 'tc_nat' )
% 1.25/1.67 ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.25/1.67 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.25/1.67 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.25/1.67 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.25/1.67 ) ],
% 1.25/1.67 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 X ), Y ), Y ) ) ],
% 1.25/1.67 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.25/1.67 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.25/1.67 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.25/1.67 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 1.25/1.67 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.25/1.67 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.25/1.67 , hAPP( 'c_Suc', X ) ), Z ) ) ), =( Y, Z ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.25/1.67 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.25/1.67 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.25/1.67 [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 1.25/1.67 [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.25/1.67 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.25/1.67 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.25/1.67 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.25/1.67 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.25/1.67 ), Z ), Y ), 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.25/1.67 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.25/1.67 , X ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 X ), Y ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X
% 1.25/1.67 ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.25/1.67 ), =( Z, Y ) ],
% 1.25/1.67 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.25/1.67 ) ],
% 1.25/1.67 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.25/1.67 ) ],
% 1.25/1.67 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.25/1.67 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.25/1.67 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.25/1.67 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.25/1.67 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.25/1.67 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.25/1.67 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.25/1.67 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.25/1.67 , 'c_FFT__Mirabelle_Oroot'( X ) ), X ), 'c_HOL_Oone__class_Oone'(
% 1.25/1.67 'tc_Complex_Ocomplex' ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.25/1.67 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.25/1.67 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.25/1.67 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.25/1.67 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.25/1.67 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.25/1.67 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.25/1.67 , Y ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.25/1.67 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.25/1.67 , X ) ), T ), X ) ) ],
% 1.25/1.67 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.25/1.67 Y ) ],
% 1.25/1.67 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.25/1.67 Y ) ],
% 1.25/1.67 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.25/1.67 Y ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.25/1.67 Y ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.25/1.67 Y ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.25/1.67 Y ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), hAPP(
% 1.25/1.67 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.25/1.67 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), Z ) ) ],
% 1.25/1.67 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.25/1.67 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.25/1.67 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.25/1.67 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.25/1.67 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.25/1.67 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.25/1.67 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.25/1.67 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.25/1.67 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.25/1.67 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.25/1.67 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.25/1.67 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.25/1.67 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.25/1.67 , T, X ) ) ), =( Z, T ) ],
% 1.25/1.67 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.25/1.67 , T, X ) ) ), =( Y, Z ) ],
% 1.25/1.67 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.25/1.67 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.25/1.67 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.25/1.67 T, X ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.25/1.67 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.25/1.67 T, X ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.25/1.67 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.25/1.67 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.25/1.67 ), X ), Z ), 'tc_nat' ) ) ],
% 1.25/1.67 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.25/1.67 ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.25/1.67 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.25/1.67 ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.25/1.67 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.25/1.67 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y ),
% 1.25/1.67 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ),
% 1.25/1.67 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), =( hAPP(
% 1.25/1.67 'c_Suc', X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.25/1.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.25/1.67 , X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.25/1.67 [ ~( 'c_HOL_Oord__class_Oless'( 'v_i____', hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ) ) ],
% 1.25/1.67 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.25/1.67 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.25/1.67 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.25/1.67 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.25/1.67 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( 'v_i____', hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ) ), 'tc_nat' ) ],
% 1.25/1.67 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( 'v_i____',
% 1.25/1.67 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ) ],
% 1.25/1.67 [ ~( =( 'c_HOL_Ominus__class_Ominus'( 'c_FFT__Mirabelle_OIDFT'( hAPP(
% 1.25/1.67 hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'c_COMBB'( 'v_a____', hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat'
% 1.25/1.67 ), 'c_HOL_Ominus__class_Ominus'( 'v_i____', hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 1.25/1.67 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ) ) ), 'tc_Complex_Ocomplex' )
% 1.25/1.67 ), 'c_HOL_Ominus__class_Ominus'( 'v_i____', hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ) ) ),
% 1.25/1.67 'c_FFT__Mirabelle_OIDFT'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.25/1.67 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.25/1.67 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'c_COMBB'(
% 1.25/1.67 'v_a____', 'c_COMBB'( 'c_Suc', hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.25/1.67 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.25/1.67 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat',
% 1.25/1.67 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus'( 'v_i____', hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ) ) ),
% 1.25/1.67 'tc_Complex_Ocomplex' ), 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.25/1.67 'c_FFT__Mirabelle_OIFFT'( 'v_ka____', 'c_COMBB'( 'v_a____', hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat'
% 1.25/1.67 ) ), 'c_HOL_Ominus__class_Ominus'( 'v_i____', hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ) ), hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.25/1.67 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 1.25/1.67 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP(
% 1.25/1.67 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ) ) ), 'tc_Complex_Ocomplex' )
% 1.25/1.67 ), 'c_HOL_Ominus__class_Ominus'( 'v_i____', hAPP( hAPP(
% 1.25/1.67 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ) ) ), hAPP(
% 1.25/1.67 'c_FFT__Mirabelle_OIFFT'( 'v_ka____', 'c_COMBB'( 'v_a____', 'c_COMBB'(
% 1.25/1.67 'c_Suc', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat'
% 1.25/1.67 , 'tc_Complex_Ocomplex', 'tc_nat' ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.25/1.67 'v_i____', hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.25/1.67 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.25/1.67 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ) ) ),
% 1.25/1.67 'tc_Complex_Ocomplex' ) ) ) ],
% 1.25/1.67 [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ), ~(
% 1.25/1.67 'class_Lattices_Oboolean__algebra'( Y ) ) ],
% 1.25/1.67 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.25/1.67 'class_Orderings_Opreorder'( Y ) ) ],
% 1.25/1.67 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.25/1.67 'class_Orderings_Oorder'( Y ) ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.25/1.67 ],
% 1.25/1.67 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.25/1.67 ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.25/1.67 ],
% 1.25/1.67 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.25/1.67 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.25/1.67 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.25/1.67 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.25/1.67 ],
% 1.25/1.67 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.25/1.67 ],
% 1.25/1.67 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.25/1.67 'tc_Complex_Ocomplex' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.25/1.67 'tc_Complex_Ocomplex' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.25/1.67 'tc_Complex_Ocomplex' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.25/1.67 ],
% 1.25/1.67 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.25/1.67 ],
% 1.25/1.67 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.25/1.67 ],
% 1.25/1.67 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.25/1.67 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.25/1.67 [ 'class_RealVector_Oreal__field'( 'tc_Complex_Ocomplex' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.25/1.67 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.25/1.67 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.25/1.67 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.25/1.67 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.25/1.67 [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ],
% 1.25/1.67 [ =( 'c_COMBC'( X, Y, Z, T, U, W ), hAPP( hAPP( X, Z ), Y ) ) ],
% 1.25/1.67 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.25/1.67 ,
% 1.25/1.67 [ 'c_fequal'( X, X, Y ) ],
% 1.25/1.67 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.25/1.67 ] .
% 1.25/1.67
% 1.25/1.67
% 1.25/1.67 percentage equality = 0.223565, percentage horn = 0.849446
% 1.25/1.67 This is a problem with some equality
% 1.25/1.67
% 1.25/1.67
% 1.25/1.67
% 1.25/1.67 Options Used:
% 1.25/1.67
% 1.25/1.67 useres = 1
% 1.25/1.67 useparamod = 1
% 1.25/1.67 useeqrefl = 1
% 1.25/1.67 useeqfact = 1
% 1.25/1.67 usefactor = 1
% 1.25/1.67 usesimpsplitting = 0
% 1.25/1.67 usesimpdemod = 5
% 1.25/1.67 usesimpres = 3
% 1.25/1.67
% 1.25/1.67 resimpinuse = 1000
% 1.25/1.67 resimpclauses = 20000
% 1.25/1.67 substype = eqrewr
% 1.25/1.67 backwardsubs = 1
% 1.25/1.67 selectoldest = 5
% 1.25/1.67
% 1.25/1.67 litorderings [0] = split
% 1.25/1.67 litorderings [1] = extend the termordering, first sorting on arguments
% 1.25/1.67
% 1.25/1.67 termordering = kbo
% 1.25/1.67
% 1.25/1.67 litapriori = 0
% 1.25/1.67 termapriori = 1
% 1.25/1.67 litaposteriori = 0
% 1.25/1.67 termaposteriori = 0
% 1.25/1.67 demodaposteriori = 0
% 1.25/1.67 ordereqreflfact = 0
% 1.25/1.67
% 1.25/1.67 litselect = negord
% 1.25/1.67
% 1.25/1.67 maxweight = 15
% 1.25/1.67 maxdepth = 30000
% 1.25/1.67 maxlength = 115
% 1.25/1.67 maxnrvars = 195
% 1.25/1.67 excuselevel = 1
% 1.25/1.67 increasemaxweight = 1
% 1.25/1.67
% 1.25/1.67 maxselected = 10000000
% 1.25/1.67 maxnrclauses = 10000000
% 1.25/1.67
% 1.25/1.67 showgenerated = 0
% 1.25/1.67 showkept = 0
% 1.25/1.67 showselected = 0
% 1.25/1.67 showdeleted = 0
% 1.25/1.67 showresimp = 1
% 1.25/1.67 showstatus = 2000
% 1.25/1.67
% 1.25/1.67 prologoutput = 1
% 1.25/1.67 nrgoals = 5000000
% 1.25/1.67 totalproof = 1
% 1.25/1.67
% 1.25/1.67 Symbols occurring in the translation:
% 1.25/1.67
% 1.25/1.67 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.25/1.67 . [1, 2] (w:1, o:151, a:1, s:1, b:0),
% 1.25/1.67 ! [4, 1] (w:0, o:73, a:1, s:1, b:0),
% 1.25/1.67 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.25/1.67 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.25/1.67 'tc_nat' [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.25/1.67 'c_HOL_Otimes__class_Otimes' [40, 1] (w:1, o:78, a:1, s:1, b:0),
% 1.25/1.67 hAPP [42, 2] (w:1, o:176, a:1, s:1, b:0),
% 1.25/1.67 'c_Divides_Odiv__class_Odiv' [45, 3] (w:1, o:184, a:1, s:1, b:0),
% 1.25/1.67 'c_HOL_Ozero__class_Ozero' [46, 1] (w:1, o:79, a:1, s:1, b:0),
% 1.25/1.67 'class_Divides_Osemiring__div' [48, 1] (w:1, o:81, a:1, s:1, b:0),
% 1.25/1.67 'class_Ring__and__Field_Opordered__semiring' [52, 1] (w:1, o:94, a:1
% 1.25/1.67 , s:1, b:0),
% 1.25/1.67 'c_lessequals' [54, 3] (w:1, o:185, a:1, s:1, b:0),
% 1.25/1.67 'c_HOL_Oplus__class_Oplus' [55, 1] (w:1, o:96, a:1, s:1, b:0),
% 1.25/1.67 'c_HOL_Oone__class_Oone' [56, 1] (w:1, o:95, a:1, s:1, b:0),
% 1.25/1.67 'class_OrderedGroup_Oordered__ab__group__add' [57, 1] (w:1, o:97, a:1
% 1.25/1.67 , s:1, b:0),
% 1.25/1.67 'c_HOL_Ouminus__class_Ouminus' [58, 2] (w:1, o:177, a:1, s:1, b:0),
% 1.25/1.67 'c_Suc' [59, 0] (w:1, o:30, a:1, s:1, b:0),
% 1.25/1.67 'c_Groebner__Basis_Ogb__semiring' [66, 6] (w:1, o:194, a:1, s:1, b:0)
% 1.25/1.67 ,
% 1.25/1.67 'class_Ring__and__Field_Oordered__ring__strict' [67, 1] (w:1, o:85
% 1.25/1.67 , a:1, s:1, b:0),
% 1.25/1.67 'c_HOL_Oord__class_Oless' [69, 3] (w:1, o:186, a:1, s:1, b:0),
% 1.25/1.67 'c_Divides_Odiv__class_Omod' [72, 3] (w:1, o:187, a:1, s:1, b:0),
% 1.25/1.67 hBOOL [73, 1] (w:1, o:98, a:1, s:1, b:0),
% 1.25/1.67 'class_OrderedGroup_Olordered__ab__group__add' [74, 1] (w:1, o:99, a:
% 1.25/1.67 1, s:1, b:0),
% 1.25/1.67 'class_Ring__and__Field_Oordered__idom' [75, 1] (w:1, o:86, a:1, s:1
% 1.25/1.67 , b:0),
% 1.25/1.67 'c_Power_Opower__class_Opower' [76, 1] (w:1, o:100, a:1, s:1, b:0),
% 1.25/1.67 'c_Parity_Oeven__odd__class_Oeven' [77, 2] (w:1, o:178, a:1, s:1, b:0
% 1.25/1.67 ),
% 1.25/1.67 'class_OrderedGroup_Opordered__ab__group__add__abs' [78, 1] (w:1, o:
% 1.25/1.67 101, a:1, s:1, b:0),
% 1.25/1.67 'c_HOL_Oabs__class_Oabs' [79, 2] (w:1, o:179, a:1, s:1, b:0),
% 1.25/1.67 'c_HOL_Ominus__class_Ominus' [80, 3] (w:1, o:188, a:1, s:1, b:0),
% 1.25/1.67 'class_Ring__and__Field_Opordered__cancel__semiring' [81, 1] (w:1, o:
% 1.25/1.67 102, a:1, s:1, b:0),
% 1.25/1.67 'class_Ring__and__Field_Opordered__ring' [82, 1] (w:1, o:92, a:1, s:1
% 1.25/1.67 , b:0),
% 1.25/1.67 'class_Ring__and__Field_Oordered__field' [83, 1] (w:1, o:87, a:1, s:1
% 3.82/4.17 , b:0),
% 3.82/4.17 'class_Ring__and__Field_Odivision__by__zero' [84, 1] (w:1, o:106, a:1
% 3.82/4.17 , s:1, b:0),
% 3.82/4.17 'c_HOL_Oinverse__class_Odivide' [85, 3] (w:1, o:189, a:1, s:1, b:0),
% 3.82/4.17
% 3.82/4.17 'c_Fact_Ofact__class_Ofact' [87, 2] (w:1, o:180, a:1, s:1, b:0),
% 3.82/4.17 'class_Divides_Oring__div' [88, 1] (w:1, o:80, a:1, s:1, b:0),
% 3.82/4.17 'class_OrderedGroup_Ogroup__add' [89, 1] (w:1, o:107, a:1, s:1, b:0)
% 3.82/4.17 ,
% 3.82/4.17 'class_Ring__and__Field_Ocomm__semiring__1' [90, 1] (w:1, o:104, a:1
% 3.82/4.17 , s:1, b:0),
% 3.82/4.17 'class_OrderedGroup_Oab__group__add' [91, 1] (w:1, o:108, a:1, s:1
% 3.82/4.17 , b:0),
% 3.82/4.17 'class_Int_Onumber__ring' [92, 1] (w:1, o:109, a:1, s:1, b:0),
% 3.82/4.17 'class_Ring__and__Field_Ofield' [93, 1] (w:1, o:110, a:1, s:1, b:0),
% 3.82/4.17
% 3.82/4.17 'class_Ring__and__Field_Oidom' [100, 1] (w:1, o:111, a:1, s:1, b:0),
% 3.82/4.17
% 3.82/4.17 'class_OrderedGroup_Ocancel__ab__semigroup__add' [101, 1] (w:1, o:112
% 3.82/4.17 , a:1, s:1, b:0),
% 3.82/4.17 'class_OrderedGroup_Ocancel__semigroup__add' [102, 1] (w:1, o:113, a:
% 3.82/4.17 1, s:1, b:0),
% 3.82/4.17 'class_OrderedGroup_Opordered__comm__monoid__add' [103, 1] (w:1, o:
% 3.82/4.17 114, a:1, s:1, b:0),
% 3.82/4.17 'class_OrderedGroup_Opordered__ab__group__add' [104, 1] (w:1, o:115
% 3.82/4.17 , a:1, s:1, b:0),
% 3.82/4.17 'c_Int_Onumber__class_Onumber__of' [106, 2] (w:1, o:181, a:1, s:1, b:
% 3.82/4.17 0),
% 3.82/4.17 'c_Int_OMin' [108, 0] (w:1, o:51, a:1, s:1, b:0),
% 3.82/4.17 'class_OrderedGroup_Opordered__ab__semigroup__add' [110, 1] (w:1, o:
% 3.82/4.17 116, a:1, s:1, b:0),
% 3.82/4.17 'class_Ring__and__Field_Omult__mono' [112, 1] (w:1, o:117, a:1, s:1
% 3.82/4.17 , b:0),
% 3.82/4.17 'class_Ring__and__Field_Omult__mono1' [113, 1] (w:1, o:118, a:1, s:1
% 3.82/4.17 , b:0),
% 3.82/4.17 'class_Ring__and__Field_Oordered__semidom' [114, 1] (w:1, o:88, a:1
% 3.82/4.17 , s:1, b:0),
% 3.82/4.17 'class_Ring__and__Field_Osemiring__0' [115, 1] (w:1, o:123, a:1, s:1
% 3.82/4.17 , b:0),
% 3.82/4.17 'class_Power_Opower' [116, 1] (w:1, o:137, a:1, s:1, b:0),
% 3.82/4.17 'class_Ring__and__Field_Ozero__neq__one' [117, 1] (w:1, o:138, a:1
% 3.82/4.17 , s:1, b:0),
% 3.82/4.17 'class_Ring__and__Field_Ono__zero__divisors' [118, 1] (w:1, o:84, a:1
% 3.82/4.17 , s:1, b:0),
% 3.82/4.17 'class_Ring__and__Field_Omult__zero' [119, 1] (w:1, o:83, a:1, s:1
% 3.82/4.17 , b:0),
% 3.82/4.17 'class_Ring__and__Field_Opordered__ring__abs' [120, 1] (w:1, o:93, a:
% 3.82/4.17 1, s:1, b:0),
% 3.82/4.17 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [121, 1]
% 3.82/4.17 (w:1, o:124, a:1, s:1, b:0),
% 3.82/4.17 'class_Orderings_Oorder' [122, 1] (w:1, o:125, a:1, s:1, b:0),
% 3.82/4.17 'tc_Int_Oint' [123, 0] (w:1, o:53, a:1, s:1, b:0),
% 3.82/4.17 'class_Lattices_Oboolean__algebra' [124, 1] (w:1, o:139, a:1, s:1, b:
% 3.82/4.17 0),
% 3.82/4.17 'class_OrderedGroup_Olordered__ab__group__add__abs' [125, 1] (w:1, o:
% 3.82/4.17 126, a:1, s:1, b:0),
% 3.82/4.17 'tc_Complex_Ocomplex' [126, 0] (w:1, o:54, a:1, s:1, b:0),
% 3.82/4.17 'c_Complex_Oii' [127, 0] (w:1, o:55, a:1, s:1, b:0),
% 3.82/4.17 'class_Ring__and__Field_Oabs__if' [128, 1] (w:1, o:140, a:1, s:1, b:0
% 3.82/4.17 ),
% 3.82/4.17 'class_Orderings_Olinorder' [129, 1] (w:1, o:127, a:1, s:1, b:0),
% 3.82/4.17 'class_OrderedGroup_Ocomm__monoid__add' [130, 1] (w:1, o:128, a:1, s:
% 3.82/4.17 1, b:0),
% 3.82/4.17 'c_Int_OPls' [131, 0] (w:1, o:56, a:1, s:1, b:0),
% 3.82/4.17 'class_Ring__and__Field_Ocomm__ring__1' [132, 1] (w:1, o:103, a:1, s:
% 3.82/4.17 1, b:0),
% 3.82/4.17 'c_Int_OBit0' [133, 1] (w:1, o:141, a:1, s:1, b:0),
% 3.82/4.17 'c_Int_OBit1' [134, 1] (w:1, o:142, a:1, s:1, b:0),
% 3.82/4.17 'class_Ring__and__Field_Olordered__ring' [141, 1] (w:1, o:82, a:1, s:
% 3.82/4.17 1, b:0),
% 3.82/4.17 'class_OrderedGroup_Oab__semigroup__add' [142, 1] (w:1, o:129, a:1
% 3.82/4.17 , s:1, b:0),
% 3.82/4.17 'class_OrderedGroup_Omonoid__mult' [143, 1] (w:1, o:130, a:1, s:1, b:
% 3.82/4.17 0),
% 3.82/4.17 'class_OrderedGroup_Omonoid__add' [144, 1] (w:1, o:131, a:1, s:1, b:0
% 3.82/4.17 ),
% 3.82/4.17 'class_Orderings_Opreorder' [145, 1] (w:1, o:132, a:1, s:1, b:0),
% 3.82/4.17 'c_FFT__Mirabelle_OIFFT' [148, 2] (w:1, o:182, a:1, s:1, b:0),
% 3.82/4.17 'class_Ring__and__Field_Oordered__semiring__strict' [149, 1] (w:1, o:
% 3.82/4.17 89, a:1, s:1, b:0),
% 3.82/4.17 'class_Ring__and__Field_Oordered__comm__semiring__strict' [150, 1]
% 3.82/4.17 (w:1, o:90, a:1, s:1, b:0),
% 3.82/4.17 'class_Int_Onumber' [151, 1] (w:1, o:143, a:1, s:1, b:0),
% 3.82/4.17 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [152, 1]
% 14.90/15.26 (w:1, o:133, a:1, s:1, b:0),
% 14.90/15.26 'class_Ring__and__Field_Oordered__semiring' [153, 1] (w:1, o:91, a:1
% 14.90/15.26 , s:1, b:0),
% 14.90/15.26 'class_Ring__and__Field_Oring' [154, 1] (w:1, o:119, a:1, s:1, b:0),
% 14.90/15.26
% 14.90/15.26 'class_Ring__and__Field_Oring__no__zero__divisors' [155, 1] (w:1, o:
% 14.90/15.26 120, a:1, s:1, b:0),
% 14.90/15.26 'class_RealVector_Oreal__normed__algebra' [156, 1] (w:1, o:144, a:1
% 14.90/15.26 , s:1, b:0),
% 14.90/15.26 'class_Ring__and__Field_Ocomm__semiring' [157, 1] (w:1, o:105, a:1
% 14.90/15.26 , s:1, b:0),
% 14.90/15.26 'class_Ring__and__Field_Osemiring' [159, 1] (w:1, o:145, a:1, s:1, b:
% 14.90/15.26 0),
% 14.90/15.26 'c_FFT__Mirabelle_Oroot' [165, 1] (w:1, o:146, a:1, s:1, b:0),
% 14.90/15.26 'c_Fun_Oinj__on' [167, 4] (w:1, o:192, a:1, s:1, b:0),
% 14.90/15.26 'class_Ring__and__Field_Oring__1__no__zero__divisors' [168, 1] (w:1
% 14.90/15.26 , o:121, a:1, s:1, b:0),
% 14.90/15.26 'class_RealVector_Oreal__normed__field' [169, 1] (w:1, o:147, a:1, s:
% 14.90/15.26 1, b:0),
% 14.90/15.26 'class_Ring__and__Field_Oring__1' [170, 1] (w:1, o:122, a:1, s:1, b:0
% 14.90/15.26 ),
% 14.90/15.26 'class_RealVector_Oreal__field' [171, 1] (w:1, o:148, a:1, s:1, b:0)
% 14.90/15.26 ,
% 14.90/15.26 'class_Ring__and__Field_Osemiring__1' [173, 1] (w:1, o:149, a:1, s:1
% 14.90/15.26 , b:0),
% 14.90/15.26 'c_COMBB' [175, 5] (w:1, o:193, a:1, s:1, b:0),
% 14.90/15.26 'v_ka____' [176, 0] (w:1, o:61, a:1, s:1, b:0),
% 14.90/15.26 'c_FFT__Mirabelle_OIDFT' [177, 3] (w:1, o:190, a:1, s:1, b:0),
% 14.90/15.26 'v_i____' [179, 0] (w:1, o:63, a:1, s:1, b:0),
% 14.90/15.26 'class_OrderedGroup_Oab__semigroup__mult' [180, 1] (w:1, o:134, a:1
% 14.90/15.26 , s:1, b:0),
% 14.90/15.26 'class_OrderedGroup_Ocomm__monoid__mult' [181, 1] (w:1, o:135, a:1
% 14.90/15.26 , s:1, b:0),
% 14.90/15.26 'class_OrderedGroup_Oab__semigroup__idem__mult' [182, 1] (w:1, o:136
% 14.90/15.26 , a:1, s:1, b:0),
% 14.90/15.26 'class_Int_Oring__char__0' [187, 1] (w:1, o:150, a:1, s:1, b:0),
% 14.90/15.26 'v_a____' [188, 0] (w:1, o:68, a:1, s:1, b:0),
% 14.90/15.26 'tc_fun' [191, 2] (w:1, o:183, a:1, s:1, b:0),
% 14.90/15.26 'c_COMBC' [192, 6] (w:1, o:195, a:1, s:1, b:0),
% 14.90/15.26 'c_fequal' [193, 3] (w:1, o:191, a:1, s:1, b:0).
% 14.90/15.26
% 14.90/15.26
% 14.90/15.26 Starting Search:
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26
% 14.90/15.26 Intermediate Status:
% 14.90/15.26 Generated: 4370
% 14.90/15.26 Kept: 2088
% 14.90/15.26 Inuse: 50
% 14.90/15.26 Deleted: 1
% 14.90/15.26 Deletedinuse: 0
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26
% 14.90/15.26 Intermediate Status:
% 14.90/15.26 Generated: 11459
% 14.90/15.26 Kept: 4577
% 14.90/15.26 Inuse: 158
% 14.90/15.26 Deleted: 5
% 14.90/15.26 Deletedinuse: 2
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26
% 14.90/15.26 Intermediate Status:
% 14.90/15.26 Generated: 19562
% 14.90/15.26 Kept: 6763
% 14.90/15.26 Inuse: 197
% 14.90/15.26 Deleted: 7
% 14.90/15.26 Deletedinuse: 3
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26
% 14.90/15.26 Intermediate Status:
% 14.90/15.26 Generated: 25655
% 14.90/15.26 Kept: 8783
% 14.90/15.26 Inuse: 302
% 14.90/15.26 Deleted: 12
% 14.90/15.26 Deletedinuse: 3
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26
% 14.90/15.26 Intermediate Status:
% 14.90/15.26 Generated: 32288
% 14.90/15.26 Kept: 10809
% 14.90/15.26 Inuse: 358
% 14.90/15.26 Deleted: 16
% 14.90/15.26 Deletedinuse: 3
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26
% 14.90/15.26 Intermediate Status:
% 14.90/15.26 Generated: 37936
% 14.90/15.26 Kept: 12862
% 14.90/15.26 Inuse: 378
% 14.90/15.26 Deleted: 16
% 14.90/15.26 Deletedinuse: 3
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26
% 14.90/15.26 Intermediate Status:
% 14.90/15.26 Generated: 46304
% 14.90/15.26 Kept: 14864
% 14.90/15.26 Inuse: 412
% 14.90/15.26 Deleted: 16
% 14.90/15.26 Deletedinuse: 3
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26
% 14.90/15.26 Intermediate Status:
% 14.90/15.26 Generated: 59321
% 14.90/15.26 Kept: 17258
% 14.90/15.26 Inuse: 428
% 14.90/15.26 Deleted: 16
% 14.90/15.26 Deletedinuse: 3
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26
% 14.90/15.26 Intermediate Status:
% 14.90/15.26 Generated: 68442
% 14.90/15.26 Kept: 19443
% 14.90/15.26 Inuse: 467
% 14.90/15.26 Deleted: 17
% 14.90/15.26 Deletedinuse: 3
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26 Resimplifying clauses:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26
% 14.90/15.26 Intermediate Status:
% 14.90/15.26 Generated: 78120
% 14.90/15.26 Kept: 21746
% 14.90/15.26 Inuse: 492
% 14.90/15.26 Deleted: 633
% 14.90/15.26 Deletedinuse: 3
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26
% 14.90/15.26 Intermediate Status:
% 14.90/15.26 Generated: 85383
% 14.90/15.26 Kept: 23869
% 14.90/15.26 Inuse: 522
% 14.90/15.26 Deleted: 633
% 14.90/15.26 Deletedinuse: 3
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26
% 14.90/15.26 Intermediate Status:
% 14.90/15.26 Generated: 104624
% 14.90/15.26 Kept: 26571
% 14.90/15.26 Inuse: 542
% 14.90/15.26 Deleted: 633
% 14.90/15.26 Deletedinuse: 3
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26 Resimplifying inuse:
% 14.90/15.26 Done
% 14.90/15.26
% 14.90/15.26
% 14.90/15.26 Intermediate Status:
% 14.90/15.26 Generated: 122598
% 14.90/15.26 Kept: 28698
% 14.90/15.26 Inuse: 557
% 14.90/15.26 Deleted: 633
% 32.54/32.93 Deletedinuse: 3
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 130365
% 32.54/32.93 Kept: 30961
% 32.54/32.93 Inuse: 592
% 32.54/32.93 Deleted: 633
% 32.54/32.93 Deletedinuse: 3
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 139007
% 32.54/32.93 Kept: 33209
% 32.54/32.93 Inuse: 632
% 32.54/32.93 Deleted: 633
% 32.54/32.93 Deletedinuse: 3
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 147216
% 32.54/32.93 Kept: 35545
% 32.54/32.93 Inuse: 662
% 32.54/32.93 Deleted: 633
% 32.54/32.93 Deletedinuse: 3
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 154430
% 32.54/32.93 Kept: 37576
% 32.54/32.93 Inuse: 692
% 32.54/32.93 Deleted: 633
% 32.54/32.93 Deletedinuse: 3
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 161543
% 32.54/32.93 Kept: 39586
% 32.54/32.93 Inuse: 722
% 32.54/32.93 Deleted: 633
% 32.54/32.93 Deletedinuse: 3
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 171234
% 32.54/32.93 Kept: 41645
% 32.54/32.93 Inuse: 742
% 32.54/32.93 Deleted: 633
% 32.54/32.93 Deletedinuse: 3
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying clauses:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 186032
% 32.54/32.93 Kept: 44436
% 32.54/32.93 Inuse: 752
% 32.54/32.93 Deleted: 1114
% 32.54/32.93 Deletedinuse: 4
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 197916
% 32.54/32.93 Kept: 47119
% 32.54/32.93 Inuse: 756
% 32.54/32.93 Deleted: 1121
% 32.54/32.93 Deletedinuse: 5
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 206029
% 32.54/32.93 Kept: 50110
% 32.54/32.93 Inuse: 766
% 32.54/32.93 Deleted: 1126
% 32.54/32.93 Deletedinuse: 5
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 214520
% 32.54/32.93 Kept: 53361
% 32.54/32.93 Inuse: 777
% 32.54/32.93 Deleted: 1127
% 32.54/32.93 Deletedinuse: 5
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 222905
% 32.54/32.93 Kept: 55379
% 32.54/32.93 Inuse: 793
% 32.54/32.93 Deleted: 1127
% 32.54/32.93 Deletedinuse: 5
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 230669
% 32.54/32.93 Kept: 57415
% 32.54/32.93 Inuse: 806
% 32.54/32.93 Deleted: 1127
% 32.54/32.93 Deletedinuse: 5
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 238177
% 32.54/32.93 Kept: 59469
% 32.54/32.93 Inuse: 835
% 32.54/32.93 Deleted: 1127
% 32.54/32.93 Deletedinuse: 5
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 247936
% 32.54/32.93 Kept: 61498
% 32.54/32.93 Inuse: 853
% 32.54/32.93 Deleted: 1127
% 32.54/32.93 Deletedinuse: 5
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying clauses:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 259217
% 32.54/32.93 Kept: 64271
% 32.54/32.93 Inuse: 860
% 32.54/32.93 Deleted: 1438
% 32.54/32.93 Deletedinuse: 5
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 268784
% 32.54/32.93 Kept: 67099
% 32.54/32.93 Inuse: 870
% 32.54/32.93 Deleted: 1438
% 32.54/32.93 Deletedinuse: 5
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 279253
% 32.54/32.93 Kept: 69780
% 32.54/32.93 Inuse: 895
% 32.54/32.93 Deleted: 1438
% 32.54/32.93 Deletedinuse: 5
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 284496
% 32.54/32.93 Kept: 71786
% 32.54/32.93 Inuse: 901
% 32.54/32.93 Deleted: 1438
% 32.54/32.93 Deletedinuse: 5
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 292292
% 32.54/32.93 Kept: 73811
% 32.54/32.93 Inuse: 924
% 32.54/32.93 Deleted: 1438
% 32.54/32.93 Deletedinuse: 5
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 302016
% 32.54/32.93 Kept: 76121
% 32.54/32.93 Inuse: 942
% 32.54/32.93 Deleted: 1444
% 32.54/32.93 Deletedinuse: 8
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 309932
% 32.54/32.93 Kept: 78268
% 32.54/32.93 Inuse: 956
% 32.54/32.93 Deleted: 1445
% 32.54/32.93 Deletedinuse: 8
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 318798
% 32.54/32.93 Kept: 80436
% 32.54/32.93 Inuse: 980
% 32.54/32.93 Deleted: 1446
% 32.54/32.93 Deletedinuse: 8
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 329925
% 32.54/32.93 Kept: 82532
% 32.54/32.93 Inuse: 1015
% 32.54/32.93 Deleted: 1446
% 32.54/32.93 Deletedinuse: 8
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying clauses:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93
% 32.54/32.93 Intermediate Status:
% 32.54/32.93 Generated: 349597
% 32.54/32.93 Kept: 85009
% 32.54/32.93 Inuse: 1040
% 32.54/32.93 Deleted: 10327
% 32.54/32.93 Deletedinuse: 14
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 32.54/32.93 Done
% 32.54/32.93
% 32.54/32.93 Resimplifying inuse:
% 69.71/70.09 Done
% 69.71/70.09
% 69.71/70.09
% 69.71/70.09 Intermediate Status:
% 69.71/70.09 Generated: 363267
% 69.71/70.09 Kept: 87261
% 69.71/70.09 Inuse: 1080
% 69.71/70.09 Deleted: 10327
% 69.71/70.09 Deletedinuse: 14
% 69.71/70.09
% 69.71/70.09 Resimplifying inuse:
% 69.71/70.09 Done
% 69.71/70.09
% 69.71/70.09 Resimplifying inuse:
% 69.71/70.09 Done
% 69.71/70.09
% 69.71/70.09
% 69.71/70.09 Intermediate Status:
% 69.71/70.09 Generated: 375348
% 69.71/70.09 Kept: 89327
% 69.71/70.09 Inuse: 1110
% 69.71/70.09 Deleted: 10327
% 69.71/70.09 Deletedinuse: 14
% 69.71/70.09
% 69.71/70.09 Resimplifying inuse:
% 69.71/70.09 Done
% 69.71/70.09
% 69.71/70.09 Resimplifying inuse:
% 69.71/70.09 Done
% 69.71/70.09
% 69.71/70.09
% 69.71/70.09 Intermediate Status:
% 69.71/70.09 Generated: 389384
% 69.71/70.09 Kept: 92324
% 69.71/70.09 Inuse: 1135
% 69.71/70.09 Deleted: 10327
% 69.71/70.09 Deletedinuse: 14
% 69.71/70.09
% 69.71/70.09 Resimplifying inuse:
% 69.71/70.09 Done
% 69.71/70.09
% 69.71/70.09 Resimplifying inuse:
% 69.71/70.09 Done
% 69.71/70.09
% 69.71/70.09
% 69.71/70.09 Intermediate Status:
% 69.71/70.09 Generated: 398919
% 69.71/70.09 Kept: 94340
% 69.71/70.09 Inuse: 1151
% 69.71/70.09 Deleted: 10327
% 69.71/70.09 Deletedinuse: 14
% 69.71/70.09
% 69.71/70.09 Resimplifying inuse:
% 69.71/70.09 Done
% 69.71/70.09
% 69.71/70.09
% 69.71/70.09 Intermediate Status:
% 69.71/70.09 Generated: 411496
% 69.71/70.09 Kept: 96911
% 69.71/70.09 Inuse: 1170
% 69.71/70.09 Deleted: 10327
% 69.71/70.09 Deletedinuse: 14
% 69.71/70.09
% 69.71/70.09 Resimplifying inuse:
% 69.71/70.09 Done
% 69.71/70.09
% 69.71/70.09 Resimplifying inuse:
% 69.71/70.09 Done
% 69.71/70.09
% 69.71/70.09
% 69.71/70.09 Intermediate Status:
% 69.71/70.09 Generated: 420449
% 69.71/70.09 Kept: 98930
% 69.71/70.09 Inuse: 1185
% 69.71/70.09 Deleted: 10327
% 69.71/70.09 Deletedinuse: 14
% 69.71/70.09
% 69.71/70.09 Resimplifying inuse:
% 69.71/70.09 Done
% 69.71/70.09
% 69.71/70.09 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10
% 69.71/70.10 Intermediate Status:
% 69.71/70.10 Generated: 431926
% 69.71/70.10 Kept: 100998
% 69.71/70.10 Inuse: 1220
% 69.71/70.10 Deleted: 10327
% 69.71/70.10 Deletedinuse: 14
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10 Resimplifying clauses:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10
% 69.71/70.10 Intermediate Status:
% 69.71/70.10 Generated: 442548
% 69.71/70.10 Kept: 103012
% 69.71/70.10 Inuse: 1238
% 69.71/70.10 Deleted: 11527
% 69.71/70.10 Deletedinuse: 15
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10
% 69.71/70.10 Intermediate Status:
% 69.71/70.10 Generated: 452460
% 69.71/70.10 Kept: 105015
% 69.71/70.10 Inuse: 1265
% 69.71/70.10 Deleted: 11527
% 69.71/70.10 Deletedinuse: 15
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10
% 69.71/70.10 Intermediate Status:
% 69.71/70.10 Generated: 463556
% 69.71/70.10 Kept: 107042
% 69.71/70.10 Inuse: 1293
% 69.71/70.10 Deleted: 11527
% 69.71/70.10 Deletedinuse: 15
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10
% 69.71/70.10 Intermediate Status:
% 69.71/70.10 Generated: 475600
% 69.71/70.10 Kept: 110191
% 69.71/70.10 Inuse: 1315
% 69.71/70.10 Deleted: 11527
% 69.71/70.10 Deletedinuse: 15
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10
% 69.71/70.10 Intermediate Status:
% 69.71/70.10 Generated: 482243
% 69.71/70.10 Kept: 112217
% 69.71/70.10 Inuse: 1337
% 69.71/70.10 Deleted: 11528
% 69.71/70.10 Deletedinuse: 15
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10
% 69.71/70.10 Intermediate Status:
% 69.71/70.10 Generated: 490736
% 69.71/70.10 Kept: 114224
% 69.71/70.10 Inuse: 1349
% 69.71/70.10 Deleted: 11528
% 69.71/70.10 Deletedinuse: 15
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10
% 69.71/70.10 Intermediate Status:
% 69.71/70.10 Generated: 497840
% 69.71/70.10 Kept: 116235
% 69.71/70.10 Inuse: 1374
% 69.71/70.10 Deleted: 11529
% 69.71/70.10 Deletedinuse: 16
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10
% 69.71/70.10 Intermediate Status:
% 69.71/70.10 Generated: 505954
% 69.71/70.10 Kept: 118346
% 69.71/70.10 Inuse: 1397
% 69.71/70.10 Deleted: 11529
% 69.71/70.10 Deletedinuse: 16
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10
% 69.71/70.10 Intermediate Status:
% 69.71/70.10 Generated: 518086
% 69.71/70.10 Kept: 120668
% 69.71/70.10 Inuse: 1422
% 69.71/70.10 Deleted: 11529
% 69.71/70.10 Deletedinuse: 16
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10
% 69.71/70.10 Intermediate Status:
% 69.71/70.10 Generated: 528580
% 69.71/70.10 Kept: 122901
% 69.71/70.10 Inuse: 1447
% 69.71/70.10 Deleted: 11529
% 69.71/70.10 Deletedinuse: 16
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10 Resimplifying clauses:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10
% 69.71/70.10 Intermediate Status:
% 69.71/70.10 Generated: 537033
% 69.71/70.10 Kept: 124921
% 69.71/70.10 Inuse: 1470
% 69.71/70.10 Deleted: 12079
% 69.71/70.10 Deletedinuse: 16
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10
% 69.71/70.10 Intermediate Status:
% 69.71/70.10 Generated: 544570
% 69.71/70.10 Kept: 127031
% 69.71/70.10 Inuse: 1487
% 69.71/70.10 Deleted: 12079
% 69.71/70.10 Deletedinuse: 16
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10
% 69.71/70.10 Intermediate Status:
% 69.71/70.10 Generated: 560438
% 69.71/70.10 Kept: 130738
% 69.71/70.10 Inuse: 1497
% 69.71/70.10 Deleted: 12079
% 69.71/70.10 Deletedinuse: 16
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10
% 69.71/70.10 Intermediate Status:
% 69.71/70.10 Generated: 571000
% 69.71/70.10 Kept: 132810
% 69.71/70.10 Inuse: 1527
% 69.71/70.10 Deleted: 12079
% 69.71/70.10 Deletedinuse: 16
% 69.71/70.10
% 69.71/70.10
% 69.71/70.10 Intermediate Status:
% 69.71/70.10 Generated: 579677
% 69.71/70.10 Kept: 134954
% 69.71/70.10 Inuse: 1532
% 69.71/70.10 Deleted: 12079
% 69.71/70.10 Deletedinuse: 16
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10
% 69.71/70.10 Intermediate Status:
% 69.71/70.10 Generated: 588389
% 69.71/70.10 Kept: 137104
% 69.71/70.10 Inuse: 1537
% 69.71/70.10 Deleted: 12079
% 69.71/70.10 Deletedinuse: 16
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10
% 69.71/70.10 Intermediate Status:
% 69.71/70.10 Generated: 618573
% 69.71/70.10 Kept: 140955
% 69.71/70.10 Inuse: 1577
% 69.71/70.10 Deleted: 12079
% 69.71/70.10 Deletedinuse: 16
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10 Resimplifying inuse:
% 69.71/70.10 Done
% 69.71/70.10
% 69.71/70.10
% 69.71/70.10 Intermediate Status:
% 69.71/70.10 Generated: 628156
% 69.71/70.10 Kept: 143072
% 69.71/70.10 Inuse: 1587
% 157.17/157.59 Deleted: 12079
% 157.17/157.59 Deletedinuse: 16
% 157.17/157.59
% 157.17/157.59 Resimplifying clauses:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 637331
% 157.17/157.59 Kept: 145106
% 157.17/157.59 Inuse: 1607
% 157.17/157.59 Deleted: 12414
% 157.17/157.59 Deletedinuse: 16
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 649615
% 157.17/157.59 Kept: 147275
% 157.17/157.59 Inuse: 1637
% 157.17/157.59 Deleted: 12414
% 157.17/157.59 Deletedinuse: 16
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 664846
% 157.17/157.59 Kept: 151182
% 157.17/157.59 Inuse: 1662
% 157.17/157.59 Deleted: 12414
% 157.17/157.59 Deletedinuse: 16
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 677569
% 157.17/157.59 Kept: 153183
% 157.17/157.59 Inuse: 1689
% 157.17/157.59 Deleted: 12414
% 157.17/157.59 Deletedinuse: 16
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 688508
% 157.17/157.59 Kept: 155191
% 157.17/157.59 Inuse: 1716
% 157.17/157.59 Deleted: 12414
% 157.17/157.59 Deletedinuse: 16
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 698940
% 157.17/157.59 Kept: 157310
% 157.17/157.59 Inuse: 1742
% 157.17/157.59 Deleted: 12414
% 157.17/157.59 Deletedinuse: 16
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 713681
% 157.17/157.59 Kept: 159397
% 157.17/157.59 Inuse: 1782
% 157.17/157.59 Deleted: 12414
% 157.17/157.59 Deletedinuse: 16
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 722884
% 157.17/157.59 Kept: 161481
% 157.17/157.59 Inuse: 1802
% 157.17/157.59 Deleted: 12414
% 157.17/157.59 Deletedinuse: 16
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying clauses:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 742050
% 157.17/157.59 Kept: 165341
% 157.17/157.59 Inuse: 1822
% 157.17/157.59 Deleted: 13196
% 157.17/157.59 Deletedinuse: 17
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 750404
% 157.17/157.59 Kept: 167986
% 157.17/157.59 Inuse: 1832
% 157.17/157.59 Deleted: 13197
% 157.17/157.59 Deletedinuse: 18
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 758851
% 157.17/157.59 Kept: 170509
% 157.17/157.59 Inuse: 1842
% 157.17/157.59 Deleted: 13197
% 157.17/157.59 Deletedinuse: 18
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 768719
% 157.17/157.59 Kept: 172733
% 157.17/157.59 Inuse: 1862
% 157.17/157.59 Deleted: 13197
% 157.17/157.59 Deletedinuse: 18
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 778678
% 157.17/157.59 Kept: 174749
% 157.17/157.59 Inuse: 1880
% 157.17/157.59 Deleted: 13197
% 157.17/157.59 Deletedinuse: 18
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 788228
% 157.17/157.59 Kept: 176822
% 157.17/157.59 Inuse: 1897
% 157.17/157.59 Deleted: 13197
% 157.17/157.59 Deletedinuse: 18
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 798210
% 157.17/157.59 Kept: 178844
% 157.17/157.59 Inuse: 1918
% 157.17/157.59 Deleted: 13197
% 157.17/157.59 Deletedinuse: 18
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 808178
% 157.17/157.59 Kept: 181182
% 157.17/157.59 Inuse: 1937
% 157.17/157.59 Deleted: 13197
% 157.17/157.59 Deletedinuse: 18
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 816828
% 157.17/157.59 Kept: 183303
% 157.17/157.59 Inuse: 1952
% 157.17/157.59 Deleted: 13197
% 157.17/157.59 Deletedinuse: 18
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying clauses:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 826655
% 157.17/157.59 Kept: 185318
% 157.17/157.59 Inuse: 1979
% 157.17/157.59 Deleted: 13676
% 157.17/157.59 Deletedinuse: 18
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 834449
% 157.17/157.59 Kept: 187598
% 157.17/157.59 Inuse: 1997
% 157.17/157.59 Deleted: 13676
% 157.17/157.59 Deletedinuse: 18
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 843651
% 157.17/157.59 Kept: 189651
% 157.17/157.59 Inuse: 2022
% 157.17/157.59 Deleted: 13676
% 157.17/157.59 Deletedinuse: 18
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 852246
% 157.17/157.59 Kept: 191948
% 157.17/157.59 Inuse: 2042
% 157.17/157.59 Deleted: 13676
% 157.17/157.59 Deletedinuse: 18
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 860645
% 157.17/157.59 Kept: 194099
% 157.17/157.59 Inuse: 2062
% 157.17/157.59 Deleted: 13676
% 157.17/157.59 Deletedinuse: 18
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate Status:
% 157.17/157.59 Generated: 869220
% 157.17/157.59 Kept: 196110
% 157.17/157.59 Inuse: 2080
% 157.17/157.59 Deleted: 13677
% 157.17/157.59 Deletedinuse: 18
% 157.17/157.59
% 157.17/157.59 Resimplifying inuse:
% 157.17/157.59 Done
% 157.17/157.59
% 157.17/157.59
% 157.17/157.59 Intermediate StCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------