TSTP Solution File: SWV705-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV705-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:27:56 EDT 2022
% Result : Timeout 296.33s 296.79s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV705-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Wed Jun 15 16:49:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.35/1.71 *** allocated 10000 integers for termspace/termends
% 1.35/1.71 *** allocated 10000 integers for clauses
% 1.35/1.71 *** allocated 10000 integers for justifications
% 1.35/1.71 *** allocated 15000 integers for termspace/termends
% 1.35/1.71 *** allocated 22500 integers for termspace/termends
% 1.35/1.71 *** allocated 33750 integers for termspace/termends
% 1.35/1.71 *** allocated 50625 integers for termspace/termends
% 1.35/1.71 Bliksem 1.12
% 1.35/1.71
% 1.35/1.71
% 1.35/1.71 Automatic Strategy Selection
% 1.35/1.71
% 1.35/1.71 Clauses:
% 1.35/1.71 [
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.35/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.35/1.71 ],
% 1.35/1.71 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.71 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.35/1.71 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.35/1.71 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ), ~(
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.35/1.71 'tc_nat' ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.71 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.35/1.71 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 1.35/1.71 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.71 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.71 , X ) ) ],
% 1.35/1.71 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.35/1.71 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.35/1.71 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), T, X ),
% 1.35/1.71 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.71 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.71 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ),
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.35/1.71 , T, X ) ) ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), X ) ), =( Z,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.71 ) ],
% 1.35/1.71 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.35/1.71 V3, V4 ) ), hBOOL( hAPP( hAPP( W, Z ), hAPP( hAPP(
% 1.35/1.71 'c_Power_Opower_Opower'( V1, V2, V4 ), hAPP( V0, V5 ) ),
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.35/1.71 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 1.35/1.71 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.35/1.71 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.35/1.71 'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.35/1.71 'tc_nat' ) ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.71 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.35/1.71 ,
% 1.35/1.71 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), hAPP( U, W
% 1.35/1.71 ) ), V0 ) ), hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), W
% 1.35/1.71 ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( V1, U, V2, V3, V4,
% 1.35/1.71 V5, X, Y, Z, V6, T ) ) ],
% 1.35/1.71 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ), W ) )
% 1.35/1.71 , hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), hAPP( X, U ) ), W ) ),
% 1.35/1.71 ~( 'c_Ring__and__Field_Oordered__idom'( V0, V1, V2, V3, V4, V5, X, Y, Z,
% 1.35/1.71 V6, T ) ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.35/1.71 , Z ) ), Z ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.35/1.71 ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.35/1.71 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.35/1.71 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.35/1.71 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.35/1.71 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.71 X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.71 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.35/1.71 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.71 X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.71 X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.71 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.71 X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.71 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.71 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.35/1.71 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.71 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.71 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.35/1.71 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.35/1.71 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), U ), W ) ), hAPP( hAPP(
% 1.35/1.71 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.35/1.71 X, Y, Z ), T ), U ) ), W ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z
% 1.35/1.71 ) ) ],
% 1.35/1.71 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.71 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.71 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.35/1.71 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.71 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.71 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.71 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.35/1.71 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.35/1.71 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.35/1.71 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.35/1.71 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.35/1.71 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.35/1.71 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.71 'tc_nat' ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.35/1.71 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.35/1.71 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.35/1.71 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.35/1.71 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.35/1.71 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.35/1.71 ), X ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.71 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.71 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.35/1.71 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.35/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.71 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.35/1.71 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.71 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.35/1.71 ), X ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.71 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.71 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.35/1.71 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.35/1.71 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.71 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.71 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.35/1.71 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.35/1.71 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.71 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.35/1.71 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.35/1.71 'tc_nat' ) ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.71 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.35/1.71 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.71 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.71 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ), hAPP(
% 1.35/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.35/1.71 'tc_nat' ) ) ), 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.35/1.71 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.71 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.35/1.71 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.35/1.71 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.35/1.71 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.71 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.35/1.71 ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.71 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.35/1.71 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.71 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.35/1.71 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.71 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.71 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.35/1.71 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.35/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.35/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.35/1.71 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.35/1.71 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.35/1.71 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.35/1.71 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.35/1.71 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.71 'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z,
% 1.35/1.71 'tc_nat' ) ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.35/1.71 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.71 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.71 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.35/1.71 , ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.71 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.35/1.71 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.71 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.71 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.35/1.71 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.71 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.35/1.71 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.71 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.71 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.35/1.71 , ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.35/1.71 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.71 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.71 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.35/1.71 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.71 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), X ), T ), X ), ~(
% 1.35/1.71 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.35/1.71 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.35/1.71 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.35/1.71 'c_lessequals'( Y, T, X ) ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.35/1.71 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.35/1.71 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.35/1.71 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.35/1.71 'c_lessequals'( Z, T, X ) ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.35/1.71 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.35/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.35/1.71 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.35/1.71 'c_lessequals'( Y, T, X ) ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.35/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.35/1.71 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.35/1.71 'c_lessequals'( Z, T, X ) ) ],
% 1.35/1.71 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.35/1.71 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ),
% 1.35/1.71 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.35/1.71 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.35/1.71 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.35/1.71 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ),
% 1.35/1.71 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.71 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.71 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.35/1.71 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( T, X ), X ) )
% 1.35/1.71 , ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.35/1.71 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.71 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.35/1.71 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.35/1.71 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.35/1.71 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.35/1.71 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.35/1.71 , Y, 'tc_nat' ) ) ],
% 1.35/1.71 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), =( Y, X ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ],
% 1.35/1.71 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.35/1.71 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.35/1.71 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.35/1.71 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.35/1.71 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.35/1.71 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.35/1.71 , X ) ) ), =( Y, Z ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.35/1.71 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.35/1.71 , X ) ) ), =( Y, Z ) ],
% 1.35/1.71 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.35/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.35/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ), Z ) ]
% 1.35/1.71 ,
% 1.35/1.71 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 1.35/1.71 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.35/1.71 'c_HOL_Oabs__class_Oabs'( T, X ) ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), Z, X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.71 X ), Y ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.71 X ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.35/1.71 ,
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.71 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.71 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.71 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.35/1.71 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.35/1.71 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.35/1.71 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.35/1.71 ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.35/1.71 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.35/1.71 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.35/1.71 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.71 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.35/1.71 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.35/1.71 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ), ~( 'c_lessequals'( Z
% 1.35/1.71 , Y, 'tc_nat' ) ) ],
% 1.35/1.71 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.35/1.71 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.71 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), Y ) ), ~(
% 1.35/1.71 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 1.35/1.71 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( 'c_Suc',
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.35/1.71 ],
% 1.35/1.71 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.71 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.71 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.71 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.71 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.71 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.35/1.71 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.71 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.71 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.35/1.71 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.35/1.71 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.35/1.71 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.35/1.71 ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.35/1.71 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.71 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.35/1.71 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.71 ), Y ), T ), Z, X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.35/1.71 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.71 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.35/1.71 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.71 X ), T ), Z ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.35/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.35/1.71 ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.35/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.35/1.71 ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.35/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.35/1.71 ,
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.35/1.71 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.35/1.71 ,
% 1.35/1.71 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.35/1.71 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.35/1.71 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.35/1.71 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.35/1.71 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.71 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.35/1.71 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.71 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.71 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 'tc_nat' ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'( X
% 1.35/1.71 ) ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.71 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.35/1.71 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.35/1.71 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.35/1.71 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.35/1.71 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.71 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.35/1.71 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.71 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.35/1.71 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ),
% 1.35/1.71 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.35/1.71 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), W ) ), hAPP( hAPP( Y, hAPP(
% 1.35/1.71 hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), U ) ), hAPP( hAPP(
% 1.35/1.71 'c_Power_Opower_Opower'( X, Y, Z ), T ), W ) ) ), ~(
% 1.35/1.71 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.71 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.71 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.35/1.71 ,
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.71 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.35/1.71 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.35/1.71 ,
% 1.35/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.35/1.71 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.71 'c_Int_OMin', X ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.35/1.71 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.35/1.71 Z, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.71 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.71 X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.71 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.71 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'( Y
% 1.35/1.71 , T, X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.35/1.71 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.35/1.71 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.35/1.71 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.35/1.71 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.71 ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.71 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.71 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.71 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.71 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.71 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.35/1.71 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.71 , Y ), Z ), T, X ) ) ],
% 1.35/1.71 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.71 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.71 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.35/1.71 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.71 , Y ), T ), Z, X ) ) ],
% 1.35/1.71 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.35/1.71 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.71 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.35/1.71 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.35/1.71 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.35/1.71 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.35/1.71 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.71 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.35/1.71 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.35/1.71 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.71 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.35/1.71 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.35/1.71 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.71 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.35/1.71 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.35/1.71 ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.35/1.71 ,
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.71 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.35/1.71 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.35/1.71 Y, X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.71 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.35/1.71 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.35/1.71 ,
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.71 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.71 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.35/1.71 ,
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.71 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.71 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.35/1.71 ,
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.35/1.71 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.35/1.71 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.35/1.71 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.35/1.71 Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.71 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ), Y )
% 1.35/1.71 ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.35/1.71 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.35/1.71 , X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 1.35/1.71 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.71 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.35/1.71 ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.71 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.35/1.71 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.35/1.71 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.71 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.35/1.71 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.35/1.71 , 'tc_nat' ) ) ],
% 1.35/1.71 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.71 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.35/1.71 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.35/1.71 , 'tc_nat' ) ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.71 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.35/1.71 ,
% 1.35/1.71 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.35/1.71 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.71 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.35/1.71 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.71 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.35/1.71 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.35/1.71 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.35/1.71 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.35/1.71 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.35/1.71 Y, X ), Z, X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.35/1.71 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.71 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.35/1.71 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.35/1.71 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.71 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.35/1.71 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.35/1.71 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.71 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( Z
% 1.35/1.71 , T, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.35/1.71 X ), Y, X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.71 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.71 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.35/1.71 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.35/1.71 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.35/1.71 ,
% 1.35/1.71 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 1.35/1.71 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.71 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.71 X ), Y ), Z ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.71 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.71 X ), Z ), Y ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.71 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.71 X ), Y ), Z ), X ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.71 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.71 X ), Z ), Y ), X ) ) ],
% 1.35/1.71 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.35/1.71 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.35/1.71 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc',
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.35/1.71 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 1.35/1.71 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 1.35/1.71 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.71 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.35/1.71 , U ) ), hAPP( hAPP( Y, hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T
% 1.35/1.71 ), U ) ), T ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.35/1.71 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.35/1.71 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.72 X ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.72 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.35/1.72 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.72 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.35/1.72 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.35/1.72 , X ) ), 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_nat' ) ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ), ~( 'c_lessequals'(
% 1.35/1.72 T, Z, 'tc_nat' ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.35/1.72 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.35/1.72 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.35/1.72 Y, X ) ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.35/1.72 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.35/1.72 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.72 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.35/1.72 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.72 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.35/1.72 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.72 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.35/1.72 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.35/1.72 , X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.35/1.72 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.35/1.72 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.35/1.72 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.35/1.72 , X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.35/1.72 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.35/1.72 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.35/1.72 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.35/1.72 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.35/1.72 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.35/1.72 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.35/1.72 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.35/1.72 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ],
% 1.35/1.72 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.35/1.72 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.35/1.72 ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP( X, Z ), Y ) ),
% 1.35/1.72 =( Z, Y ), ~( 'c_Ring__and__Field_Oordered__idom'( T, U, W, V0, V1, X, V2
% 1.35/1.72 , V3, V4, V5, V6 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( Y, Z ) ), hAPP( hAPP( X, Z ),
% 1.35/1.72 Z ) ), ~( 'c_Ring__and__Field_Oordered__idom'( T, U, W, V0, V1, V2, Y, V3
% 1.35/1.72 , X, V4, V5 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( T, Z ) ), Z ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1, V2, V3, T, V4, X, Y,
% 1.35/1.72 V5 ) ) ],
% 1.35/1.72 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.35/1.72 hAPP( X, T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1,
% 1.35/1.72 V2, V3, V4, V5, Y, X, V6 ) ) ],
% 1.35/1.72 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.35/1.72 hAPP( X, T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1,
% 1.35/1.72 V2, V3, X, V4, Y, V5, V6 ) ) ],
% 1.35/1.72 [ =( hAPP( X, hAPP( X, Y ) ), hAPP( X, Y ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( Z, T, U, W, V0, V1, V2, V3, V4, X,
% 1.35/1.72 V5 ) ) ],
% 1.35/1.72 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.35/1.72 V3, V4 ) ), =( hAPP( V3, Z ), Z ) ],
% 1.35/1.72 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( Z, T ), U, W, V0,
% 1.35/1.72 V1, V2, V3, Z, V4 ) ), =( T, hAPP( Z, T ) ) ],
% 1.35/1.72 [ =( hAPP( X, Y ), hAPP( hAPP( Z, Y ), hAPP( T, Y ) ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1, V2, V3, X, V4, Z, T,
% 1.35/1.72 V5 ) ) ],
% 1.35/1.72 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z,
% 1.35/1.72 T, U ), hAPP( W, Y ) ), V0 ) ) ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, V4, X, W, Z, T, V5, U
% 1.35/1.72 ) ), =( V0, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.35/1.72 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.35/1.72 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.35/1.72 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.35/1.72 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.35/1.72 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.35/1.72 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.72 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.35/1.72 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.35/1.72 ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.35/1.72 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.72 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.35/1.72 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.35/1.72 ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.35/1.72 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.35/1.72 ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.35/1.72 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.35/1.72 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.35/1.72 ) ],
% 1.35/1.72 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.35/1.72 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.35/1.72 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.35/1.72 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.35/1.72 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.35/1.72 Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.72 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.72 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.35/1.72 ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.35/1.72 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.35/1.72 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.35/1.72 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.35/1.72 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.72 , 'tc_nat' ), 'tc_nat' ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.72 , 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.72 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.35/1.72 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y,
% 1.35/1.72 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.72 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.35/1.72 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.72 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.35/1.72 ), X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.35/1.72 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.35/1.72 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.35/1.72 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.35/1.72 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.35/1.72 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.35/1.72 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oabs__class_Oabs'(
% 1.35/1.72 Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.35/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.35/1.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.35/1.72 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.35/1.72 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.35/1.72 ), Y ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 1.35/1.72 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.35/1.72 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.35/1.72 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 1.35/1.72 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 1.35/1.72 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.35/1.72 , hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), X ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.35/1.72 , X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 1.35/1.72 ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.72 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X
% 1.35/1.72 ) ],
% 1.35/1.72 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'tc_nat' ),
% 1.35/1.72 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.35/1.72 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.35/1.72 , X ), Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.35/1.72 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 1.35/1.72 , X ) ) ],
% 1.35/1.72 [ 'c_lessequals'( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ),
% 1.35/1.72 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.35/1.72 X, Y, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.35/1.72 'tc_nat' ) ), Y ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( Y
% 1.35/1.72 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.35/1.72 ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.35/1.72 ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, X, Z ), T )
% 1.35/1.72 , U ) ), T ), hAPP( hAPP( X, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y
% 1.35/1.72 , X, Z ), T ), U ) ) ), ~( 'c_OrderedGroup_Omonoid__mult'( Y, X, Z ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.35/1.72 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.35/1.72 ],
% 1.35/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.72 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), hAPP(
% 1.35/1.72 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), Z ) ) ],
% 1.35/1.72 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.35/1.72 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.35/1.72 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.35/1.72 ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), X,
% 1.35/1.72 'tc_nat' ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.35/1.72 X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X
% 1.35/1.72 ), X ) ],
% 1.35/1.72 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.35/1.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), T ), ~(
% 1.35/1.72 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.35/1.72 ), X ), Y ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ), Y ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.35/1.72 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.72 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.35/1.72 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.72 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.35/1.72 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 X ), Y ), Z ) ), T ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 X ), Y ), Z ) ), T ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.35/1.72 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.35/1.72 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.35/1.72 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP(
% 1.35/1.72 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.35/1.72 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.35/1.72 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 X ), Y ), Z ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.72 ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.35/1.72 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.35/1.72 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.72 ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), 'c_HOL_Ominus__class_Ominus'( T
% 1.35/1.72 , Z, 'tc_nat' ) ) ), 'c_lessequals'( T, Z, 'tc_nat' ), =( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.35/1.72 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.35/1.72 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ) ), X ), Z, X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ) ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 Y, Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.35/1.72 ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Z, X ) ), =( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.35/1.72 , T, X ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), T, X ) ), =( T,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.35/1.72 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.35/1.72 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.72 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.35/1.72 Y, Z, X ) ) ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), X ) ), =( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.72 ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.35/1.72 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.35/1.72 X ) ) ) ],
% 1.35/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 1.35/1.72 Y, Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.35/1.72 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.35/1.72 X ) ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.35/1.72 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.35/1.72 X ) ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.35/1.72 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.35/1.72 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.35/1.72 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.35/1.72 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.35/1.72 , V0, U, V1 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.35/1.72 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.35/1.72 , V0, U, V1 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.35/1.72 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.35/1.72 X, T, U, Y, W, V0 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.35/1.72 X, T, U, Z, W, V0 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.35/1.72 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.35/1.72 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.35/1.72 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.35/1.72 T, X, U, Y, W, V0 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.35/1.72 T, X, U, Z, W, V0 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.35/1.72 T, X, U, W, Y, V0 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.35/1.72 T, X, U, W, Z, V0 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.35/1.72 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.35/1.72 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.35/1.72 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.35/1.72 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.35/1.72 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.35/1.72 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.35/1.72 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.35/1.72 , V0, V1, V2 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.35/1.72 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.35/1.72 W, V0, V1, V2 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.35/1.72 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.35/1.72 , V0, V1, V2 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.35/1.72 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.35/1.72 W, V0, V1, V2 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.35/1.72 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.35/1.72 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.35/1.72 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.35/1.72 W, V0, V1, V2 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.35/1.72 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.35/1.72 W, V0, V1, V2 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.35/1.72 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.35/1.72 , V0, V1, V2 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.35/1.72 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.35/1.72 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.35/1.72 , V0, V1, V2 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.35/1.72 X, T, U, Y, W, V0 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.35/1.72 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.35/1.72 , V0, V1, V2 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.35/1.72 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.35/1.72 T, X, U, Y, W, V0 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.35/1.72 T, X, U, W, Y, V0 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.35/1.72 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.35/1.72 , V0, V1, V2 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.35/1.72 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.35/1.72 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.35/1.72 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.35/1.72 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.35/1.72 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.35/1.72 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.35/1.72 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.35/1.72 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.72 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.35/1.72 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.35/1.72 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.35/1.72 ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.35/1.72 'c_lessequals'( Y, Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.35/1.72 'c_lessequals'( Y, Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.35/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.35/1.72 ) ],
% 1.35/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.35/1.72 ) ],
% 1.35/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.35/1.72 ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.35/1.72 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ), X ) ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.35/1.72 ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =(
% 1.35/1.72 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 'tc_nat' ), X ), Y ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) )
% 1.35/1.72 ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.72 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.72 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.35/1.72 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.35/1.72 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.35/1.72 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.35/1.72 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.35/1.72 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X
% 1.35/1.72 ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ), =( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.72 ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.72 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.35/1.72 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.35/1.72 U ), hAPP( W, V0 ) ), V1 ) ) ), =( V0, Y ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, V4, V5, X, W, Z, T, V6, U
% 1.35/1.72 ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.35/1.72 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.35/1.72 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.35/1.72 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.72 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.72 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.35/1.72 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.35/1.72 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.72 ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X ) ],
% 1.35/1.72 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.35/1.72 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.35/1.72 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.35/1.72 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.35/1.72 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.35/1.72 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), Y, 'tc_nat' ) ) ],
% 1.35/1.72 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.35/1.72 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.35/1.72 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.35/1.72 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.35/1.72 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.35/1.72 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.35/1.72 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.72 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.35/1.72 , X ) ), T, X ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.72 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.35/1.72 ), Z ), T, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.35/1.72 ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.35/1.72 ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.35/1.72 ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.35/1.72 ), X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.35/1.72 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.72 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.35/1.72 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.35/1.72 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.35/1.72 ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.35/1.72 X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.35/1.72 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.72 X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.35/1.72 Z, X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.35/1.72 Y, Z, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.35/1.72 'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.72 'c_Int_OMin', X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.35/1.72 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.35/1.72 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Y,
% 1.35/1.72 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.35/1.72 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.35/1.72 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.72 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.35/1.72 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.72 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.35/1.72 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.35/1.72 , T, 'tc_nat' ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ) ), ~( 'c_lessequals'(
% 1.35/1.72 T, Z, 'tc_nat' ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.35/1.72 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.35/1.72 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.35/1.72 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.35/1.72 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.72 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.72 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.35/1.72 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.72 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.72 , X ) ) ],
% 1.35/1.72 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 1.35/1.72 ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.35/1.72 ), Z ) ), T ) ) ],
% 1.35/1.72 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.35/1.72 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X
% 1.35/1.72 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.72 'tc_nat' ) ) ],
% 1.35/1.72 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.35/1.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.72 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.35/1.72 Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.35/1.72 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.72 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_OrderedGroup_Omonoid__mult'( Z
% 1.35/1.72 , X, T ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_OrderedGroup_Omonoid__mult'( Y
% 1.35/1.72 , X, T ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.35/1.72 , 'tc_nat' ), 'tc_nat' ), 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.72 X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.35/1.72 X ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.35/1.72 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.35/1.72 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.35/1.72 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X,
% 1.35/1.72 'tc_nat' ) ],
% 1.35/1.72 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), Z, 'tc_nat' ), 'tc_nat'
% 1.35/1.72 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( =( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) )
% 1.35/1.72 , Y ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat'
% 1.35/1.72 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.35/1.72 ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.35/1.72 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.35/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.35/1.72 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.35/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.35/1.72 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.35/1.72 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.72 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OMin',
% 1.35/1.72 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OMin',
% 1.35/1.72 'tc_Int_Oint' ) ) ],
% 1.35/1.72 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OMin', 'tc_Int_Oint' ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OMin',
% 1.35/1.72 'tc_Int_Oint' ) ) ],
% 1.35/1.72 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.35/1.72 ), 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 'tc_nat' ) ],
% 1.35/1.72 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ),
% 1.35/1.72 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'(
% 1.35/1.72 'tc_nat' ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ), =( X,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.72 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.35/1.72 , Y, 'tc_nat' ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( U, T ), W ) ), ~( hBOOL( hAPP( hAPP( X, Z ), V0 ) ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Y, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.35/1.72 hAPP( X, U ), Z ) ) ), hBOOL( hAPP( hAPP( W, V0 ), T ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Y, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Z, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.35/1.72 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Z, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( U, Z ), W ) ), ~( hBOOL( hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Y, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.35/1.72 hAPP( X, U ), T ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Z ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Y, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Z, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.35/1.72 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Z, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( U, T ), W ) ), ~( hBOOL( hAPP( hAPP( X, Z ), V0 ) ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Y, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.35/1.72 hAPP( X, U ), Z ) ) ), hBOOL( hAPP( hAPP( W, V0 ), T ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Y, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Z, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.35/1.72 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Z, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( U, Z ), W ) ), ~( hBOOL( hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Y, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.35/1.72 hAPP( X, U ), T ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Z ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Y, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Z, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.35/1.72 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Z, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.35/1.72 Y ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Y, V0, V1, X
% 1.35/1.72 , V2, V3, V4, Z, V5 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.35/1.72 T, Z ) ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Y, V0, V1, X
% 1.35/1.72 , V2, V3, V4, T, V5 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.35/1.72 Z ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, T, V0, V1, X
% 1.35/1.72 , V2, V3, V4, Y, V5 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, hAPP( T, Y
% 1.35/1.72 ) ), Z ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Z, V0, V1, X
% 1.35/1.72 , V2, V3, V4, T, V5 ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.35/1.72 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T,
% 1.35/1.72 'tc_nat' ) ) ],
% 1.35/1.72 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.72 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.35/1.72 ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.35/1.72 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.35/1.72 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.35/1.72 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.72 X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 1.35/1.72 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.35/1.72 , X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.72 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.35/1.72 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.35/1.72 , hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.35/1.72 ) ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ), X ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.35/1.72 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', 'tc_nat' ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X
% 1.35/1.72 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), Y ) ) ), =( X,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.35/1.72 Z ), X ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.35/1.72 ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.35/1.72 ), T ) ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.35/1.72 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 1.35/1.72 ), T ) ) ) ],
% 1.35/1.72 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.35/1.72 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ),
% 1.35/1.72 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.35/1.72 Z, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.35/1.72 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.35/1.72 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.35/1.72 , X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.35/1.72 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.35/1.72 Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc',
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ),
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ),
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.72 'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.35/1.72 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.35/1.72 ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.35/1.72 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.35/1.72 ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.35/1.72 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.35/1.72 ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.35/1.72 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.35/1.72 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OPls', 'tc_Int_Oint' )
% 1.35/1.72 ],
% 1.35/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.35/1.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.35/1.72 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.35/1.72 'tc_Int_Oint' ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.35/1.72 'c_HOL_Ominus__class_Ominus'( Y, T, X ), X ) ), 'c_HOL_Oabs__class_Oabs'(
% 1.35/1.72 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ) ), X ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.35/1.72 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.72 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ =( hAPP( X, Y ), hAPP( Z, T ) ), ~( hBOOL( hAPP( hAPP( U, Y ), W ) ) )
% 1.35/1.72 , ~( 'c_Ring__and__Field_Oordered__idom'( V0, Z, W, V1, V2, U, V3, T, V4
% 1.35/1.72 , X, V5 ) ) ],
% 1.35/1.72 [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( T, U ), Y ) ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( W, V0, U, V1, V2, T, V3, Z, V4, X,
% 1.35/1.72 V5 ) ) ],
% 1.35/1.72 [ ~( =( hAPP( X, Y ), hAPP( Z, T ) ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( U, Z, W, V0, V1, V2, V3, T, V4, X,
% 1.35/1.72 V5 ) ), hBOOL( hAPP( hAPP( V2, Y ), W ) ) ],
% 1.35/1.72 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 1.35/1.72 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 1.35/1.72 'tc_nat' ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.72 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.35/1.72 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.72 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.35/1.72 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.35/1.72 ) ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.35/1.72 ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.35/1.72 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.35/1.72 X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.35/1.72 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.35/1.72 ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.72 X ) ) ],
% 1.35/1.72 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 'tc_Int_Oint' ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit0'( X ),
% 1.35/1.72 'tc_Int_Oint' ) ) ],
% 1.35/1.72 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit0'( X ),
% 1.35/1.72 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X,
% 1.35/1.72 'tc_Int_Oint' ) ) ],
% 1.35/1.72 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 'tc_Int_Oint' ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit1'( X ),
% 1.35/1.72 'tc_Int_Oint' ) ) ],
% 1.35/1.72 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit1'( X ),
% 1.35/1.72 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X,
% 1.35/1.72 'tc_Int_Oint' ) ) ],
% 1.35/1.72 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ),
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.35/1.72 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y
% 1.35/1.72 , 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z,
% 1.35/1.72 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.35/1.72 ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.72 ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.35/1.72 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.72 'c_lessequals'( Z, Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.35/1.72 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.72 'c_lessequals'( Z, Y, X ) ) ],
% 1.35/1.72 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.35/1.72 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.35/1.72 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.35/1.72 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 1.35/1.72 X ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.35/1.72 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.35/1.72 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.35/1.72 ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.72 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.35/1.72 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.72 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.35/1.72 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.35/1.72 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.35/1.72 Y ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.35/1.72 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.35/1.72 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.72 ), Y ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.35/1.72 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.72 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.35/1.72 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.35/1.72 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.35/1.72 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.35/1.72 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 1.35/1.72 'tc_nat' ), ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.35/1.72 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.35/1.72 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 1.35/1.72 X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.35/1.72 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.35/1.72 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.72 'tc_nat' ), 'tc_nat' ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ) ) ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.35/1.72 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.35/1.72 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y,
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.72 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.35/1.72 ), 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.72 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.35/1.72 ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.72 'c_Int_OMin', X ) ), Y ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.35/1.72 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.35/1.72 , 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.35/1.72 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.35/1.72 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.35/1.72 U ), hAPP( W, V0 ) ), V1 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'(
% 1.35/1.72 V2, V3, Y, V4, X, V5, W, Z, T, V6, U ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.35/1.72 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.35/1.72 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.72 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.35/1.72 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.72 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.35/1.72 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.35/1.72 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.35/1.72 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.35/1.72 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.35/1.72 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.35/1.72 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.35/1.72 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.72 Y ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.35/1.72 Y ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.72 Y ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.35/1.72 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.35/1.72 Y ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.35/1.72 Y ) ],
% 1.35/1.72 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.35/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.72 Y ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.35/1.72 Y ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 'c_lessequals'(
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 'c_lessequals'(
% 1.35/1.72 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.35/1.72 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.35/1.72 ), Y ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.35/1.72 ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.35/1.72 ) ) ],
% 1.35/1.72 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.35/1.72 ), Y ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.35/1.72 ), Y ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.35/1.72 ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.35/1.72 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.35/1.72 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.35/1.72 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.35/1.72 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.35/1.72 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.35/1.72 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.35/1.72 ) ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.35/1.72 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.35/1.72 ) ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.35/1.72 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.35/1.72 , X ) ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.35/1.72 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.35/1.72 , X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.35/1.72 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.35/1.72 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.72 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.35/1.72 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.35/1.72 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.35/1.72 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.35/1.72 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.72 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.35/1.72 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.35/1.72 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.35/1.72 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.72 T, X ) ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.35/1.72 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.35/1.72 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.35/1.72 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.35/1.72 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.35/1.72 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.35/1.72 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.35/1.72 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 Z, Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.35/1.72 , X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.35/1.72 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.35/1.72 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.35/1.72 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.35/1.72 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.35/1.72 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.35/1.72 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.35/1.72 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.35/1.72 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.35/1.72 , X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.35/1.72 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.35/1.72 , X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.35/1.72 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.35/1.72 , X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.35/1.72 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.35/1.72 , X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.72 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.35/1.72 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.35/1.72 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.35/1.72 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.72 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.35/1.72 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.35/1.72 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.35/1.72 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.72 X ), Y ), T ), Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.35/1.72 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.35/1.72 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.72 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.35/1.72 , 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.35/1.72 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.35/1.72 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.35/1.72 , ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.35/1.72 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.35/1.72 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.35/1.72 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.72 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.35/1.72 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.72 , Y ), T ), Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.35/1.72 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.72 , Y ), T ), Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.35/1.72 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.35/1.72 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.72 ), T ), Z ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.35/1.72 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.72 ), T ), Z ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.35/1.72 , X ) ), Z ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.35/1.72 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.35/1.72 Y, X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.35/1.72 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.35/1.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.35/1.72 [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.35/1.72 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 'tc_nat' ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.35/1.72 ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.72 ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.35/1.72 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.35/1.72 , X ) ), Z ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.35/1.72 , 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ), X ),
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.35/1.72 , Y ), Z ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.72 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.35/1.72 ) ), Z ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.35/1.72 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.35/1.72 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~(
% 1.35/1.72 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.35/1.72 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc',
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.72 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.72 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.35/1.72 , T, 'tc_nat' ) ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ), =( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.35/1.72 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.72 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.35/1.72 'tc_nat' ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Int_Oiszero'( Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ), Z
% 1.35/1.72 ), 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.72 ), Y ), Z ), X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.35/1.72 X ) ) ],
% 1.35/1.72 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.72 'tc_nat' ) ) ) ],
% 1.35/1.72 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_Int_Oint' ) ) ],
% 1.35/1.72 [ ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.35/1.72 ), Y ), X ), 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), X, 'tc_nat' ), Y ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.35/1.72 , X ), Y ), 'tc_nat' ) ],
% 1.35/1.72 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.35/1.72 , X ), Y ), 'tc_nat' ) ],
% 1.35/1.72 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.35/1.72 , Y ), X ), 'tc_nat' ) ],
% 1.35/1.72 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.35/1.72 , X ), Y ), 'tc_nat' ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.72 X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.35/1.72 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ),
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.35/1.72 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ),
% 1.35/1.72 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.35/1.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ), =( hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.72 , X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.35/1.72 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.35/1.72 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.35/1.72 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.35/1.72 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.35/1.72 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.35/1.72 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.35/1.72 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.35/1.72 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.35/1.72 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.72 , X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.72 X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.35/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.72 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Y ), X ), ~(
% 1.35/1.72 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.35/1.72 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ), ~( 'c_lessequals'(
% 1.35/1.72 X, Y, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y, hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y,
% 1.35/1.72 X, 'tc_nat' ) ), X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.72 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ),
% 1.35/1.72 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat'
% 1.35/1.72 ) ) ],
% 1.35/1.72 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.35/1.72 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ),
% 1.35/1.72 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.72 'tc_nat' ), X ), Y ), Z, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 1.35/1.72 ) ) ],
% 1.35/1.72 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.35/1.72 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 1.35/1.72 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OMin',
% 1.35/1.72 'tc_Int_Oint' ) ) ],
% 1.35/1.72 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.35/1.72 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.72 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.72 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.35/1.72 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.35/1.72 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.35/1.72 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.35/1.72 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.35/1.72 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.72 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.35/1.72 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.35/1.72 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.35/1.72 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y
% 1.35/1.72 , Z, X ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X
% 1.35/1.72 ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.35/1.72 ) ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ),
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ), X ) ), Y ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.35/1.72 'c_HOL_Oone__class_Oone'( X ), X ) ), 'c_Parity_Oeven__odd__class_Oeven'(
% 1.35/1.72 Y, 'tc_nat' ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 1.35/1.72 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.35/1.72 Z, X ) ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.35/1.72 Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.72 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.35/1.72 [ 'c_HOL_Oord__class_Oless'( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' )
% 1.35/1.72 , 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.72 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), 'c_Int_Oiszero'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.35/1.72 ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.35/1.72 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.35/1.72 ) ],
% 1.35/1.72 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.35/1.72 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.35/1.72 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 1.35/1.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.35/1.72 ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.72 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.35/1.72 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.35/1.72 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.72 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.35/1.72 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.72 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.35/1.72 ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.35/1.72 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.35/1.72 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.35/1.72 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.35/1.72 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ), =( Z,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 1.35/1.72 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.35/1.72 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X
% 1.35/1.72 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.35/1.72 Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.35/1.72 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.72 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.35/1.72 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.35/1.72 X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.35/1.72 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.72 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.35/1.72 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.35/1.72 , X ) ],
% 1.35/1.72 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, hAPP( V1
% 1.35/1.72 , V2 ), V3, V1, V4 ) ), hBOOL( hAPP( hAPP( W, Z ), V2 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.35/1.72 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, W ), Z ) ) ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Y, V0, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.35/1.72 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, U ), Y ) ) ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Z, V0, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.35/1.72 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Z, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.35/1.72 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Z, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.35/1.72 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, W ), Y ) ), W ) ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Z, V0, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.35/1.72 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, U ), Z ) ), U ) ) ), ~(
% 1.35/1.72 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Y, V0, V5,
% 1.35/1.72 V6 ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.72 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.35/1.72 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.35/1.72 ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.72 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.35/1.72 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.72 T, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.35/1.72 , X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.35/1.72 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.35/1.72 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.35/1.72 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.72 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.35/1.72 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.35/1.72 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.72 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.72 X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.72 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.35/1.72 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.72 T, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.35/1.72 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.35/1.72 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.72 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.35/1.72 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.72 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.72 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.35/1.72 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.35/1.72 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.72 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.35/1.72 ,
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.72 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.35/1.72 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.72 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.72 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.35/1.72 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.35/1.72 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.35/1.72 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.35/1.72 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.35/1.72 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.35/1.72 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.35/1.72 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.35/1.72 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.35/1.72 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.72 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.72 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.35/1.72 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.35/1.72 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.72 , Z ), T ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ominus__class_Ominus'( Z, T, X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.35/1.72 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.72 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.35/1.72 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.72 , X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.72 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.35/1.72 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.35/1.72 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.72 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.72 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.35/1.72 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.72 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.72 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.72 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.35/1.72 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.72 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.35/1.72 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.72 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.72 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.35/1.72 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.72 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.35/1.72 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.35/1.72 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.72 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.35/1.72 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.72 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.72 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.72 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.35/1.72 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.35/1.72 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.72 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.35/1.72 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.72 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.35/1.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.72 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.35/1.73 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.35/1.73 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.35/1.73 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.73 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.35/1.73 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.73 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.73 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.73 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.73 , X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.35/1.73 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.35/1.73 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.73 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.35/1.73 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.35/1.73 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.73 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.35/1.73 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.73 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.73 , X ), X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.73 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.35/1.73 ), X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.35/1.73 , X ), X ), Z, X ) ) ],
% 1.35/1.73 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.73 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.35/1.73 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.35/1.73 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.73 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.35/1.73 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.35/1.73 ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.73 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.73 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.73 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.35/1.73 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.35/1.73 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.35/1.73 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.35/1.73 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.35/1.73 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.35/1.73 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.35/1.73 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.35/1.73 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.35/1.73 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.35/1.73 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.73 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.35/1.73 'c_HOL_Oabs__class_Oabs'( Y, X ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.35/1.73 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.35/1.73 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.35/1.73 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.35/1.73 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.35/1.73 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.73 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.35/1.73 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.73 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.35/1.73 ) ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.35/1.73 ), 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.35/1.73 ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.35/1.73 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.35/1.73 , X ) ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.35/1.73 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.35/1.73 , X ) ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.35/1.73 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.35/1.73 ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.35/1.73 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.35/1.73 ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.35/1.73 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.35/1.73 ) ) ],
% 1.35/1.73 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.35/1.73 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.35/1.73 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.35/1.73 ) ) ],
% 1.35/1.73 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.35/1.73 ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.35/1.73 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.73 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.35/1.73 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.35/1.73 , X ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), Y ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X
% 1.35/1.73 ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.35/1.73 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.35/1.73 ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.73 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.35/1.73 hAPP( U, Z ), W ) ), hBOOL( hAPP( hAPP( U, W ), Z ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Y, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.35/1.73 hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Y, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.35/1.73 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, Z ), W ) ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Y, V0, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.35/1.73 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, Y ), U ) ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Z, V0, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.35/1.73 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Z, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.35/1.73 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Z, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.35/1.73 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Y ), W ) ), W ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Z, V0, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.35/1.73 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Z ), U ) ), U ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Y, V0, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.35/1.73 hAPP( U, T ), W ) ), hBOOL( hAPP( hAPP( U, W ), T ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Y, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.35/1.73 hAPP( X, U ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Y, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.35/1.73 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, W ), Z ) ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Y, V0, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.35/1.73 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, U ), Y ) ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Z, V0, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.35/1.73 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Z, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.35/1.73 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Z, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.35/1.73 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, W ), Y ) ), W ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Z, V0, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.35/1.73 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, U ), Z ) ), U ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Y, V0, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.35/1.73 hAPP( U, Z ), W ) ), hBOOL( hAPP( hAPP( U, W ), Z ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Y, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.35/1.73 hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Y, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.35/1.73 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, Z ), W ) ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Y, V0, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.35/1.73 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, Y ), U ) ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Z, V0, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.35/1.73 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Z, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.35/1.73 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Z, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.35/1.73 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Y ), W ) ), W ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Z, V0, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.35/1.73 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Z ), U ) ), U ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Y, V0, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.35/1.73 hAPP( U, T ), W ) ), hBOOL( hAPP( hAPP( U, W ), T ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Y, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.35/1.73 hAPP( X, U ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Y, V5,
% 1.35/1.73 V6 ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.35/1.73 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OMin',
% 1.35/1.73 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.35/1.73 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.35/1.73 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.73 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.73 'tc_nat' ) ) ) ],
% 1.35/1.73 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.35/1.73 , Y ) ) ],
% 1.35/1.73 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.35/1.73 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.35/1.73 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 1.35/1.73 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.73 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.35/1.73 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.35/1.73 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.35/1.73 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.35/1.73 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.35/1.73 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.73 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.73 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.35/1.73 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.35/1.73 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ), =( X,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.73 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.35/1.73 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.35/1.73 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.35/1.73 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.35/1.73 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.35/1.73 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.35/1.73 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.35/1.73 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), Y, X ),
% 1.35/1.73 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.35/1.73 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~( 'c_Int_Oiszero'(
% 1.35/1.73 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Z ), Y ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ),
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.73 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.73 ), =( 'c_HOL_Oinverse__class_Odivide'( Y, U, X ),
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.35/1.73 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.73 X, 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 'tc_nat' ), X ), 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ), Y,
% 1.35/1.73 'tc_nat' ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.35/1.73 ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.35/1.73 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.35/1.73 ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.35/1.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.35/1.73 Y, X ), X ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y, X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.35/1.73 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.35/1.73 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.35/1.73 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.35/1.73 Y, X ) ) ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.35/1.73 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.35/1.73 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.35/1.73 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.35/1.73 Z, X ) ) ) ],
% 1.35/1.73 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.35/1.73 'c_lessequals'( Z, Y, X ) ],
% 1.35/1.73 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.35/1.73 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.35/1.73 , Y, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.35/1.73 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.35/1.73 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.35/1.73 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.35/1.73 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.35/1.73 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.73 , 'tc_nat' ), 'tc_nat' ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.35/1.73 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.73 , 'tc_nat' ), 'tc_nat' ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), =( Y,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( Y, hAPP( hAPP( Y, T ), T ) )
% 1.35/1.73 , T ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.35/1.73 ~( hBOOL( hAPP( X, T ) ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), hAPP( 'c_Suc', T ) ),
% 1.35/1.73 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 'tc_nat' ), Z ), T ), Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.73 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( 'c_Suc',
% 1.35/1.73 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ), 'tc_nat' ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), X, 'tc_nat' ),
% 1.35/1.73 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), Z ) ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.35/1.73 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.35/1.73 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc',
% 1.35/1.73 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.35/1.73 'tc_nat' ), Y, 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 1.35/1.73 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.35/1.73 , Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X,
% 1.35/1.73 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ =( hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X,
% 1.35/1.73 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ) ), T ), U, 'tc_nat'
% 1.35/1.73 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z
% 1.35/1.73 ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ), 'tc_nat' ) ),
% 1.35/1.73 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.35/1.73 ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.35/1.73 ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ) ), Y ) ), Z ), U, 'tc_nat'
% 1.35/1.73 ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), T ) ), U ), 'tc_nat' )
% 1.35/1.73 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T
% 1.35/1.73 ) ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ), 'tc_nat' ) ),
% 1.35/1.73 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.35/1.73 ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.35/1.73 ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ) ), Y ) ), U ), 'tc_nat' )
% 1.35/1.73 ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.35/1.73 'tc_nat' ) ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.73 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.73 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y,
% 1.35/1.73 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ],
% 1.35/1.73 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.73 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.73 ), Y ), T ), Z, X ) ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.35/1.73 Y ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.35/1.73 Y ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.35/1.73 Y ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.35/1.73 Y ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.35/1.73 Y ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.35/1.73 Y ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.35/1.73 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.35/1.73 ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.35/1.73 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.35/1.73 ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.35/1.73 ) ],
% 1.35/1.73 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.73 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.35/1.73 T, X ) ), T, X ) ) ],
% 1.35/1.73 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.73 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.35/1.73 ) ), Z ), T, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.35/1.73 , X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.35/1.73 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.35/1.73 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.73 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.73 ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.73 ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.35/1.73 , 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.35/1.73 , X ) ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.35/1.73 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.35/1.73 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.35/1.73 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.35/1.73 , X ) ), T ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.73 ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.73 ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.73 'c_Int_OMin', X ) ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.35/1.73 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ),
% 1.35/1.73 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.35/1.73 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.35/1.73 ) ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ),
% 1.35/1.73 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.73 ) ],
% 1.35/1.73 [ ~( 'class_RealVector_Oreal__field'( X ) ), =(
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), W, X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), Y ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.35/1.73 Z, U, X ), W, X ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, T, X )
% 1.35/1.73 , W, X ) ), U ) ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.35/1.73 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.73 ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( T, hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.35/1.73 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X
% 1.35/1.73 ) ), U ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), T ), U ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ), W, X ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.35/1.73 ) ), T ) ), U ), W, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), Y ), T ) ), U ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.35/1.73 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.35/1.73 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.35/1.73 X ) ) ],
% 1.35/1.73 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.35/1.73 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.35/1.73 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.35/1.73 X ), Z, X ) ) ],
% 1.35/1.73 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.35/1.73 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.35/1.73 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.35/1.73 , T, X ), X ), T, X ) ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.35/1.73 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 1.35/1.73 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X ), X ) )
% 1.35/1.73 ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.35/1.73 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.35/1.73 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.35/1.73 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.35/1.73 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.35/1.73 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.35/1.73 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.73 ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.73 ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.35/1.73 ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.73 ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.35/1.73 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.35/1.73 ), Z ), Y ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.73 ) ), =( Y, Z ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.73 ) ), =( Y, Z ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.35/1.73 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.73 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'(
% 1.35/1.73 Y, T, X ) ), 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.73 , Y ), Z ), Z, X ), Y ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.35/1.73 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.35/1.73 X ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), =( Y,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.35/1.73 Z, 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.73 'tc_nat' ) ), X ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.35/1.73 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.35/1.73 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.35/1.73 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.35/1.73 ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.35/1.73 'c_HOL_Oone__class_Oone'( X ), X ) ), Z ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.35/1.73 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 1.35/1.73 , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.35/1.73 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ),
% 1.35/1.73 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.35/1.73 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.35/1.73 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.35/1.73 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.73 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ), ~(
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.35/1.73 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.73 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.35/1.73 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.73 'c_Int_OMin', X ) ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.73 'c_Int_OMin', X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.35/1.73 [ =( 'c_Int_OBit1'( 'c_Int_OMin' ), 'c_Int_OMin' ) ],
% 1.35/1.73 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OMin' ) ), =( X, 'c_Int_OMin' ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( =( 'c_Int_OMin', 'c_Int_OBit1'( X ) ) ), =( 'c_Int_OMin', X ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.35/1.73 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.35/1.73 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.35/1.73 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.35/1.73 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ =( 'c_Int_OMin', 'c_Int_OBit1'( 'c_Int_OMin' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', X
% 1.35/1.73 ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.35/1.73 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'(
% 1.35/1.73 X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'c_lessequals'( hAPP( 'c_Suc', X ), X, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', X
% 1.35/1.73 ), Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.35/1.73 X, Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.35/1.73 , U ) ), hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z
% 1.35/1.73 ), T ), U ) ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.35/1.73 'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), X ), Y ) ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.35/1.73 X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), X ), Y ) ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.35/1.73 X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.35/1.73 'c_Suc', Y ) ) ) ],
% 1.35/1.73 [ =( X, hAPP( 'c_Suc', Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.35/1.73 'c_lessequals'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.35/1.73 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.35/1.73 V0, V1 ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.35/1.73 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.35/1.73 V0, V1 ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.35/1.73 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W
% 1.35/1.73 , V0, V1 ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.35/1.73 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W
% 1.35/1.73 , V0, V1 ) ) ],
% 1.35/1.73 [ =( 'c_FFT__Mirabelle_OFFT'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.35/1.73 ), X ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.35/1.73 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.73 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), X ), X ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.35/1.73 ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.35/1.73 ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.73 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.73 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.35/1.73 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.35/1.73 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.35/1.73 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.73 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.73 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.35/1.73 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.35/1.73 ), Z ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.35/1.73 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.35/1.73 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.35/1.73 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.35/1.73 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.35/1.73 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.35/1.73 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.35/1.73 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.35/1.73 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.35/1.73 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.35/1.73 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.35/1.73 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.35/1.73 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.35/1.73 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.35/1.73 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.35/1.73 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.35/1.73 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) )
% 1.35/1.73 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 1.35/1.73 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 1.35/1.73 ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.35/1.73 ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.35/1.73 ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.35/1.73 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.35/1.73 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.35/1.73 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.35/1.73 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X
% 1.35/1.73 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( T, Y, X ), X ), Z, X ) ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.35/1.73 , X ) ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.35/1.73 , X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.35/1.73 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.35/1.73 , X ) ), T ) ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.35/1.73 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.35/1.73 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.73 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X
% 1.35/1.73 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), 'c_HOL_Ominus__class_Ominus'( Y, T, X ) ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, T, X
% 1.35/1.73 ) ), U ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( T, Y, X
% 1.35/1.73 ) ), Z ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ) ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X
% 1.35/1.73 ) ), Z ) ), T ), W ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X
% 1.35/1.73 ) ), Z ) ), W ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.35/1.73 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.35/1.73 , T ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.35/1.73 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y,
% 1.35/1.73 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.73 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.35/1.73 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.35/1.73 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.35/1.73 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.35/1.73 ) ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.73 'c_Int_OBit1'( Y ), X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.73 'c_Int_OPls', X ) ), Y ) ],
% 1.35/1.73 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.73 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.35/1.73 [ ~( 'class_Int_Onumber__ring'( X ) ), 'c_Int_Oiszero'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ) ],
% 1.35/1.73 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.73 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.35/1.73 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.35/1.73 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 Y ), X ), X ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.35/1.73 , X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.35/1.73 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.35/1.73 ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y
% 1.35/1.73 ), X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.35/1.73 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.73 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.35/1.73 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.35/1.73 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.35/1.73 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.35/1.73 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.73 hAPP( 'c_Suc', Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.35/1.73 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.35/1.73 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.35/1.73 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.35/1.73 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.73 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.73 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.35/1.73 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.35/1.73 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 X, hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.35/1.73 ), 'tc_nat' ) ) ],
% 1.35/1.73 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.73 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 1.35/1.73 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 1.35/1.73 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 1.35/1.73 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.35/1.73 hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 1.35/1.73 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.73 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 1.35/1.73 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.35/1.73 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.35/1.73 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.35/1.73 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.35/1.73 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.35/1.73 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X,
% 1.35/1.73 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.35/1.73 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.35/1.73 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_Fun_Oinj__on'( 'c_Suc', X, 'tc_nat', 'tc_nat' ) ],
% 1.35/1.73 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.35/1.73 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =(
% 1.35/1.73 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), 'c_lessequals'( Y,
% 1.35/1.73 X, 'tc_nat' ) ],
% 1.35/1.73 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP(
% 1.35/1.73 'c_Suc', Y ), X, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', X ), 'tc_nat' ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ),
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.35/1.73 [ ~( =( 'c_Int_OPls', 'c_Int_OMin' ) ) ],
% 1.35/1.73 [ ~( =( 'c_Int_OMin', 'c_Int_OPls' ) ) ],
% 1.35/1.73 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OPls',
% 1.35/1.73 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.35/1.73 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.35/1.73 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.73 hAPP( 'c_Suc', T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z
% 1.35/1.73 ), hAPP( 'c_Suc', T ) ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.35/1.73 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ) )
% 1.35/1.73 , =( Y, T ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) )
% 1.35/1.73 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.35/1.73 'tc_nat' ) ), Y ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.35/1.73 'tc_nat' ) ), Y ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.35/1.73 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.35/1.73 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.35/1.73 , X ) ), Z ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.35/1.73 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.73 ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.35/1.73 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.73 ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.35/1.73 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.35/1.73 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.35/1.73 , Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.35/1.73 'c_HOL_Oabs__class_Oabs'( Y, X ) ), Z ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.35/1.73 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.35/1.73 ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.35/1.73 , Z ), Y ), 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.35/1.73 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.35/1.73 ],
% 1.35/1.73 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.73 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.35/1.73 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.35/1.73 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 X, T, 'tc_nat' ) ],
% 1.35/1.73 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.35/1.73 ), 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.35/1.73 ), 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.35/1.73 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.35/1.73 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.35/1.73 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( =( 'c_Int_OMin', 'c_Int_OBit0'( X ) ) ) ],
% 1.35/1.73 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OMin' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.35/1.73 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.35/1.73 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.35/1.73 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.35/1.73 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.35/1.73 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.35/1.73 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.73 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.35/1.73 , ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.35/1.73 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), Y ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ), ~(
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.73 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.35/1.73 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.35/1.73 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.35/1.73 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.73 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.35/1.73 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.35/1.73 [ =( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 'tc_nat' ), Z ), hAPP( 'c_Suc', X ) ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), Y,
% 1.35/1.73 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.73 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.35/1.73 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.35/1.73 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.73 'tc_nat' ) ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( 'c_Suc',
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 1.35/1.73 ), 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', Z ), Y, 'tc_nat' ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.35/1.73 ), X, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc',
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.35/1.73 ), X, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc',
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), 'tc_nat' ) ],
% 1.35/1.73 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ) ), 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), U ), Z ) ), X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.35/1.73 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), U ), X ) ), Z ) ), =( Y,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ),
% 1.35/1.73 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 1.35/1.73 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.35/1.73 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.35/1.73 , 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.73 'tc_nat' ), X, 'tc_nat' ) ],
% 1.35/1.73 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.35/1.73 , 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.73 'tc_nat' ), Y, 'tc_nat' ) ],
% 1.35/1.73 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.35/1.73 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.35/1.73 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z )
% 1.35/1.73 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ),
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.35/1.73 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X )
% 1.35/1.73 , Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ),
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc',
% 1.35/1.73 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.35/1.73 'tc_nat' ), Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( 'c_Suc',
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), X ), Z ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 1.35/1.73 Z, Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc',
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z, 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ), ~(
% 1.35/1.73 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.35/1.73 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.35/1.73 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.35/1.73 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.35/1.73 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.35/1.73 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.35/1.73 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.35/1.73 , Z ) ],
% 1.35/1.73 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.35/1.73 , Z ) ],
% 1.35/1.73 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.35/1.73 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.35/1.73 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.35/1.73 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.35/1.73 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.35/1.73 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.35/1.73 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.35/1.73 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.35/1.73 ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) )
% 1.35/1.73 , 'tc_nat' ) ],
% 1.35/1.73 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T )
% 1.35/1.73 , 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.35/1.73 , Z, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.35/1.73 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.35/1.73 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.35/1.73 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.35/1.73 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.35/1.73 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.35/1.73 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.35/1.73 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.73 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.35/1.73 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.35/1.73 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.73 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.35/1.73 V3, V4 ) ), =( hAPP( hAPP( 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ],
% 1.35/1.73 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower_Opower'( U, W, V0 ), X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U
% 1.35/1.73 , W, V0 ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Y ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, T, Z, V4, V5, U, W, V6,
% 1.35/1.73 V0 ) ) ],
% 1.35/1.73 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower_Opower'( U, W, V0 ), V1 ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U
% 1.35/1.73 , W, V0 ), X ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Y ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, T, Z, V4, V5, U, W, V6,
% 1.35/1.73 V0 ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.35/1.73 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.35/1.73 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 1.35/1.73 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP( Z, hAPP(
% 1.35/1.73 hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.35/1.73 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z, V2, V3, V4, T, U, V5
% 1.35/1.73 , W ) ), =( V0, hAPP( hAPP( Z, hAPP( hAPP( 'c_Power_Opower_Opower'( T, U
% 1.35/1.73 , W ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower_Opower'( T, U, W ), V1 ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.35/1.73 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP( Z, hAPP(
% 1.35/1.73 hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.35/1.73 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z, V2, V3, V4, T, U, V5
% 1.35/1.73 , W ) ), =( V1, hAPP( hAPP( Z, hAPP( hAPP( 'c_Power_Opower_Opower'( T, U
% 1.35/1.73 , W ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower_Opower'( T, U, W ), V1 ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.35/1.73 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, X, V4, V5, T, U, V6, W
% 1.35/1.73 ) ) ],
% 1.35/1.73 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.35/1.73 V3, V4 ) ), hBOOL( hAPP( hAPP( U, hAPP( hAPP( T, hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( V1
% 1.35/1.73 , V2, V4 ), Z ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Z ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.35/1.73 U ), W ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, V2, X, V3, V4, Z, T, V5,
% 1.35/1.73 U ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( Y, T ), T ) ), ~(
% 1.35/1.73 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.35/1.73 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), V0, V1, V2, V3, Z, T, V4, U ) ), =( W,
% 1.35/1.73 hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.35/1.73 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y
% 1.35/1.73 , Z, T ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, V4, X, Y, Z, V5,
% 1.35/1.73 T ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.35/1.73 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, V4, T, X, Y, V5,
% 1.35/1.73 Z ) ) ],
% 1.35/1.73 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.35/1.73 V3, V4 ) ), =( hAPP( hAPP( T, hAPP( hAPP( 'c_Power_Opower_Opower'( V1, V2
% 1.35/1.73 , V4 ), Z ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.73 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.35/1.73 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T
% 1.35/1.73 ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), W ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, V3, X, V4, Y, Z, V5,
% 1.35/1.73 T ) ) ],
% 1.35/1.73 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z,
% 1.35/1.73 T, U ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( W, V0, Y, V1, V2, X, V3, Z, T, V4, U
% 1.35/1.73 ) ) ],
% 1.35/1.73 [ ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z
% 1.35/1.73 , T, U ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), V1 ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V2, V3, V1, Y, V4, X, V5, Z, T, V6,
% 1.35/1.73 U ) ) ],
% 1.35/1.73 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower_Opower'( T, U, W ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.35/1.73 , U, W ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, Z, V2, X, V3, T, U, V4, W
% 1.35/1.73 ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.35/1.73 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( V0, Y ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, V4, X, V5, T, U, V6, W
% 1.35/1.73 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.35/1.73 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( V1, Y ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, V4, X, V5, T, U, V6, W
% 1.35/1.73 ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.35/1.73 U ), W ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( W, Y ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, V2, V3, X, V4, Z, T, V5,
% 1.35/1.73 U ) ) ],
% 1.35/1.73 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.35/1.73 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.73 ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.35/1.73 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.35/1.73 ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ),
% 1.35/1.73 hAPP( hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.35/1.73 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ), 'tc_nat' ), ~( 'c_lessequals'( Y,
% 1.35/1.73 Z, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y )
% 1.35/1.73 , 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.35/1.73 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.35/1.73 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.35/1.73 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.35/1.73 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, hAPP(
% 1.35/1.73 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.35/1.73 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.35/1.73 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.35/1.73 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ),
% 1.35/1.73 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.35/1.73 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.35/1.73 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.35/1.73 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.35/1.73 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.35/1.73 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.35/1.73 , Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.35/1.73 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.35/1.73 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.35/1.73 , X, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.35/1.73 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.35/1.73 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.35/1.73 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.35/1.73 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.35/1.73 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.35/1.73 , X, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.73 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.73 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.35/1.73 ), 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.73 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.73 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.35/1.73 ), 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.73 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.73 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.73 'tc_nat' ) ), =( Y, Z ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.35/1.73 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.35/1.73 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ),
% 1.35/1.73 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.35/1.73 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.35/1.73 hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~(
% 1.35/1.73 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.35/1.73 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.35/1.73 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 1.35/1.73 ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.35/1.73 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.35/1.73 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 1.35/1.73 , 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.35/1.73 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 1.35/1.73 ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.35/1.73 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.35/1.73 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.35/1.73 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 1.35/1.73 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.35/1.73 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.35/1.73 ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.35/1.73 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X,
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ) ) ],
% 1.35/1.73 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~(
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.35/1.73 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.35/1.73 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.35/1.73 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), hAPP(
% 1.35/1.73 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), hAPP( 'c_Suc',
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), hAPP(
% 1.35/1.73 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), hAPP( 'c_Suc',
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.35/1.73 [ ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y )
% 1.35/1.73 , hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, hAPP(
% 1.35/1.73 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.35/1.73 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.35/1.73 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.73 'tc_nat' ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP(
% 1.35/1.73 hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 'tc_nat' ) )
% 1.35/1.73 ],
% 1.35/1.73 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.35/1.73 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.73 'tc_nat' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ),
% 1.35/1.73 X ), 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.73 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.73 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ),
% 1.35/1.73 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.73 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), X ), X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.35/1.73 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.35/1.73 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.35/1.73 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.35/1.73 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.35/1.73 X, Y, Z ), T ), U ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.35/1.73 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.35/1.73 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.35/1.73 U ), W ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), V0 ) ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, X, V4, V5, Z, T, V6,
% 1.35/1.73 U ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower_Opower'( X, Y, Z ), U ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ) ), ~(
% 1.35/1.73 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, V0, T, V1, V2, Z ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, X ) ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ), X ), ~(
% 1.35/1.73 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ), T ) ), U ), W, X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ), W, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.73 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), U ) ), W ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.35/1.73 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.35/1.73 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.35/1.73 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.35/1.73 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.35/1.73 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.35/1.73 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.73 'tc_nat' ) ), Y ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.73 'tc_nat' ) ) ) ],
% 1.35/1.73 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.35/1.73 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.35/1.73 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.35/1.73 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.35/1.73 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.35/1.73 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.35/1.73 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.35/1.73 ), X ), X ), 'tc_nat' ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.35/1.73 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.35/1.73 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.35/1.73 ), X ), Z ), 'tc_nat' ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.35/1.73 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, 'c_Divides_Odiv__class_Omod'( Y, X,
% 1.35/1.73 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.73 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( X, 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.35/1.73 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.35/1.73 ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.35/1.73 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ) ), Y ) ), U ), 'tc_nat' )
% 1.35/1.73 ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.35/1.73 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), T ) ), U ), 'tc_nat' )
% 1.35/1.73 , ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), X ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ), 'tc_nat' ) ),
% 1.35/1.73 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.35/1.73 ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ) ), Y ) ), Z ), U, 'tc_nat'
% 1.35/1.73 ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ) ), T ), U, 'tc_nat'
% 1.35/1.73 ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.35/1.73 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), T ),
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ), 'tc_nat' ) ),
% 1.35/1.73 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y
% 1.35/1.73 , X, 'tc_nat' ) ), Z ) ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z
% 1.35/1.73 ) ), T ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.73 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ),
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ) ), Y ) ), U ), 'tc_nat' )
% 1.35/1.73 ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ) ), Y ) ), Z ), U, 'tc_nat'
% 1.35/1.73 ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~(
% 1.35/1.73 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z, hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( T
% 1.35/1.73 , X, 'tc_nat' ) ), Y ) ), U ) ) ],
% 1.35/1.73 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~(
% 1.35/1.73 'c_lessequals'( T, X, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X
% 1.35/1.73 , T, 'tc_nat' ) ), Y ) ), Z ), U ) ],
% 1.35/1.73 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y
% 1.35/1.73 , X, 'tc_nat' ) ), Z ) ), T ) ) ) ],
% 1.35/1.73 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 1.35/1.73 hBOOL( hAPP( X, Z ) ) ],
% 1.35/1.73 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 1.35/1.73 hBOOL( hAPP( X, Z ) ) ],
% 1.35/1.73 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.35/1.73 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.35/1.73 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.73 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.35/1.73 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.35/1.73 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.35/1.73 ],
% 1.35/1.73 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.35/1.73 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 1.35/1.73 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.35/1.73 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.35/1.73 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.35/1.73 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.35/1.73 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.35/1.73 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.35/1.73 , 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat'
% 1.35/1.73 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.35/1.73 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.35/1.73 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.35/1.73 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 1.35/1.73 'tc_nat' ) ],
% 1.35/1.73 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.35/1.73 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.35/1.73 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.35/1.73 ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ),
% 1.35/1.73 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.73 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.35/1.73 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.73 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.35/1.73 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.35/1.73 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.35/1.73 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.73 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.35/1.73 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.35/1.73 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.73 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.73 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.73 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.35/1.73 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.35/1.73 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.35/1.73 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 1.35/1.73 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Odiv'(
% 1.35/1.73 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.35/1.73 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 1.35/1.73 ,
% 1.35/1.73 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.73 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.35/1.73 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.73 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.35/1.73 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.73 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.73 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.35/1.73 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.35/1.73 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.73 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.35/1.73 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.73 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.35/1.73 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.73 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.35/1.73 ), Y ), Y ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.73 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.73 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.73 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.35/1.73 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.73 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.35/1.73 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.73 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.73 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.73 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.35/1.73 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.73 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.35/1.73 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.35/1.73 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.73 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.73 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.35/1.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.35/1.73 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.35/1.73 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.35/1.74 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T
% 1.35/1.74 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.74 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.74 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.74 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.74 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.35/1.74 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.74 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.74 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.35/1.74 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.74 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.35/1.74 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.35/1.74 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.74 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.74 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.74 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.74 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.74 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.74 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.35/1.74 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.74 ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.74 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.74 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.74 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.35/1.74 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.74 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.74 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.74 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.74 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.74 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.74 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.35/1.74 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.74 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.74 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.35/1.74 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.35/1.74 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.35/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.35/1.74 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.35/1.74 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.74 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) )
% 1.35/1.74 ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.74 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.74 ), X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.35/1.74 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) )
% 1.35/1.74 ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_OPls'
% 1.35/1.74 , Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.35/1.74 ), X ) ) ],
% 1.35/1.74 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.74 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.35/1.74 ), Y ), hAPP( 'c_Suc', Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.35/1.74 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.35/1.74 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.35/1.74 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.35/1.74 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.35/1.74 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.35/1.74 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.74 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.35/1.74 ) ) ],
% 1.35/1.74 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.35/1.74 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.35/1.74 ) ],
% 1.35/1.74 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.35/1.74 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.35/1.74 ), Y ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.35/1.74 ), Y ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.35/1.74 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.35/1.74 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X
% 1.35/1.74 ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.35/1.74 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.35/1.74 ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.74 X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.74 X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.35/1.74 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.35/1.74 'tc_nat' ) ) ],
% 1.35/1.74 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.35/1.74 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.35/1.74 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' )
% 1.35/1.74 ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.35/1.74 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.35/1.74 , ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.35/1.74 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, X ) ),
% 1.35/1.74 hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ) ), hAPP( T, X ) ), ~(
% 1.35/1.74 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.35/1.74 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.35/1.74 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ) ), hAPP( hAPP( Y, T ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.35/1.74 X, Y, Z ), T ), U ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.74 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.35/1.74 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.35/1.74 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.35/1.74 U ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.35/1.74 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ) ) ), V0 ) ), ~( hBOOL( hAPP( hAPP(
% 1.35/1.74 X, U ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3
% 1.35/1.74 , V4, X, V5, Y, Z, V6, T ) ) ],
% 1.35/1.74 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.35/1.74 hAPP( 'c_Power_Opower_Opower'( T, U, W ), Z ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), V0 ) ) ) ) ) ), ~(
% 1.35/1.74 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, X, V4, V5, T, U, V6,
% 1.35/1.74 W ) ) ],
% 1.35/1.74 [ =( X, hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.74 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.74 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 1.35/1.74 'c_Parity_Osko__Parity__Xodd__Suc__mult__two__ex__1__1'( X ) ) ) ),
% 1.35/1.74 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.35/1.74 ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), X ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.35/1.74 'c_HOL_Oone__class_Oone'( X ), X ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.74 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.35/1.74 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc',
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.74 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.74 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.35/1.74 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.74 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.74 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.35/1.74 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.74 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.35/1.74 [ =( hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X, hAPP( 'c_Suc',
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.74 'tc_nat' ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, hAPP(
% 1.35/1.74 'c_Suc', Y ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.35/1.74 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( X
% 1.35/1.74 , 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat'
% 1.35/1.74 ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.35/1.74 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.74 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.74 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 'tc_nat' ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.74 'tc_nat' ) ) ],
% 1.35/1.74 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.74 'c_Int_OMin', X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.35/1.74 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.35/1.74 'c_HOL_Oone__class_Oone'( X ), X ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.35/1.74 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.35/1.74 [ =( hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.35/1.74 , 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.74 'tc_nat' ) ) ],
% 1.35/1.74 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ominus__class_Ominus'(
% 1.35/1.74 hAPP( 'c_Suc', Z ), T, 'tc_nat' ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.35/1.74 , T, 'tc_nat' ) ) ), Y ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ) ],
% 1.35/1.74 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.35/1.74 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc'
% 1.35/1.74 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.35/1.74 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.35/1.74 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.35/1.74 , X, Z, U, W, V0 ) ) ],
% 1.35/1.74 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.35/1.74 'c_Suc', X ), Y, 'tc_nat' ), 'tc_nat' ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.35/1.74 hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ), 'c_Fact_Ofact__class_Ofact'(
% 1.35/1.74 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 'tc_nat' ) ) ],
% 1.35/1.74 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.35/1.74 , 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.74 'tc_nat' ), X ), Y ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.74 'tc_nat' ), X ), Z ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.35/1.74 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( Y ) ), Z ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.35/1.74 'tc_nat' ) ) ],
% 1.35/1.74 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.35/1.74 , Y ) ) ],
% 1.35/1.74 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.74 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.35/1.74 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.35/1.74 ) ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.35/1.74 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.35/1.74 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.74 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) )
% 1.35/1.74 ) ],
% 1.35/1.74 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.35/1.74 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.74 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.35/1.74 ) ],
% 1.35/1.74 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.35/1.74 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.35/1.74 , Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.35/1.74 ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.35/1.74 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.35/1.74 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.35/1.74 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.35/1.74 'tc_nat' ), X ), X ) ) ],
% 1.35/1.74 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ) ],
% 1.35/1.74 [ 'c_Fun_Oinj__on'( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), X, 'tc_nat', 'tc_nat' ) ],
% 1.35/1.74 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.74 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.74 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.35/1.74 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.35/1.74 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.35/1.74 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.74 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.35/1.74 ) ), 'c_Complex_Oii' ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.35/1.74 ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.35/1.74 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.35/1.74 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 X, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.35/1.74 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.35/1.74 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.35/1.74 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.35/1.74 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'tc_nat' ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.35/1.74 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ) ],
% 1.35/1.74 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.35/1.74 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.74 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.35/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.35/1.74 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.35/1.74 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ) ), =( X,
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.35/1.74 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.35/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.74 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.35/1.74 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.35/1.74 'tc_nat' ) ) ],
% 1.35/1.74 [ 'c_Fun_Oinj__on'( 'c_COMBB'( 'c_Suc', hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), X,
% 1.35/1.74 'tc_nat', 'tc_nat' ) ],
% 1.35/1.74 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.35/1.74 X ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.74 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ), X ) )
% 1.35/1.74 ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.35/1.74 ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.74 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.74 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ),
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.35/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.35/1.74 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.74 'c_Int_OMin', X ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.35/1.74 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.35/1.74 ) ],
% 1.35/1.74 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.35/1.74 , X ) ) ],
% 1.35/1.74 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.35/1.74 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.35/1.74 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.35/1.74 , Y, X ) ) ],
% 1.35/1.74 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.35/1.74 , Y, X ) ) ],
% 1.35/1.74 [ =( 'c_FFT__Mirabelle_ODFT'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.35/1.74 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.74 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), X, Y ), hAPP(
% 1.35/1.74 'c_FFT__Mirabelle_OFFT'( 'v_ka____', X ), Y ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.35/1.74 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.74 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ) )
% 1.35/1.74 ],
% 1.35/1.74 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.35/1.74 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.35/1.74 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.35/1.74 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.35/1.74 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.35/1.74 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.35/1.74 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.35/1.74 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.35/1.74 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.35/1.74 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.35/1.74 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.35/1.74 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ),
% 1.35/1.74 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.35/1.74 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 1.35/1.74 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.35/1.74 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y
% 1.35/1.74 ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.35/1.74 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.35/1.74 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.35/1.74 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.35/1.74 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.35/1.74 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.35/1.74 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 1.35/1.74 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.35/1.74 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.74 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.35/1.74 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.35/1.74 , 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.74 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.74 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.35/1.74 'c_FFT__Mirabelle_Oroot'( X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.74 'tc_nat' ), Y ), Z ) ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.35/1.74 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.74 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( T, X ) ),
% 1.35/1.74 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.35/1.74 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 1.35/1.74 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.35/1.74 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.35/1.74 'tc_nat' ), hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.35/1.74 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.35/1.74 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.35/1.74 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.35/1.74 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.35/1.74 'c_Suc', X ), Y, 'tc_nat' ), hAPP( 'c_Suc', Z ), 'tc_nat' ),
% 1.35/1.74 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.35/1.74 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.35/1.74 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.35/1.74 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.35/1.74 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ), Y, 'tc_nat'
% 1.35/1.74 ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.35/1.74 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.35/1.74 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.35/1.74 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 'tc_nat' ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.35/1.74 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.35/1.74 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( 'v_i____', hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( 'c_Suc', 'v_ka____' ) ), 'tc_nat' )
% 1.35/1.74 ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.35/1.74 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.35/1.74 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.35/1.74 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.74 X ), Y ), Y ) ) ],
% 1.35/1.74 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.35/1.74 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.35/1.74 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.35/1.74 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.35/1.74 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.35/1.74 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.35/1.74 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 1.35/1.74 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.35/1.74 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.35/1.74 , hAPP( 'c_Suc', X ) ), Z ) ) ), =( Y, Z ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.35/1.74 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.35/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.35/1.74 [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 1.35/1.74 [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 1.35/1.74 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.35/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.74 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.35/1.74 ), Z ), Y ), 'tc_nat' ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.74 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.35/1.74 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.35/1.74 ), =( Z, Y ) ],
% 1.35/1.74 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.35/1.74 ) ],
% 1.35/1.74 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.35/1.74 ) ],
% 1.35/1.74 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.35/1.74 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.35/1.74 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.35/1.74 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.35/1.74 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.35/1.74 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.35/1.74 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.35/1.74 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.35/1.74 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.35/1.74 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.35/1.74 , Y ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.35/1.74 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.35/1.74 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.35/1.74 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.35/1.74 , X ) ), T ), X ) ) ],
% 1.35/1.74 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.35/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.35/1.74 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.35/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.35/1.74 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.35/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.35/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.35/1.74 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.35/1.74 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.35/1.74 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.35/1.74 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.35/1.74 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.35/1.74 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.35/1.74 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.35/1.74 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.35/1.74 , T, X ) ) ), =( Z, T ) ],
% 1.35/1.74 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.35/1.74 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.35/1.74 , T, X ) ) ), =( Y, Z ) ],
% 1.35/1.74 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.74 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.35/1.74 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.35/1.74 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.35/1.74 T, X ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.35/1.74 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.35/1.74 T, X ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.35/1.74 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ),
% 1.35/1.74 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.74 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.35/1.74 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.35/1.74 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.35/1.74 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ),
% 1.35/1.74 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.74 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.35/1.74 ), X ), Z ), 'tc_nat' ) ) ],
% 1.35/1.74 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.35/1.74 ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.35/1.74 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.35/1.74 ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.35/1.74 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.35/1.74 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.35/1.74 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.35/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.74 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y ),
% 1.35/1.74 'tc_nat' ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.74 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ),
% 1.35/1.74 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), =( hAPP(
% 1.35/1.74 'c_Suc', X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.35/1.74 [ ~( 'c_HOL_Oord__class_Oless'( 'v_i____', hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.35/1.74 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.35/1.74 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.35/1.74 'tc_nat' ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.35/1.74 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( 'v_i____', hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ) ), 'tc_nat' ) ],
% 1.35/1.74 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( 'v_i____',
% 1.35/1.74 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ) ],
% 1.35/1.74 [ ~( =( 'c_FFT__Mirabelle_ODFT'( hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ) ), 'v_a____', 'v_i____' ),
% 1.35/1.74 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_FFT__Mirabelle_OFFT'( 'v_ka____',
% 1.35/1.74 'c_COMBB'( 'v_a____', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat'
% 1.35/1.74 ) ), 'c_HOL_Ominus__class_Ominus'( 'v_i____', hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ) ), hAPP( hAPP(
% 1.35/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.35/1.74 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.35/1.74 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.35/1.74 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ) ) ) ),
% 1.35/1.74 'c_HOL_Ominus__class_Ominus'( 'v_i____', hAPP( hAPP(
% 1.35/1.74 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ) ) ), hAPP(
% 1.35/1.74 'c_FFT__Mirabelle_OFFT'( 'v_ka____', 'c_COMBB'( 'v_a____', 'c_COMBB'(
% 1.35/1.74 'c_Suc', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat'
% 1.35/1.74 , 'tc_Complex_Ocomplex', 'tc_nat' ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.35/1.74 'v_i____', hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.35/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.35/1.74 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ) ) ),
% 1.35/1.74 'tc_Complex_Ocomplex' ) ) ) ],
% 1.35/1.74 [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ), ~(
% 1.35/1.74 'class_Lattices_Oboolean__algebra'( Y ) ) ],
% 1.35/1.74 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.35/1.74 'class_Orderings_Opreorder'( Y ) ) ],
% 1.35/1.74 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.35/1.74 'class_Orderings_Oorder'( Y ) ) ],
% 1.35/1.74 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.35/1.74 ],
% 1.35/1.74 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.35/1.74 ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.35/1.74 ],
% 1.35/1.74 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.35/1.74 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.35/1.74 'tc_Int_Oint' ) ],
% 1.35/1.74 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.35/1.74 'tc_Int_Oint' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.35/1.74 'tc_Int_Oint' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.35/1.74 ],
% 1.35/1.74 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.35/1.74 ],
% 1.35/1.74 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.35/1.74 ,
% 1.35/1.74 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.35/1.74 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.35/1.74 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.35/1.74 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_Int_Oint' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.35/1.74 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.35/1.74 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.35/1.74 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.35/1.74 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.35/1.75 'tc_Complex_Ocomplex' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.35/1.75 'tc_Complex_Ocomplex' ) ],
% 1.35/1.75 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.35/1.75 'tc_Complex_Ocomplex' ) ],
% 1.35/1.75 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.35/1.75 ],
% 1.35/1.75 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.35/1.75 ],
% 1.35/1.75 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.35/1.75 ],
% 1.35/1.75 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.35/1.75 ,
% 1.35/1.75 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.35/1.75 ,
% 1.35/1.75 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.35/1.75 ,
% 1.35/1.75 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.35/1.75 ,
% 1.35/1.75 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.35/1.75 ,
% 1.35/1.75 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_Complex_Ocomplex' ) ]
% 1.35/1.75 ,
% 1.35/1.75 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.35/1.75 ,
% 1.35/1.75 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.35/1.75 ,
% 1.35/1.75 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.35/1.75 ,
% 1.35/1.75 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.35/1.75 ,
% 1.35/1.75 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.35/1.75 ,
% 1.35/1.75 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.35/1.75 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.35/1.75 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.35/1.75 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.35/1.75 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.35/1.75 [ 'class_RealVector_Oreal__field'( 'tc_Complex_Ocomplex' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.35/1.75 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.35/1.75 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.35/1.75 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.35/1.75 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.35/1.75 [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ],
% 1.35/1.75 [ =( 'c_COMBC'( X, Y, Z, T, U, W ), hAPP( hAPP( X, Z ), Y ) ) ],
% 1.35/1.75 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.35/1.75 ,
% 1.35/1.75 [ 'c_fequal'( X, X, Y ) ],
% 1.35/1.75 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.35/1.75 ] .
% 1.35/1.75
% 1.35/1.75
% 1.35/1.75 percentage equality = 0.236577, percentage horn = 0.839388
% 1.35/1.75 This is a problem with some equality
% 1.35/1.75
% 1.35/1.75
% 1.35/1.75
% 1.35/1.75 Options Used:
% 1.35/1.75
% 1.35/1.75 useres = 1
% 1.35/1.75 useparamod = 1
% 1.35/1.75 useeqrefl = 1
% 1.35/1.75 useeqfact = 1
% 1.35/1.75 usefactor = 1
% 1.35/1.75 usesimpsplitting = 0
% 1.35/1.75 usesimpdemod = 5
% 1.35/1.75 usesimpres = 3
% 1.35/1.75
% 1.35/1.75 resimpinuse = 1000
% 1.35/1.75 resimpclauses = 20000
% 1.35/1.75 substype = eqrewr
% 1.35/1.75 backwardsubs = 1
% 1.35/1.75 selectoldest = 5
% 1.35/1.75
% 1.35/1.75 litorderings [0] = split
% 1.35/1.75 litorderings [1] = extend the termordering, first sorting on arguments
% 1.35/1.75
% 1.35/1.75 termordering = kbo
% 1.35/1.75
% 1.35/1.75 litapriori = 0
% 1.35/1.75 termapriori = 1
% 1.35/1.75 litaposteriori = 0
% 1.35/1.75 termaposteriori = 0
% 1.35/1.75 demodaposteriori = 0
% 1.35/1.75 ordereqreflfact = 0
% 1.35/1.75
% 1.35/1.75 litselect = negord
% 1.35/1.75
% 1.35/1.75 maxweight = 15
% 1.35/1.75 maxdepth = 30000
% 1.35/1.75 maxlength = 115
% 1.35/1.75 maxnrvars = 195
% 1.35/1.75 excuselevel = 1
% 1.35/1.75 increasemaxweight = 1
% 1.35/1.75
% 1.35/1.75 maxselected = 10000000
% 1.35/1.75 maxnrclauses = 10000000
% 1.35/1.75
% 1.35/1.75 showgenerated = 0
% 1.35/1.75 showkept = 0
% 1.35/1.75 showselected = 0
% 1.35/1.75 showdeleted = 0
% 1.35/1.75 showresimp = 1
% 1.35/1.75 showstatus = 2000
% 1.35/1.75
% 1.35/1.75 prologoutput = 1
% 1.35/1.75 nrgoals = 5000000
% 1.35/1.75 totalproof = 1
% 1.35/1.75
% 1.35/1.75 Symbols occurring in the translation:
% 1.35/1.75
% 1.35/1.75 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.35/1.75 . [1, 2] (w:1, o:163, a:1, s:1, b:0),
% 1.35/1.75 ! [4, 1] (w:0, o:83, a:1, s:1, b:0),
% 1.35/1.75 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.35/1.75 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.35/1.75 'class_Ring__and__Field_Omult__mono1' [40, 1] (w:1, o:89, a:1, s:1
% 1.35/1.75 , b:0),
% 1.35/1.75 'c_HOL_Otimes__class_Otimes' [41, 1] (w:1, o:90, a:1, s:1, b:0),
% 1.35/1.75 hAPP [43, 2] (w:1, o:188, a:1, s:1, b:0),
% 1.35/1.75 'c_lessequals' [46, 3] (w:1, o:198, a:1, s:1, b:0),
% 1.35/1.75 'c_HOL_Ozero__class_Ozero' [47, 1] (w:1, o:91, a:1, s:1, b:0),
% 1.35/1.75 'tc_nat' [48, 0] (w:1, o:17, a:1, s:1, b:0),
% 1.35/1.75 'c_HOL_Oplus__class_Oplus' [49, 1] (w:1, o:93, a:1, s:1, b:0),
% 1.35/1.75 'c_Divides_Odiv__class_Omod' [51, 3] (w:1, o:199, a:1, s:1, b:0),
% 1.35/1.75 'c_HOL_Oord__class_Oless' [53, 3] (w:1, o:200, a:1, s:1, b:0),
% 1.35/1.75 'class_Ring__and__Field_Ofield' [54, 1] (w:1, o:94, a:1, s:1, b:0),
% 1.35/1.75 'class_Ring__and__Field_Odivision__by__zero' [55, 1] (w:1, o:98, a:1
% 1.35/1.75 , s:1, b:0),
% 1.35/1.75 'c_HOL_Oinverse__class_Odivide' [56, 3] (w:1, o:201, a:1, s:1, b:0),
% 1.35/1.75
% 1.35/1.75 'c_HOL_Oinverse__class_Oinverse' [57, 2] (w:1, o:189, a:1, s:1, b:0)
% 1.35/1.75 ,
% 1.35/1.75 'class_Ring__and__Field_Oordered__field' [58, 1] (w:1, o:102, a:1, s:
% 1.35/1.75 1, b:0),
% 1.35/1.75 'class_RealVector_Oreal__normed__field' [59, 1] (w:1, o:103, a:1, s:1
% 1.35/1.75 , b:0),
% 1.35/1.75 'c_HOL_Ominus__class_Ominus' [60, 3] (w:1, o:202, a:1, s:1, b:0),
% 1.35/1.75 'c_HOL_Ouminus__class_Ouminus' [62, 2] (w:1, o:190, a:1, s:1, b:0),
% 1.35/1.75 'c_Ring__and__Field_Oordered__idom' [73, 11] (w:1, o:213, a:1, s:1
% 1.35/1.75 , b:0),
% 1.35/1.75 'c_Power_Opower_Opower' [74, 3] (w:1, o:204, a:1, s:1, b:0),
% 1.35/1.75 hBOOL [75, 1] (w:1, o:104, a:1, s:1, b:0),
% 1.35/1.75 'c_Divides_Odiv__class_Odiv' [76, 3] (w:1, o:205, a:1, s:1, b:0),
% 1.35/1.75 'class_Ring__and__Field_Oordered__semidom' [77, 1] (w:1, o:106, a:1
% 1.35/1.75 , s:1, b:0),
% 1.35/1.75 'class_OrderedGroup_Ogroup__add' [79, 1] (w:1, o:107, a:1, s:1, b:0)
% 1.35/1.75 ,
% 1.35/1.75 'class_OrderedGroup_Ocomm__monoid__add' [80, 1] (w:1, o:108, a:1, s:1
% 1.35/1.75 , b:0),
% 1.35/1.75 'class_OrderedGroup_Opordered__ab__group__add__abs' [81, 1] (w:1, o:
% 1.35/1.75 110, a:1, s:1, b:0),
% 1.35/1.75 'c_HOL_Oabs__class_Oabs' [82, 2] (w:1, o:191, a:1, s:1, b:0),
% 1.35/1.75 'class_Ring__and__Field_Oordered__ring__strict' [83, 1] (w:1, o:105
% 1.35/1.75 , a:1, s:1, b:0),
% 1.35/1.75 'class_Divides_Osemiring__div' [84, 1] (w:1, o:112, a:1, s:1, b:0),
% 1.35/1.75 'class_Ring__and__Field_Oordered__idom' [85, 1] (w:1, o:113, a:1, s:1
% 1.35/1.75 , b:0),
% 1.35/1.75 'c_OrderedGroup_Omonoid__mult' [87, 3] (w:1, o:203, a:1, s:1, b:0),
% 1.35/1.75 'c_Suc' [89, 0] (w:1, o:59, a:1, s:1, b:0),
% 1.35/1.75 'c_Parity_Oeven__odd__class_Oeven' [90, 2] (w:1, o:192, a:1, s:1, b:0
% 3.70/4.07 ),
% 3.70/4.07 'class_Ring__and__Field_Osemiring__0' [91, 1] (w:1, o:118, a:1, s:1
% 3.70/4.07 , b:0),
% 3.70/4.07 'class_Power_Opower' [92, 1] (w:1, o:138, a:1, s:1, b:0),
% 3.70/4.07 'c_Power_Opower__class_Opower' [93, 1] (w:1, o:139, a:1, s:1, b:0),
% 3.70/4.07 'class_Ring__and__Field_Ozero__neq__one' [94, 1] (w:1, o:140, a:1, s:
% 3.70/4.07 1, b:0),
% 3.70/4.07 'class_Ring__and__Field_Ono__zero__divisors' [95, 1] (w:1, o:101, a:1
% 3.70/4.07 , s:1, b:0),
% 3.70/4.07 'class_Ring__and__Field_Omult__zero' [96, 1] (w:1, o:99, a:1, s:1, b:
% 3.70/4.07 0),
% 3.70/4.07 'class_Int_Onumber' [97, 1] (w:1, o:141, a:1, s:1, b:0),
% 3.70/4.07 'c_Int_Onumber__class_Onumber__of' [99, 2] (w:1, o:193, a:1, s:1, b:0
% 3.70/4.07 ),
% 3.70/4.07 'class_Ring__and__Field_Ocomm__semiring__1' [100, 1] (w:1, o:96, a:1
% 3.70/4.07 , s:1, b:0),
% 3.70/4.07 'c_HOL_Oone__class_Oone' [101, 1] (w:1, o:92, a:1, s:1, b:0),
% 3.70/4.07 'class_OrderedGroup_Opordered__ab__group__add' [103, 1] (w:1, o:119
% 3.70/4.07 , a:1, s:1, b:0),
% 3.70/4.07 'c_Fact_Ofact__class_Ofact' [104, 2] (w:1, o:194, a:1, s:1, b:0),
% 3.70/4.07 'class_OrderedGroup_Olordered__ab__group__add' [105, 1] (w:1, o:120
% 3.70/4.07 , a:1, s:1, b:0),
% 3.70/4.07 'class_Ring__and__Field_Opordered__ring__abs' [106, 1] (w:1, o:145
% 3.70/4.07 , a:1, s:1, b:0),
% 3.70/4.07 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [107, 1]
% 3.70/4.07 (w:1, o:121, a:1, s:1, b:0),
% 3.70/4.07 'class_OrderedGroup_Opordered__ab__semigroup__add' [108, 1] (w:1, o:
% 3.70/4.07 122, a:1, s:1, b:0),
% 3.70/4.07 'class_Orderings_Oorder' [113, 1] (w:1, o:123, a:1, s:1, b:0),
% 3.70/4.07 'tc_Int_Oint' [114, 0] (w:1, o:61, a:1, s:1, b:0),
% 3.70/4.07 'class_Lattices_Oboolean__algebra' [115, 1] (w:1, o:146, a:1, s:1, b:
% 3.70/4.07 0),
% 3.70/4.07 'class_OrderedGroup_Olordered__ab__group__add__abs' [116, 1] (w:1, o:
% 3.70/4.07 124, a:1, s:1, b:0),
% 3.70/4.07 'class_OrderedGroup_Opordered__comm__monoid__add' [117, 1] (w:1, o:
% 3.70/4.07 125, a:1, s:1, b:0),
% 3.70/4.07 'class_Ring__and__Field_Omult__mono' [118, 1] (w:1, o:100, a:1, s:1
% 3.70/4.07 , b:0),
% 3.70/4.07 'class_Ring__and__Field_Opordered__ring' [119, 1] (w:1, o:147, a:1
% 3.70/4.07 , s:1, b:0),
% 3.70/4.07 'class_Ring__and__Field_Oidom' [121, 1] (w:1, o:148, a:1, s:1, b:0),
% 3.70/4.07
% 3.70/4.07 'class_Int_Onumber__ring' [122, 1] (w:1, o:149, a:1, s:1, b:0),
% 3.70/4.07 'class_Ring__and__Field_Odivision__ring' [123, 1] (w:1, o:150, a:1
% 3.70/4.07 , s:1, b:0),
% 3.70/4.07 'c_Int_OMin' [124, 0] (w:1, o:63, a:1, s:1, b:0),
% 3.70/4.07 'class_Ring__and__Field_Opordered__cancel__semiring' [125, 1] (w:1
% 3.70/4.07 , o:151, a:1, s:1, b:0),
% 3.70/4.07 'c_Groebner__Basis_Ogb__semiring' [133, 6] (w:1, o:210, a:1, s:1, b:0
% 3.70/4.07 ),
% 3.70/4.07 'class_OrderedGroup_Oordered__ab__group__add' [134, 1] (w:1, o:109
% 3.70/4.07 , a:1, s:1, b:0),
% 3.70/4.07 'class_Ring__and__Field_Opordered__semiring' [135, 1] (w:1, o:152, a:
% 3.70/4.07 1, s:1, b:0),
% 3.70/4.07 'class_Ring__and__Field_Oabs__if' [136, 1] (w:1, o:153, a:1, s:1, b:0
% 3.70/4.07 ),
% 3.70/4.07 'class_Orderings_Olinorder' [137, 1] (w:1, o:126, a:1, s:1, b:0),
% 3.70/4.07 'c_Int_OPls' [139, 0] (w:1, o:66, a:1, s:1, b:0),
% 3.70/4.07 'class_Ring__and__Field_Olordered__ring' [140, 1] (w:1, o:88, a:1, s:
% 3.70/4.07 1, b:0),
% 3.70/4.07 'class_OrderedGroup_Oab__group__add' [141, 1] (w:1, o:127, a:1, s:1
% 3.70/4.07 , b:0),
% 3.70/4.07 'class_OrderedGroup_Oab__semigroup__add' [142, 1] (w:1, o:128, a:1
% 3.70/4.07 , s:1, b:0),
% 3.70/4.07 'class_Divides_Oring__div' [143, 1] (w:1, o:111, a:1, s:1, b:0),
% 3.70/4.07 'class_OrderedGroup_Ocancel__ab__semigroup__add' [148, 1] (w:1, o:129
% 3.70/4.07 , a:1, s:1, b:0),
% 3.70/4.07 'class_OrderedGroup_Ocancel__semigroup__add' [149, 1] (w:1, o:130, a:
% 3.70/4.07 1, s:1, b:0),
% 3.70/4.07 'class_Ring__and__Field_Ocomm__ring__1' [150, 1] (w:1, o:95, a:1, s:1
% 3.70/4.07 , b:0),
% 3.70/4.07 'class_OrderedGroup_Omonoid__mult' [151, 1] (w:1, o:131, a:1, s:1, b:
% 3.70/4.07 0),
% 3.70/4.07 'c_Int_Oiszero' [152, 2] (w:1, o:195, a:1, s:1, b:0),
% 3.70/4.07 'c_Int_OBit1' [153, 1] (w:1, o:155, a:1, s:1, b:0),
% 3.70/4.07 'c_Int_OBit0' [157, 1] (w:1, o:154, a:1, s:1, b:0),
% 3.70/4.07 'class_OrderedGroup_Omonoid__add' [160, 1] (w:1, o:132, a:1, s:1, b:0
% 3.70/4.07 ),
% 3.70/4.07 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [162, 1]
% 3.70/4.07 (w:1, o:133, a:1, s:1, b:0),
% 3.70/4.07 'class_Orderings_Opreorder' [163, 1] (w:1, o:134, a:1, s:1, b:0),
% 3.70/4.07 'class_Ring__and__Field_Oordered__semiring__strict' [164, 1] (w:1, o:
% 3.70/4.07 142, a:1, s:1, b:0),
% 3.70/4.07 'class_Ring__and__Field_Osemiring__1' [165, 1] (w:1, o:156, a:1, s:1
% 14.67/15.01 , b:0),
% 14.67/15.01 'class_Ring__and__Field_Oordered__semiring' [168, 1] (w:1, o:143, a:1
% 14.67/15.01 , s:1, b:0),
% 14.67/15.01 'class_Ring__and__Field_Oring' [169, 1] (w:1, o:114, a:1, s:1, b:0),
% 14.67/15.01
% 14.67/15.01 'class_Ring__and__Field_Oring__no__zero__divisors' [170, 1] (w:1, o:
% 14.67/15.01 115, a:1, s:1, b:0),
% 14.67/15.01 'class_RealVector_Oreal__normed__algebra' [171, 1] (w:1, o:157, a:1
% 14.67/15.01 , s:1, b:0),
% 14.67/15.01 'class_Ring__and__Field_Ocomm__semiring' [172, 1] (w:1, o:97, a:1, s:
% 14.67/15.01 1, b:0),
% 14.67/15.01 'class_OrderedGroup_Ocomm__monoid__mult' [174, 1] (w:1, o:135, a:1
% 14.67/15.01 , s:1, b:0),
% 14.67/15.01 'class_Ring__and__Field_Osemiring' [175, 1] (w:1, o:158, a:1, s:1, b:
% 14.67/15.01 0),
% 14.67/15.01 'class_RealVector_Oreal__field' [177, 1] (w:1, o:159, a:1, s:1, b:0)
% 14.67/15.01 ,
% 14.67/15.01 'class_Ring__and__Field_Oring__1' [180, 1] (w:1, o:116, a:1, s:1, b:0
% 14.67/15.01 ),
% 14.67/15.01 'c_FFT__Mirabelle_OFFT' [184, 2] (w:1, o:196, a:1, s:1, b:0),
% 14.67/15.01 'class_Ring__and__Field_Oordered__comm__semiring__strict' [185, 1]
% 14.67/15.01 (w:1, o:144, a:1, s:1, b:0),
% 14.67/15.01 'class_Int_Oring__char__0' [186, 1] (w:1, o:160, a:1, s:1, b:0),
% 14.67/15.01 'c_Fun_Oinj__on' [187, 4] (w:1, o:208, a:1, s:1, b:0),
% 14.67/15.01 'class_Ring__and__Field_Oring__1__no__zero__divisors' [188, 1] (w:1
% 14.67/15.01 , o:117, a:1, s:1, b:0),
% 14.67/15.01 'c_Ring__and__Field_Ocomm__ring__1' [189, 7] (w:1, o:212, a:1, s:1
% 14.67/15.01 , b:0),
% 14.67/15.01 'c_Parity_Osko__Parity__Xodd__Suc__mult__two__ex__1__1' [190, 1] (w:1
% 14.67/15.01 , o:161, a:1, s:1, b:0),
% 14.67/15.01 'tc_Complex_Ocomplex' [191, 0] (w:1, o:69, a:1, s:1, b:0),
% 14.67/15.01 'c_FFT__Mirabelle_Oroot' [192, 1] (w:1, o:162, a:1, s:1, b:0),
% 14.67/15.01 'c_Complex_Oii' [194, 0] (w:1, o:71, a:1, s:1, b:0),
% 14.67/15.01 'c_COMBB' [195, 5] (w:1, o:209, a:1, s:1, b:0),
% 14.67/15.01 'v_ka____' [196, 0] (w:1, o:72, a:1, s:1, b:0),
% 14.67/15.01 'c_FFT__Mirabelle_ODFT' [197, 3] (w:1, o:206, a:1, s:1, b:0),
% 14.67/15.01 'v_i____' [199, 0] (w:1, o:73, a:1, s:1, b:0),
% 14.67/15.01 'class_OrderedGroup_Oab__semigroup__mult' [200, 1] (w:1, o:136, a:1
% 14.67/15.01 , s:1, b:0),
% 14.67/15.01 'class_OrderedGroup_Oab__semigroup__idem__mult' [201, 1] (w:1, o:137
% 14.67/15.01 , a:1, s:1, b:0),
% 14.67/15.01 'v_a____' [206, 0] (w:1, o:78, a:1, s:1, b:0),
% 14.67/15.01 'tc_fun' [209, 2] (w:1, o:197, a:1, s:1, b:0),
% 14.67/15.01 'c_COMBC' [210, 6] (w:1, o:211, a:1, s:1, b:0),
% 14.67/15.01 'c_fequal' [211, 3] (w:1, o:207, a:1, s:1, b:0).
% 14.67/15.01
% 14.67/15.01
% 14.67/15.01 Starting Search:
% 14.67/15.01
% 14.67/15.01 Resimplifying inuse:
% 14.67/15.01 Done
% 14.67/15.01
% 14.67/15.01
% 14.67/15.01 Intermediate Status:
% 14.67/15.01 Generated: 4182
% 14.67/15.01 Kept: 2001
% 14.67/15.01 Inuse: 46
% 14.67/15.01 Deleted: 1
% 14.67/15.01 Deletedinuse: 0
% 14.67/15.01
% 14.67/15.01 Resimplifying inuse:
% 14.67/15.01 Done
% 14.67/15.01
% 14.67/15.01 Resimplifying inuse:
% 14.67/15.01 Done
% 14.67/15.01
% 14.67/15.01
% 14.67/15.01 Intermediate Status:
% 14.67/15.01 Generated: 10058
% 14.67/15.01 Kept: 4001
% 14.67/15.01 Inuse: 238
% 14.67/15.01 Deleted: 13
% 14.67/15.01 Deletedinuse: 0
% 14.67/15.01
% 14.67/15.01 Resimplifying inuse:
% 14.67/15.01 Done
% 14.67/15.01
% 14.67/15.01
% 14.67/15.01 Intermediate Status:
% 14.67/15.01 Generated: 18591
% 14.67/15.01 Kept: 6141
% 14.67/15.01 Inuse: 313
% 14.67/15.01 Deleted: 13
% 14.67/15.01 Deletedinuse: 0
% 14.67/15.01
% 14.67/15.01 Resimplifying inuse:
% 14.67/15.01 Done
% 14.67/15.01
% 14.67/15.01 Resimplifying inuse:
% 14.67/15.01 Done
% 14.67/15.01
% 14.67/15.01
% 14.67/15.01 Intermediate Status:
% 14.67/15.01 Generated: 26302
% 14.67/15.01 Kept: 8306
% 14.67/15.01 Inuse: 333
% 14.67/15.01 Deleted: 13
% 14.67/15.01 Deletedinuse: 0
% 14.67/15.01
% 14.67/15.01 Resimplifying inuse:
% 14.67/15.01 Done
% 14.67/15.01
% 14.67/15.01 Resimplifying inuse:
% 14.67/15.01 Done
% 14.67/15.01
% 14.67/15.01
% 14.67/15.01 Intermediate Status:
% 14.67/15.01 Generated: 31568
% 14.67/15.01 Kept: 10465
% 14.67/15.01 Inuse: 370
% 14.67/15.01 Deleted: 16
% 14.67/15.01 Deletedinuse: 0
% 14.67/15.01
% 14.67/15.01 Resimplifying inuse:
% 14.67/15.01 Done
% 14.67/15.01
% 14.67/15.01 Resimplifying inuse:
% 14.67/15.01 Done
% 14.67/15.01
% 14.67/15.01
% 14.67/15.01 Intermediate Status:
% 14.67/15.01 Generated: 37047
% 14.67/15.01 Kept: 12710
% 14.67/15.01 Inuse: 393
% 14.67/15.01 Deleted: 18
% 14.67/15.01 Deletedinuse: 0
% 14.67/15.01
% 14.67/15.01 Resimplifying inuse:
% 14.67/15.01 Done
% 14.67/15.01
% 14.67/15.01 Resimplifying inuse:
% 14.67/15.01 Done
% 14.67/15.01
% 14.67/15.01
% 14.67/15.01 Intermediate Status:
% 14.67/15.01 Generated: 43203
% 14.67/15.01 Kept: 14716
% 14.67/15.01 Inuse: 439
% 14.67/15.01 Deleted: 18
% 14.67/15.01 Deletedinuse: 0
% 14.67/15.01
% 14.67/15.01 Resimplifying inuse:
% 14.67/15.01 Done
% 14.67/15.01
% 14.67/15.01
% 14.67/15.01 Intermediate Status:
% 14.67/15.01 Generated: 64666
% 14.67/15.01 Kept: 17369
% 14.67/15.01 Inuse: 453
% 14.67/15.01 Deleted: 18
% 14.67/15.01 Deletedinuse: 0
% 14.67/15.01
% 14.67/15.01 Resimplifying inuse:
% 14.67/15.01 Done
% 14.67/15.01
% 14.67/15.01 Resimplifying inuse:
% 14.67/15.01 Done
% 14.67/15.01
% 14.67/15.01
% 14.67/15.01 Intermediate Status:
% 14.67/15.01 Generated: 72632
% 14.67/15.01 Kept: 19805
% 14.67/15.01 Inuse: 473
% 14.67/15.01 Deleted: 18
% 14.67/15.01 Deletedinuse: 0
% 14.67/15.01
% 14.67/15.01 Resimplifying clauses:
% 14.67/15.01 Done
% 14.67/15.01
% 14.67/15.01 Resimplifying inuse:
% 14.67/15.01 Done
% 14.67/15.01
% 14.67/15.01 Resimplifying inuse:
% 14.67/15.01 Done
% 14.67/15.01
% 14.67/15.01
% 14.67/15.01 Intermediate Status:
% 14.67/15.01 Generated: 80383
% 14.67/15.01 Kept: 22036
% 14.67/15.01 Inuse: 531
% 14.67/15.01 Deleted: 277
% 14.67/15.01 Deletedinuse: 0
% 14.67/15.01
% 14.67/15.01 Resimplifying inuse:
% 14.67/15.01 Done
% 14.67/15.01
% 14.67/15.01
% 14.67/15.01 Intermediate Status:
% 14.67/15.01 Generated: 107774
% 14.67/15.01 Kept: 24255
% 14.67/15.01 Inuse: 546
% 14.67/15.01 Deleted: 277
% 14.67/15.01 Deletedinuse: 0
% 14.67/15.01
% 14.67/15.01 Resimplifying inuse:
% 14.67/15.01 Done
% 14.67/15.01
% 14.67/15.01 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 115674
% 42.36/42.73 Kept: 26424
% 42.36/42.73 Inuse: 601
% 42.36/42.73 Deleted: 277
% 42.36/42.73 Deletedinuse: 0
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 129397
% 42.36/42.73 Kept: 29153
% 42.36/42.73 Inuse: 621
% 42.36/42.73 Deleted: 277
% 42.36/42.73 Deletedinuse: 0
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 140442
% 42.36/42.73 Kept: 31914
% 42.36/42.73 Inuse: 651
% 42.36/42.73 Deleted: 277
% 42.36/42.73 Deletedinuse: 0
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 150405
% 42.36/42.73 Kept: 34643
% 42.36/42.73 Inuse: 700
% 42.36/42.73 Deleted: 279
% 42.36/42.73 Deletedinuse: 1
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 160786
% 42.36/42.73 Kept: 37433
% 42.36/42.73 Inuse: 715
% 42.36/42.73 Deleted: 282
% 42.36/42.73 Deletedinuse: 4
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 172611
% 42.36/42.73 Kept: 39624
% 42.36/42.73 Inuse: 725
% 42.36/42.73 Deleted: 282
% 42.36/42.73 Deletedinuse: 4
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying clauses:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 180562
% 42.36/42.73 Kept: 41656
% 42.36/42.73 Inuse: 741
% 42.36/42.73 Deleted: 1102
% 42.36/42.73 Deletedinuse: 4
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 189215
% 42.36/42.73 Kept: 43724
% 42.36/42.73 Inuse: 750
% 42.36/42.73 Deleted: 1102
% 42.36/42.73 Deletedinuse: 4
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 203860
% 42.36/42.73 Kept: 45998
% 42.36/42.73 Inuse: 765
% 42.36/42.73 Deleted: 1102
% 42.36/42.73 Deletedinuse: 4
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 214333
% 42.36/42.73 Kept: 48001
% 42.36/42.73 Inuse: 782
% 42.36/42.73 Deleted: 1102
% 42.36/42.73 Deletedinuse: 4
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 220487
% 42.36/42.73 Kept: 50012
% 42.36/42.73 Inuse: 794
% 42.36/42.73 Deleted: 1102
% 42.36/42.73 Deletedinuse: 4
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 228918
% 42.36/42.73 Kept: 52044
% 42.36/42.73 Inuse: 823
% 42.36/42.73 Deleted: 1102
% 42.36/42.73 Deletedinuse: 4
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 239494
% 42.36/42.73 Kept: 54268
% 42.36/42.73 Inuse: 840
% 42.36/42.73 Deleted: 1102
% 42.36/42.73 Deletedinuse: 4
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 246129
% 42.36/42.73 Kept: 56278
% 42.36/42.73 Inuse: 860
% 42.36/42.73 Deleted: 1102
% 42.36/42.73 Deletedinuse: 4
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 256118
% 42.36/42.73 Kept: 59102
% 42.36/42.73 Inuse: 875
% 42.36/42.73 Deleted: 1102
% 42.36/42.73 Deletedinuse: 4
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying clauses:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 263586
% 42.36/42.73 Kept: 61103
% 42.36/42.73 Inuse: 902
% 42.36/42.73 Deleted: 1236
% 42.36/42.73 Deletedinuse: 4
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 279837
% 42.36/42.73 Kept: 64322
% 42.36/42.73 Inuse: 920
% 42.36/42.73 Deleted: 1236
% 42.36/42.73 Deletedinuse: 4
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 292608
% 42.36/42.73 Kept: 67588
% 42.36/42.73 Inuse: 930
% 42.36/42.73 Deleted: 1236
% 42.36/42.73 Deletedinuse: 4
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 299680
% 42.36/42.73 Kept: 69712
% 42.36/42.73 Inuse: 941
% 42.36/42.73 Deleted: 1256
% 42.36/42.73 Deletedinuse: 5
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 308463
% 42.36/42.73 Kept: 72613
% 42.36/42.73 Inuse: 954
% 42.36/42.73 Deleted: 1263
% 42.36/42.73 Deletedinuse: 5
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 314047
% 42.36/42.73 Kept: 74743
% 42.36/42.73 Inuse: 959
% 42.36/42.73 Deleted: 1263
% 42.36/42.73 Deletedinuse: 5
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 322073
% 42.36/42.73 Kept: 76990
% 42.36/42.73 Inuse: 984
% 42.36/42.73 Deleted: 1263
% 42.36/42.73 Deletedinuse: 5
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 334172
% 42.36/42.73 Kept: 79270
% 42.36/42.73 Inuse: 1013
% 42.36/42.73 Deleted: 1264
% 42.36/42.73 Deletedinuse: 5
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying clauses:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73
% 42.36/42.73 Intermediate Status:
% 42.36/42.73 Generated: 344058
% 42.36/42.73 Kept: 81285
% 42.36/42.73 Inuse: 1045
% 42.36/42.73 Deleted: 1928
% 42.36/42.73 Deletedinuse: 5
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 42.36/42.73 Resimplifying inuse:
% 42.36/42.73 Done
% 42.36/42.73
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 355825
% 89.73/90.11 Kept: 83629
% 89.73/90.11 Inuse: 1068
% 89.73/90.11 Deleted: 1928
% 89.73/90.11 Deletedinuse: 5
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 367265
% 89.73/90.11 Kept: 85639
% 89.73/90.11 Inuse: 1088
% 89.73/90.11 Deleted: 1928
% 89.73/90.11 Deletedinuse: 5
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 379028
% 89.73/90.11 Kept: 87784
% 89.73/90.11 Inuse: 1123
% 89.73/90.11 Deleted: 1928
% 89.73/90.11 Deletedinuse: 5
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 394123
% 89.73/90.11 Kept: 89950
% 89.73/90.11 Inuse: 1163
% 89.73/90.11 Deleted: 1928
% 89.73/90.11 Deletedinuse: 5
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 408972
% 89.73/90.11 Kept: 92056
% 89.73/90.11 Inuse: 1198
% 89.73/90.11 Deleted: 1928
% 89.73/90.11 Deletedinuse: 5
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 439857
% 89.73/90.11 Kept: 95446
% 89.73/90.11 Inuse: 1208
% 89.73/90.11 Deleted: 1928
% 89.73/90.11 Deletedinuse: 5
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 460078
% 89.73/90.11 Kept: 98654
% 89.73/90.11 Inuse: 1233
% 89.73/90.11 Deleted: 1928
% 89.73/90.11 Deletedinuse: 5
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 499222
% 89.73/90.11 Kept: 101945
% 89.73/90.11 Inuse: 1248
% 89.73/90.11 Deleted: 1928
% 89.73/90.11 Deletedinuse: 5
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying clauses:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 516948
% 89.73/90.11 Kept: 104111
% 89.73/90.11 Inuse: 1283
% 89.73/90.11 Deleted: 2076
% 89.73/90.11 Deletedinuse: 5
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 523785
% 89.73/90.11 Kept: 106143
% 89.73/90.11 Inuse: 1293
% 89.73/90.11 Deleted: 2077
% 89.73/90.11 Deletedinuse: 6
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 531222
% 89.73/90.11 Kept: 108406
% 89.73/90.11 Inuse: 1303
% 89.73/90.11 Deleted: 2077
% 89.73/90.11 Deletedinuse: 6
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 541404
% 89.73/90.11 Kept: 111252
% 89.73/90.11 Inuse: 1315
% 89.73/90.11 Deleted: 2077
% 89.73/90.11 Deletedinuse: 6
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 549739
% 89.73/90.11 Kept: 113377
% 89.73/90.11 Inuse: 1333
% 89.73/90.11 Deleted: 2077
% 89.73/90.11 Deletedinuse: 6
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 559228
% 89.73/90.11 Kept: 115661
% 89.73/90.11 Inuse: 1348
% 89.73/90.11 Deleted: 2077
% 89.73/90.11 Deletedinuse: 6
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 569110
% 89.73/90.11 Kept: 118121
% 89.73/90.11 Inuse: 1363
% 89.73/90.11 Deleted: 2077
% 89.73/90.11 Deletedinuse: 6
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 578466
% 89.73/90.11 Kept: 120335
% 89.73/90.11 Inuse: 1378
% 89.73/90.11 Deleted: 2077
% 89.73/90.11 Deletedinuse: 6
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying clauses:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 587652
% 89.73/90.11 Kept: 122943
% 89.73/90.11 Inuse: 1393
% 89.73/90.11 Deleted: 2532
% 89.73/90.11 Deletedinuse: 6
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 597863
% 89.73/90.11 Kept: 125244
% 89.73/90.11 Inuse: 1413
% 89.73/90.11 Deleted: 2532
% 89.73/90.11 Deletedinuse: 6
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 619592
% 89.73/90.11 Kept: 128272
% 89.73/90.11 Inuse: 1431
% 89.73/90.11 Deleted: 2537
% 89.73/90.11 Deletedinuse: 9
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 645161
% 89.73/90.11 Kept: 131328
% 89.73/90.11 Inuse: 1436
% 89.73/90.11 Deleted: 2542
% 89.73/90.11 Deletedinuse: 9
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 671943
% 89.73/90.11 Kept: 134605
% 89.73/90.11 Inuse: 1444
% 89.73/90.11 Deleted: 2544
% 89.73/90.11 Deletedinuse: 9
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 688027
% 89.73/90.11 Kept: 136665
% 89.73/90.11 Inuse: 1454
% 89.73/90.11 Deleted: 2544
% 89.73/90.11 Deletedinuse: 9
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 697370
% 89.73/90.11 Kept: 138685
% 89.73/90.11 Inuse: 1472
% 89.73/90.11 Deleted: 2545
% 89.73/90.11 Deletedinuse: 10
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 731760
% 89.73/90.11 Kept: 142685
% 89.73/90.11 Inuse: 1479
% 89.73/90.11 Deleted: 2545
% 89.73/90.11 Deletedinuse: 10
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying clauses:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 747954
% 89.73/90.11 Kept: 146023
% 89.73/90.11 Inuse: 1499
% 171.61/172.01 Deleted: 3449
% 171.61/172.01 Deletedinuse: 10
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 763265
% 171.61/172.01 Kept: 149341
% 171.61/172.01 Inuse: 1504
% 171.61/172.01 Deleted: 3449
% 171.61/172.01 Deletedinuse: 10
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 772723
% 171.61/172.01 Kept: 151526
% 171.61/172.01 Inuse: 1519
% 171.61/172.01 Deleted: 3449
% 171.61/172.01 Deletedinuse: 10
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 785975
% 171.61/172.01 Kept: 153632
% 171.61/172.01 Inuse: 1539
% 171.61/172.01 Deleted: 3449
% 171.61/172.01 Deletedinuse: 10
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 805534
% 171.61/172.01 Kept: 157320
% 171.61/172.01 Inuse: 1564
% 171.61/172.01 Deleted: 3449
% 171.61/172.01 Deletedinuse: 10
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 819529
% 171.61/172.01 Kept: 159690
% 171.61/172.01 Inuse: 1589
% 171.61/172.01 Deleted: 3449
% 171.61/172.01 Deletedinuse: 10
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 836442
% 171.61/172.01 Kept: 163079
% 171.61/172.01 Inuse: 1604
% 171.61/172.01 Deleted: 3449
% 171.61/172.01 Deletedinuse: 10
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying clauses:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 847097
% 171.61/172.01 Kept: 165154
% 171.61/172.01 Inuse: 1609
% 171.61/172.01 Deleted: 3773
% 171.61/172.01 Deletedinuse: 10
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 860075
% 171.61/172.01 Kept: 167235
% 171.61/172.01 Inuse: 1639
% 171.61/172.01 Deleted: 3774
% 171.61/172.01 Deletedinuse: 11
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 879460
% 171.61/172.01 Kept: 171190
% 171.61/172.01 Inuse: 1661
% 171.61/172.01 Deleted: 3777
% 171.61/172.01 Deletedinuse: 11
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 891631
% 171.61/172.01 Kept: 173682
% 171.61/172.01 Inuse: 1666
% 171.61/172.01 Deleted: 3777
% 171.61/172.01 Deletedinuse: 11
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 904896
% 171.61/172.01 Kept: 176012
% 171.61/172.01 Inuse: 1671
% 171.61/172.01 Deleted: 3777
% 171.61/172.01 Deletedinuse: 11
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 919462
% 171.61/172.01 Kept: 178140
% 171.61/172.01 Inuse: 1701
% 171.61/172.01 Deleted: 3778
% 171.61/172.01 Deletedinuse: 12
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 932663
% 171.61/172.01 Kept: 180288
% 171.61/172.01 Inuse: 1726
% 171.61/172.01 Deleted: 3778
% 171.61/172.01 Deletedinuse: 12
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 945760
% 171.61/172.01 Kept: 182987
% 171.61/172.01 Inuse: 1741
% 171.61/172.01 Deleted: 3778
% 171.61/172.01 Deletedinuse: 12
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying clauses:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 959778
% 171.61/172.01 Kept: 185219
% 171.61/172.01 Inuse: 1771
% 171.61/172.01 Deleted: 4087
% 171.61/172.01 Deletedinuse: 12
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 981589
% 171.61/172.01 Kept: 189057
% 171.61/172.01 Inuse: 1791
% 171.61/172.01 Deleted: 4087
% 171.61/172.01 Deletedinuse: 12
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 992496
% 171.61/172.01 Kept: 191890
% 171.61/172.01 Inuse: 1806
% 171.61/172.01 Deleted: 4087
% 171.61/172.01 Deletedinuse: 12
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 1001268
% 171.61/172.01 Kept: 194616
% 171.61/172.01 Inuse: 1816
% 171.61/172.01 Deleted: 4087
% 171.61/172.01 Deletedinuse: 12
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 1010228
% 171.61/172.01 Kept: 197256
% 171.61/172.01 Inuse: 1826
% 171.61/172.01 Deleted: 4087
% 171.61/172.01 Deletedinuse: 12
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 1019177
% 171.61/172.01 Kept: 199954
% 171.61/172.01 Inuse: 1836
% 171.61/172.01 Deleted: 4087
% 171.61/172.01 Deletedinuse: 12
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 1028196
% 171.61/172.01 Kept: 202671
% 171.61/172.01 Inuse: 1846
% 171.61/172.01 Deleted: 4087
% 171.61/172.01 Deletedinuse: 12
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying clauses:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 1037617
% 171.61/172.01 Kept: 205560
% 171.61/172.01 Inuse: 1856
% 171.61/172.01 Deleted: 4183
% 171.61/172.01 Deletedinuse: 12
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 1046844
% 171.61/172.01 Kept: 208264
% 171.61/172.01 Inuse: 1866
% 171.61/172.01 Deleted: 4183
% 171.61/172.01 Deletedinuse: 12
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01 Resimplifying inuse:
% 171.61/172.01 Done
% 171.61/172.01
% 171.61/172.01
% 171.61/172.01 Intermediate Status:
% 171.61/172.01 Generated: 1055901
% 171.61/172.01 Kept: 211020
% 171.61/172.01 Inuse: 1876
% 296.33/296.79 Deleted: 4183
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1063918
% 296.33/296.79 Kept: 213428
% 296.33/296.79 Inuse: 1891
% 296.33/296.79 Deleted: 4183
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1075098
% 296.33/296.79 Kept: 215581
% 296.33/296.79 Inuse: 1909
% 296.33/296.79 Deleted: 4183
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1083441
% 296.33/296.79 Kept: 217600
% 296.33/296.79 Inuse: 1921
% 296.33/296.79 Deleted: 4183
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1097770
% 296.33/296.79 Kept: 220157
% 296.33/296.79 Inuse: 1931
% 296.33/296.79 Deleted: 4183
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1110097
% 296.33/296.79 Kept: 222388
% 296.33/296.79 Inuse: 1936
% 296.33/296.79 Deleted: 4183
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1121473
% 296.33/296.79 Kept: 224573
% 296.33/296.79 Inuse: 1941
% 296.33/296.79 Deleted: 4183
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79 Resimplifying clauses:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1136562
% 296.33/296.79 Kept: 227509
% 296.33/296.79 Inuse: 1946
% 296.33/296.79 Deleted: 4286
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1147607
% 296.33/296.79 Kept: 229595
% 296.33/296.79 Inuse: 1966
% 296.33/296.79 Deleted: 4286
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1158690
% 296.33/296.79 Kept: 232171
% 296.33/296.79 Inuse: 1981
% 296.33/296.79 Deleted: 4286
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1167836
% 296.33/296.79 Kept: 234243
% 296.33/296.79 Inuse: 1991
% 296.33/296.79 Deleted: 4286
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1180096
% 296.33/296.79 Kept: 236634
% 296.33/296.79 Inuse: 2011
% 296.33/296.79 Deleted: 4286
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1202281
% 296.33/296.79 Kept: 240894
% 296.33/296.79 Inuse: 2036
% 296.33/296.79 Deleted: 4286
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1212011
% 296.33/296.79 Kept: 243257
% 296.33/296.79 Inuse: 2051
% 296.33/296.79 Deleted: 4286
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1219474
% 296.33/296.79 Kept: 245574
% 296.33/296.79 Inuse: 2056
% 296.33/296.79 Deleted: 4286
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79 Resimplifying clauses:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1233785
% 296.33/296.79 Kept: 248791
% 296.33/296.79 Inuse: 2061
% 296.33/296.79 Deleted: 4480
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1245274
% 296.33/296.79 Kept: 250959
% 296.33/296.79 Inuse: 2081
% 296.33/296.79 Deleted: 4480
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1255788
% 296.33/296.79 Kept: 253107
% 296.33/296.79 Inuse: 2101
% 296.33/296.79 Deleted: 4480
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1268128
% 296.33/296.79 Kept: 255323
% 296.33/296.79 Inuse: 2126
% 296.33/296.79 Deleted: 4480
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1288194
% 296.33/296.79 Kept: 259560
% 296.33/296.79 Inuse: 2146
% 296.33/296.79 Deleted: 4480
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1304434
% 296.33/296.79 Kept: 262402
% 296.33/296.79 Inuse: 2171
% 296.33/296.79 Deleted: 4480
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1321349
% 296.33/296.79 Kept: 264807
% 296.33/296.79 Inuse: 2196
% 296.33/296.79 Deleted: 4480
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79 Resimplifying clauses:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1333800
% 296.33/296.79 Kept: 266828
% 296.33/296.79 Inuse: 2215
% 296.33/296.79 Deleted: 4849
% 296.33/296.79 Deletedinuse: 12
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1343585
% 296.33/296.79 Kept: 269245
% 296.33/296.79 Inuse: 2231
% 296.33/296.79 Deleted: 4850
% 296.33/296.79 Deletedinuse: 13
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 Done
% 296.33/296.79
% 296.33/296.79
% 296.33/296.79 Intermediate Status:
% 296.33/296.79 Generated: 1359745
% 296.33/296.79 Kept: 272459
% 296.33/296.79 Inuse: 2256
% 296.33/296.79 Deleted: 4850
% 296.33/296.79 Deletedinuse: 13
% 296.33/296.79
% 296.33/296.79 Resimplifying inuse:
% 296.33/296.79 DoneCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------