TSTP Solution File: SWV576-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV576-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:26:50 EDT 2022
% Result : Timeout 300.03s 300.44s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV576-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Wed Jun 15 10:47:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.17/1.60 *** allocated 10000 integers for termspace/termends
% 1.17/1.60 *** allocated 10000 integers for clauses
% 1.17/1.60 *** allocated 10000 integers for justifications
% 1.17/1.60 *** allocated 15000 integers for termspace/termends
% 1.17/1.60 *** allocated 22500 integers for termspace/termends
% 1.17/1.60 *** allocated 33750 integers for termspace/termends
% 1.17/1.60 *** allocated 50625 integers for termspace/termends
% 1.17/1.60 Bliksem 1.12
% 1.17/1.60
% 1.17/1.60
% 1.17/1.60 Automatic Strategy Selection
% 1.17/1.60
% 1.17/1.60 Clauses:
% 1.17/1.60 [
% 1.17/1.60 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.17/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.17/1.60 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.17/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.17/1.60 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.17/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.17/1.60 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 1.17/1.60 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.60 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 1.17/1.60 ) ) ],
% 1.17/1.60 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.22/1.60 ), Y ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.22/1.60 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.22/1.60 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.22/1.60 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.22/1.60 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.22/1.60 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.22/1.60 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.22/1.60 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.22/1.60 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.22/1.60 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.22/1.60 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.22/1.60 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.60 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.22/1.60 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.60 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.22/1.60 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.22/1.60 ) ), T ) ), U ), W, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), Y ), T ) ), U ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.22/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ), W, X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.22/1.60 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X
% 1.22/1.60 ) ), U ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), T ), U ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.22/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( T, hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ), X ) ) ],
% 1.22/1.60 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.22/1.60 , X, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.22/1.60 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.22/1.60 , X ) ), T ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.22/1.60 ), X ) ],
% 1.22/1.60 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y,
% 1.22/1.60 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.60 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.22/1.60 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.60 , 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.60 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.22/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.22/1.60 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.60 , 'tc_nat' ), 'tc_nat' ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.60 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.22/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.22/1.60 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.22/1.60 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.22/1.60 ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.22/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.22/1.60 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.22/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.22/1.60 Z, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.22/1.60 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.22/1.60 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.22/1.60 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.22/1.60 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.22/1.60 ~( hBOOL( hAPP( X, T ) ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), 'c_Suc'( T ) ), 'tc_nat' )
% 1.22/1.60 ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.22/1.60 ), Z ), T ), Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.22/1.60 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y
% 1.22/1.60 , X, 'tc_nat' ) ), Z ) ), T ) ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( 'c_Finite__Set_Osetsum'( Y,
% 1.22/1.60 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.22/1.60 , X ), 'c_Finite__Set_Osetsum'( Y,
% 1.22/1.60 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ), 'tc_nat'
% 1.22/1.60 , X ), X ), 'c_Finite__Set_Osetsum'( Y,
% 1.22/1.60 'c_SetInterval_Oord__class_OatLeastLessThan'( U, T, 'tc_nat' ), 'tc_nat'
% 1.22/1.60 , X ) ), ~( 'c_lessequals'( U, T, 'tc_nat' ) ), ~( 'c_lessequals'( Z, U,
% 1.22/1.60 'tc_nat' ) ) ],
% 1.22/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.22/1.60 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.22/1.60 'tc_nat' ), Y, 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 1.22/1.60 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.22/1.60 , Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.60 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint' ), X ) ],
% 1.22/1.60 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.22/1.60 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.22/1.60 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.22/1.60 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.22/1.60 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.22/1.60 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.22/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.22/1.60 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~(
% 1.22/1.60 'c_lessequals'( T, X, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X
% 1.22/1.60 , T, 'tc_nat' ) ), Y ) ), Z ), U ) ],
% 1.22/1.60 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~(
% 1.22/1.60 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z, hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( T
% 1.22/1.60 , X, 'tc_nat' ) ), Y ) ), U ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.22/1.60 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.22/1.60 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.22/1.60 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.22/1.60 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.22/1.60 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.22/1.60 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.22/1.60 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X )
% 1.22/1.60 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP(
% 1.22/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.22/1.60 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 'c_Suc'(
% 1.22/1.60 Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.22/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.60 X ), X ) ) ],
% 1.22/1.60 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.22/1.60 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.22/1.60 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), X ), ~(
% 1.22/1.60 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.22/1.60 ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.22/1.60 ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ) ), Y ) ), U ), 'tc_nat' )
% 1.22/1.60 ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), T ) ), U ), 'tc_nat' )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T
% 1.22/1.60 ) ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ), 'tc_nat' ) ),
% 1.22/1.60 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.22/1.60 ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.22/1.60 ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ) ), Y ) ), Z ), U, 'tc_nat'
% 1.22/1.60 ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ) ), T ), U, 'tc_nat'
% 1.22/1.60 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z
% 1.22/1.60 ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ), 'tc_nat' ) ),
% 1.22/1.60 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.22/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.22/1.60 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( T, Y, X
% 1.22/1.60 ) ), Z ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.22/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.22/1.60 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.60 T, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.22/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.22/1.60 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.22/1.60 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 1.22/1.60 , X ) ) ],
% 1.22/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.60 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.22/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.60 ), Y ), T ), Z, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.22/1.60 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.22/1.60 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.60 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.60 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.60 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( Y
% 1.22/1.60 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.22/1.60 ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.22/1.60 ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.22/1.60 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.22/1.60 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 1.22/1.60 X, Y, 'tc_nat' ) ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.22/1.60 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ),
% 1.22/1.60 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.22/1.60 ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), hAPP(
% 1.22/1.60 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.22/1.60 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), Z ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.22/1.60 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.22/1.60 ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.22/1.60 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.22/1.60 ) ) ],
% 1.22/1.60 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.22/1.60 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.22/1.60 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), X,
% 1.22/1.60 'tc_nat' ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.22/1.60 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.60 ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.60 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.60 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.22/1.60 ), Z ), Y ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.22/1.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.22/1.60 ), X ), Y ) ],
% 1.22/1.60 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.60 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.22/1.60 , 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.60 'tc_nat' ), X, 'tc_nat' ) ],
% 1.22/1.60 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.60 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.22/1.60 , 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.60 'tc_nat' ), Y, 'tc_nat' ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.22/1.60 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.60 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.60 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.60 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.60 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.22/1.60 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.22/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.22/1.60 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.22/1.60 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.22/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.60 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.22/1.60 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.22/1.60 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.22/1.60 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.22/1.60 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.22/1.60 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.22/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.22/1.60 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.22/1.60 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.60 , 'tc_nat' ), 'tc_nat' ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 X ), Y ), Z ) ), T ) ) ],
% 1.22/1.60 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.22/1.60 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 X ), Y ), Z ) ), T ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.22/1.60 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.22/1.60 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.60 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.22/1.60 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.22/1.60 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.22/1.60 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.22/1.60 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.22/1.60 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.22/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.22/1.60 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.22/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.22/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.22/1.60 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.22/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.22/1.60 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.22/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.22/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.22/1.60 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.22/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.22/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.60 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.22/1.60 , X ) ), T, X ) ) ],
% 1.22/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.60 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.22/1.60 ), Z ), T, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.22/1.60 ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.22/1.60 ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.22/1.60 ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.22/1.60 ), X ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.22/1.60 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.60 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.22/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.22/1.60 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.22/1.60 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.22/1.60 ],
% 1.22/1.60 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.22/1.60 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 1.22/1.60 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.22/1.60 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.22/1.60 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.60 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.22/1.60 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.22/1.60 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.22/1.60 ],
% 1.22/1.60 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.22/1.60 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.22/1.60 , T, X ) ) ), =( Z, T ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.22/1.60 , T, X ) ) ), =( Y, Z ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.22/1.60 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.22/1.60 , X ) ), T ) ) ) ],
% 1.22/1.60 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.22/1.60 'tc_nat' ) ), =( Y, Z ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.22/1.60 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.22/1.60 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.22/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.22/1.60 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.22/1.60 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.22/1.60 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), T ), Z ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.60 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.22/1.60 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.60 ), Y ), T ), Z, X ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.22/1.60 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.22/1.60 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.60 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.60 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.60 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.60 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.60 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.22/1.60 ],
% 1.22/1.60 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.22/1.60 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), Y ) ), ~(
% 1.22/1.60 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 1.22/1.60 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.22/1.60 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ), ~( 'c_lessequals'( Z
% 1.22/1.60 , Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.22/1.60 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~( 'c_lessequals'( Y, Z
% 1.22/1.60 , 'tc_Int_Oint' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, Z, 'tc_Int_Oint' ),
% 1.22/1.60 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.22/1.60 [ 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.22/1.60 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.22/1.60 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint' ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ), 'tc_Int_Oint' ) )
% 1.22/1.60 ],
% 1.22/1.60 [ 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint' )
% 1.22/1.60 , 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ), 'tc_Int_Oint' )
% 1.22/1.60 , ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.22/1.60 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), Y ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ), Z ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.22/1.60 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.22/1.60 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.22/1.60 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.22/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.22/1.60 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.22/1.60 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.22/1.60 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.22/1.60 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.22/1.60 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.22/1.60 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_Int_Oint' ) ), ~(
% 1.22/1.60 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.22/1.60 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.22/1.60 , Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.22/1.60 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.22/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.22/1.60 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.22/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.22/1.60 ) ],
% 1.22/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.22/1.60 ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.22/1.60 ), =( Z, Y ) ],
% 1.22/1.60 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 'tc_nat' ), X ), Z ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y
% 1.22/1.60 , 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.22/1.60 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ),
% 1.22/1.60 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.22/1.60 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ),
% 1.22/1.60 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.22/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.22/1.60 'c_lessequals'( Z, T, X ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.22/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.22/1.60 'c_lessequals'( Y, T, X ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.22/1.60 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.22/1.60 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.22/1.60 'c_lessequals'( Z, T, X ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.22/1.60 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.22/1.60 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.22/1.60 'c_lessequals'( Y, T, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.22/1.60 , X ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), Y ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X
% 1.22/1.60 ) ) ],
% 1.22/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.22/1.60 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.22/1.60 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.22/1.60 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z,
% 1.22/1.60 'tc_nat' ) ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.22/1.60 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.22/1.60 ), Z ), Y ), 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ominus__class_Ominus'(
% 1.22/1.60 'c_Suc'( Z ), T, 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_nat' ) ) ), Y ) ), ~(
% 1.22/1.60 'c_lessequals'( T, Z, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.60 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.22/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.22/1.60 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.60 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.22/1.60 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.22/1.60 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.60 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.22/1.60 ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.60 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.22/1.60 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.22/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.22/1.60 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.22/1.60 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.60 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.60 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.22/1.60 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.60 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.22/1.60 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.60 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.22/1.60 ), X ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.60 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.60 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.22/1.60 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.22/1.60 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.22/1.60 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.22/1.60 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.22/1.60 ), X ) ],
% 1.22/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.60 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.60 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.60 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.22/1.60 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.60 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.22/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.60 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.60 X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.60 X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.22/1.60 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.60 X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.22/1.60 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.60 X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.60 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 1.22/1.60 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.22/1.60 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.22/1.60 'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.22/1.60 'tc_nat' ) ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 1.22/1.60 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.60 , X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.22/1.60 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.22/1.60 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.22/1.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.22/1.60 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.60 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.22/1.60 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.22/1.60 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.22/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.22/1.60 ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.22/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.22/1.60 ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.22/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.22/1.60 ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.22/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.22/1.60 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 1.22/1.60 ],
% 1.22/1.60 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.22/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.22/1.60 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.22/1.60 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.22/1.60 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.60 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.22/1.60 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.60 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.22/1.60 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.22/1.60 'tc_nat' ), Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.22/1.60 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'( X
% 1.22/1.60 ) ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.22/1.60 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.22/1.60 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.22/1.60 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.22/1.60 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.60 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.22/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.22/1.60 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.22/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.22/1.60 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.22/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.22/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.60 X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.22/1.60 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.22/1.60 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.22/1.60 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.22/1.60 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.60 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.22/1.60 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.22/1.60 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.22/1.60 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.22/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z )
% 1.22/1.60 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ),
% 1.22/1.60 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.22/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X )
% 1.22/1.60 , Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ),
% 1.22/1.60 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.60 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X
% 1.22/1.60 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), 'c_HOL_Ominus__class_Ominus'( Y, T, X ) ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, T, X
% 1.22/1.60 ) ), U ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ) ) ],
% 1.22/1.60 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.22/1.60 , 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat'
% 1.22/1.60 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.22/1.60 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.22/1.60 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.22/1.60 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.22/1.60 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.22/1.60 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.22/1.60 'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.22/1.60 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.22/1.60 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 1.22/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.22/1.60 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.22/1.60 , Y, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.22/1.60 ) ],
% 1.22/1.60 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.22/1.60 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 1.22/1.60 'tc_nat' ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.22/1.60 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.60 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.22/1.60 ), 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.22/1.60 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.60 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.22/1.60 ), 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.22/1.60 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.22/1.60 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ),
% 1.22/1.60 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.22/1.60 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.22/1.60 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.22/1.60 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.22/1.60 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.22/1.60 T, X ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.22/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.22/1.60 T, X ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.22/1.60 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.22/1.60 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.22/1.60 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.22/1.60 ), X ), Z ), 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.22/1.60 ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.22/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.22/1.60 ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.22/1.60 , T, 'tc_nat' ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ) ), ~( 'c_lessequals'(
% 1.22/1.60 T, Z, 'tc_nat' ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.60 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ),
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'(
% 1.22/1.60 Y, T, X ) ), 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ) ],
% 1.22/1.60 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.22/1.60 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.22/1.60 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.22/1.60 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.22/1.60 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.60 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.60 , X ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.22/1.60 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.22/1.60 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 1.22/1.60 , 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X
% 1.22/1.60 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.22/1.60 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.22/1.60 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.22/1.60 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.22/1.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.22/1.60 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 'tc_nat' ), 'c_Suc'( Z ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 'tc_nat' ), 'c_Suc'( Z ) ), Y ), 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 'tc_nat' ), 'c_Suc'( X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 'tc_nat' ), 'c_Suc'( X ) ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 Y, Z, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.22/1.60 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.60 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.22/1.60 , 'tc_nat' ), 'tc_nat' ), 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.60 X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.22/1.60 X ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.22/1.60 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.22/1.60 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.22/1.60 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X,
% 1.22/1.60 'tc_nat' ) ],
% 1.22/1.60 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), Z, 'tc_nat' ), 'tc_nat'
% 1.22/1.60 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.22/1.60 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.60 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.60 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.22/1.60 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.60 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.22/1.60 T, X ) ), T, X ) ) ],
% 1.22/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.60 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.22/1.60 ) ), Z ), T, X ) ) ],
% 1.22/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.22/1.60 , Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( Z ) ), X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( Z ) ), Y ), 'tc_nat' )
% 1.22/1.60 ) ],
% 1.22/1.60 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.60 'c_Suc'( X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.22/1.60 , 'c_Suc'( X ) ), Z ), 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 1.22/1.60 ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.22/1.60 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.22/1.60 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.22/1.60 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.22/1.60 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.22/1.60 ), 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.22/1.60 ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.22/1.60 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.60 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.22/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.60 , X ), X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.60 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.22/1.60 ), X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.22/1.60 , X ), X ), Z, X ) ) ],
% 1.22/1.60 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.22/1.60 ), X ), X ), 'tc_nat' ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.22/1.60 , X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.22/1.60 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.22/1.60 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 1.22/1.60 ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.22/1.60 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.60 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 1.22/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.22/1.60 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.22/1.60 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.22/1.60 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 1.22/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.22/1.60 ), X ), Z ), 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.22/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.60 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.22/1.60 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.22/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.22/1.60 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.22/1.60 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.22/1.60 , X, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.22/1.60 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.22/1.60 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.22/1.60 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.22/1.60 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.22/1.60 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.22/1.60 , X, 'tc_nat' ) ) ],
% 1.22/1.60 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.60 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.22/1.60 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.22/1.60 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.22/1.60 , Y, 'tc_nat' ) ) ],
% 1.22/1.60 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'c_Int_Onat'(
% 1.22/1.60 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint' ) ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.22/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.22/1.60 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.22/1.60 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.22/1.60 Z, 'c_Suc'( T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.22/1.60 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.22/1.60 , X ) ), hAPP( Y, T ) ) ), 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.22/1.60 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.22/1.60 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.22/1.60 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.22/1.60 'c_SetInterval_Oord__class_OatLeastLessThan'( T, U, 'tc_nat' ), 'tc_nat'
% 1.22/1.60 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.22/1.60 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ), 'tc_nat'
% 1.22/1.60 , X ) ), ~( 'c_lessequals'( T, U, 'tc_nat' ) ), ~( 'c_lessequals'( Z, T,
% 1.22/1.60 'tc_nat' ) ) ],
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.60 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.60 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.22/1.60 ,
% 1.22/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.22/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.22/1.61 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.22/1.61 Z, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.61 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.22/1.61 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.22/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.61 T, X ) ) ],
% 1.22/1.61 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.22/1.61 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.22/1.61 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.22/1.61 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.22/1.61 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.22/1.61 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'( Y
% 1.22/1.61 , T, X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.22/1.61 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.61 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.22/1.61 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatMost'( 'c_Suc'(
% 1.22/1.61 Z ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.22/1.61 ), 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatMost'( Z,
% 1.22/1.61 'tc_nat' ), 'tc_nat', X ) ), hAPP( Y, 'c_Suc'( Z ) ) ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.22/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.22/1.61 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 , X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.22/1.61 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.22/1.61 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.22/1.61 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.22/1.61 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.61 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.61 , Y ), Z ), T, X ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.61 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.61 , Y ), T ), Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.22/1.61 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.22/1.61 Z, T, 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 X ), hAPP( Y, Z ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.22/1.61 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_Suc'( Z ), T, 'tc_nat' )
% 1.22/1.61 , 'tc_nat', X ) ) ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.22/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.22/1.61 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.22/1.61 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.22/1.61 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.22/1.61 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.22/1.61 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.22/1.61 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.22/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.22/1.61 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.22/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.22/1.61 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.22/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.22/1.61 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.22/1.61 ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.22/1.61 , X ) ), Z ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.22/1.61 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.22/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.22/1.61 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.22/1.61 ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.61 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.22/1.61 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.61 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.22/1.61 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.22/1.61 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.22/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.22/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.22/1.61 ) ) ],
% 1.22/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.22/1.61 ) ) ],
% 1.22/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.22/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.22/1.61 ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.22/1.61 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.22/1.61 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.22/1.61 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.22/1.61 , 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.22/1.61 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.22/1.61 , 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.22/1.61 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.22/1.61 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.22/1.61 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.22/1.61 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( Z
% 1.22/1.61 , T, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.22/1.61 X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.22/1.61 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.61 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.22/1.61 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.61 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Y ), Z ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.61 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Z ), Y ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.61 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Y ), Z ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.61 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Z ), Y ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.22/1.61 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.22/1.61 ) ) ],
% 1.22/1.61 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.61 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 'c_Suc'(
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ), 'tc_nat' ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.22/1.61 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( 'c_Finite__Set_Osetsum'(
% 1.22/1.61 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.61 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.22/1.61 X ), Y ), Z ), 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), X )
% 1.22/1.61 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.61 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.22/1.61 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.61 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.22/1.61 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.22/1.61 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.22/1.61 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 'c_lessequals'(
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 'c_lessequals'(
% 1.22/1.61 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.61 , Y ), Z ), Z, X ), Y ) ],
% 1.22/1.61 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.22/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.22/1.61 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.22/1.61 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.22/1.61 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), 'c_Int_Oiszero'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Int_Oiszero'( Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.22/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.22/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.22/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.22/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.22/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.22/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.22/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.22/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.22/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.22/1.61 ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.22/1.61 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.22/1.61 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.22/1.61 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.22/1.61 ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.22/1.61 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.22/1.61 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.22/1.61 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.22/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 ) ), =( Y, Z ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 ) ), =( Y, Z ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.22/1.61 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.22/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.22/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.22/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.22/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.61 Y ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.22/1.61 Y ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.61 Y ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.22/1.61 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.22/1.61 Y ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.22/1.61 Y ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.61 Y ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.22/1.61 Y ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.22/1.61 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.22/1.61 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.22/1.61 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.22/1.61 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.22/1.61 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.22/1.61 , 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.22/1.61 , X ) ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.22/1.61 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.22/1.61 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.22/1.61 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.22/1.61 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.22/1.61 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.61 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.22/1.61 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.22/1.61 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.22/1.61 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.22/1.61 , X ) ), T ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.22/1.61 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.22/1.61 ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.22/1.61 ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.22/1.61 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.22/1.61 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.22/1.61 ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.22/1.61 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.22/1.61 ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.22/1.61 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.22/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.22/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.22/1.61 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.22/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.22/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.22/1.61 Y, X ) ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.22/1.61 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 ) ],
% 1.22/1.61 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T )
% 1.22/1.61 , 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.22/1.61 , Z, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.22/1.61 ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) )
% 1.22/1.61 , 'tc_nat' ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.22/1.61 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.22/1.61 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.61 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.22/1.61 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.61 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.22/1.61 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.22/1.61 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.22/1.61 , X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.22/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.22/1.61 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.22/1.61 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.22/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.61 ), T ), Z ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.22/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.22/1.61 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.61 ), T ), Z ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.22/1.61 , X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.22/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.22/1.61 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.22/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.61 , Y ), T ), Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.22/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.61 , Y ), T ), Z, X ) ) ],
% 1.22/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.22/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.22/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ),
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.22/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ],
% 1.22/1.61 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.61 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.22/1.61 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.22/1.61 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.61 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.22/1.61 ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.22/1.61 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.61 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.22/1.61 ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.22/1.61 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.22/1.61 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 X ), Y ), Z ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ),
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.22/1.61 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.22/1.61 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ),
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.22/1.61 'c_HOL_Oone__class_Oone'( X ) ), X ), Z, X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.22/1.61 'c_HOL_Oone__class_Oone'( X ) ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 Y, Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.22/1.61 ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Z, X ) ), =( Z,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.22/1.61 , T, X ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), T, X ) ), =( T,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.22/1.61 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.22/1.61 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.22/1.61 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.22/1.61 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.22/1.61 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.22/1.61 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.22/1.61 , V0, U, V1 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.22/1.61 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.22/1.61 , V0, U, V1 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.22/1.61 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.22/1.61 X, T, U, Y, W, V0 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.22/1.61 X, T, U, Z, W, V0 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.22/1.61 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.22/1.61 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.22/1.61 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.22/1.61 T, X, U, Y, W, V0 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.22/1.61 T, X, U, Z, W, V0 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.22/1.61 T, X, U, W, Y, V0 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.22/1.61 T, X, U, W, Z, V0 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.22/1.61 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.22/1.61 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.22/1.61 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.22/1.61 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.22/1.61 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.22/1.61 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.22/1.61 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.22/1.61 , V0, V1, V2 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.22/1.61 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.22/1.61 W, V0, V1, V2 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.22/1.61 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.22/1.61 , V0, V1, V2 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.22/1.61 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.22/1.61 W, V0, V1, V2 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.22/1.61 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.22/1.61 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.22/1.61 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.22/1.61 W, V0, V1, V2 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.22/1.61 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.22/1.61 W, V0, V1, V2 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.22/1.61 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.22/1.61 , V0, V1, V2 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.22/1.61 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.22/1.61 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.22/1.61 , V0, V1, V2 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.22/1.61 X, T, U, Y, W, V0 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.22/1.61 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.22/1.61 , V0, V1, V2 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.22/1.61 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.22/1.61 T, X, U, Y, W, V0 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.22/1.61 T, X, U, W, Y, V0 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.22/1.61 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.22/1.61 , V0, V1, V2 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.22/1.61 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.22/1.61 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.22/1.61 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.22/1.61 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.22/1.61 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.22/1.61 , T, X ), X ), T, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.22/1.61 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.22/1.61 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.22/1.61 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.22/1.61 ) ],
% 1.22/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.22/1.61 ) ],
% 1.22/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.22/1.61 ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.22/1.61 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.61 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.22/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.22/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.22/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.22/1.61 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.22/1.61 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.22/1.61 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.61 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.22/1.61 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.61 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.22/1.61 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.22/1.61 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.22/1.61 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.22/1.61 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.22/1.61 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.22/1.61 X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.22/1.61 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 , X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 'tc_nat' ) ), X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.22/1.61 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.22/1.61 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.22/1.61 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.61 'c_Suc'( T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.22/1.61 'c_Suc'( T ) ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), T ), 'c_Suc'( Z ) ) ) ), =( Y, T ),
% 1.22/1.61 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.22/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.22/1.61 ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.22/1.61 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~( 'c_Int_Oiszero'(
% 1.22/1.61 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.22/1.61 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.22/1.61 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.22/1.61 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.22/1.61 ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.22/1.61 Y ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.22/1.61 Y ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.22/1.61 Y ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.22/1.61 Y ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.22/1.61 Y ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.22/1.61 Y ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.22/1.61 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.22/1.61 ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.22/1.61 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.61 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.22/1.61 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.22/1.61 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.61 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.22/1.61 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.22/1.61 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.22/1.61 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.22/1.61 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.22/1.61 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.22/1.61 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.22/1.61 , Y ) ) ],
% 1.22/1.61 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.61 'tc_nat' ) ) ) ],
% 1.22/1.61 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 1.22/1.61 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.22/1.61 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.22/1.61 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.22/1.61 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.22/1.61 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.22/1.61 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.22/1.61 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 'tc_nat' ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 'tc_nat' ), 'tc_nat' ) ],
% 1.22/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.22/1.61 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.22/1.61 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.22/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.22/1.61 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.22/1.61 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.22/1.61 ), 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.22/1.61 ), 'tc_nat' ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.22/1.61 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 'tc_nat' ) ), Y ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 'tc_nat' ) ) ) ],
% 1.22/1.61 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.22/1.61 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.61 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.61 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.22/1.61 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.22/1.61 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.22/1.61 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.61 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.22/1.61 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 1.22/1.61 ],
% 1.22/1.61 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 1.22/1.61 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.22/1.61 ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.22/1.61 , Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.22/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), 'c_Suc'( 'c_Suc'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.22/1.61 ) ), X, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.22/1.61 ) ), X, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 1.22/1.61 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.22/1.61 Y ), 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 1.22/1.61 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.22/1.61 X ), 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.22/1.61 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.22/1.61 ) ), Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.22/1.61 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.22/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), 'c_Suc'( 'c_Suc'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.22/1.61 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.22/1.61 'tc_nat' ) ) ],
% 1.22/1.61 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.22/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), 'tc_nat' ) ],
% 1.22/1.61 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ) ), 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ],
% 1.22/1.61 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ),
% 1.22/1.61 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.22/1.61 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 1.22/1.61 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ), Y,
% 1.22/1.61 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Y,
% 1.22/1.61 'tc_nat' ) ) ],
% 1.22/1.61 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.22/1.61 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.22/1.61 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.22/1.61 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.22/1.61 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.22/1.61 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 1.22/1.61 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.22/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.22/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.22/1.61 ) ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X
% 1.22/1.61 ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ), =( Z,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.22/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), =( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.22/1.61 Z, 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.61 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.61 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.22/1.61 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 1.22/1.61 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.61 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.61 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.22/1.61 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.22/1.61 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.22/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.22/1.61 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T,
% 1.22/1.61 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.22/1.61 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.22/1.61 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T
% 1.22/1.61 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.61 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.22/1.61 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.22/1.61 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.22/1.61 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 1.22/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.22/1.61 , X ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.61 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.22/1.61 [ =( 'c_Suc'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ), X ),
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X
% 1.22/1.61 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), Y ) ) ), =( X,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.22/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.22/1.61 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.22/1.61 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.22/1.61 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 1.22/1.61 'c_Suc'( X ), 'tc_nat' ) ],
% 1.22/1.61 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.22/1.61 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ),
% 1.22/1.61 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.22/1.61 Z, 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.22/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.22/1.61 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.22/1.61 , X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.22/1.61 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 1.22/1.61 hBOOL( hAPP( X, Z ) ) ],
% 1.22/1.61 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 1.22/1.61 hBOOL( hAPP( X, Z ) ) ],
% 1.22/1.61 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ) ), Y ) ), Z ), U, 'tc_nat'
% 1.22/1.61 ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.22/1.61 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ) ), Y ) ), U ), 'tc_nat' )
% 1.22/1.61 ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.22/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), Y, 'tc_nat' ), hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.22/1.61 Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( 'c_Suc'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ),
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ),
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.22/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.22/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.22/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.22/1.61 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_RealVector_Oreal__field'( X ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), W, X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Y ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.22/1.61 Z, U, X ), W, X ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, T, X )
% 1.22/1.61 , W, X ) ), U ) ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.22/1.61 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.22/1.61 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.61 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.22/1.61 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.61 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 1.22/1.61 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.22/1.61 'tc_nat' ) ) ],
% 1.22/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ),
% 1.22/1.61 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.22/1.61 'tc_nat' ) ) ],
% 1.22/1.61 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 1.22/1.61 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 1.22/1.61 'tc_nat' ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ) ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.22/1.61 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.22/1.61 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.22/1.61 X ) ) ],
% 1.22/1.61 [ =( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 'tc_nat' ), Z ), 'c_Suc'( X ) ), 'tc_nat' ) ), ~( 'c_lessequals'( hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), Y, 'tc_nat' ) )
% 1.22/1.61 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z
% 1.22/1.61 , 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X
% 1.22/1.61 ) ), Z ) ), T ), W ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X
% 1.22/1.61 ) ), Z ) ), W ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.22/1.61 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.22/1.61 ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.22/1.61 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.22/1.61 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.61 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.61 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.22/1.61 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.22/1.61 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.22/1.61 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.22/1.61 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.22/1.61 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.22/1.61 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.22/1.61 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ),
% 1.22/1.61 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.22/1.61 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y
% 1.22/1.61 , 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z,
% 1.22/1.61 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.61 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.61 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.61 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.22/1.61 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.22/1.61 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), X, 'tc_nat' ),
% 1.22/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.61 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.61 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.22/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 X, T, 'tc_nat' ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ), X ) ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.22/1.61 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.22/1.61 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.22/1.61 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.22/1.61 'c_lessequals'( Z, Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.22/1.61 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.61 'c_lessequals'( Z, Y, X ) ) ],
% 1.22/1.61 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.22/1.61 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 1.22/1.61 ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 1.22/1.61 ) ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.22/1.61 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.22/1.61 Y ) ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.22/1.61 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'(
% 1.22/1.61 Y ) ) ) ],
% 1.22/1.61 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.22/1.61 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.22/1.61 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.22/1.61 [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.22/1.61 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.22/1.61 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.22/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X
% 1.22/1.61 ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.22/1.61 X ) ), Z ) ) ), =( Y, Z ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.22/1.61 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.22/1.61 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.22/1.61 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.22/1.61 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.22/1.61 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W, V0,
% 1.22/1.61 V1 ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.22/1.61 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W, V0,
% 1.22/1.61 V1 ) ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.22/1.61 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 1.22/1.61 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 1.22/1.61 'tc_nat' ) ],
% 1.22/1.61 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( Y )
% 1.22/1.61 , X, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ],
% 1.22/1.61 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ),
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.22/1.61 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.22/1.61 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.22/1.61 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.22/1.61 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.22/1.61 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.22/1.61 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.22/1.61 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.22/1.61 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.22/1.61 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.22/1.61 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ), 'c_lessequals'( X, Y
% 1.22/1.61 , 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.61 X, 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.22/1.61 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.22/1.61 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 1.22/1.61 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.22/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.22/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.22/1.61 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.22/1.61 'tc_nat' ) ), Y ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.22/1.61 'tc_nat' ) ), Y ) ],
% 1.22/1.61 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 1.22/1.61 'tc_nat' ), 'tc_nat' ) ) ],
% 1.22/1.61 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.22/1.61 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.22/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.22/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.22/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.22/1.61 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.22/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.22/1.61 'tc_nat' ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.22/1.61 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.22/1.61 X ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ), X ) )
% 1.22/1.61 ],
% 1.22/1.61 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.22/1.61 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.22/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.22/1.61 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.22/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 1.22/1.61 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Odiv'(
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.22/1.61 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.22/1.61 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ), X ), ~( 'c_lessequals'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, 'c_Int_OPls',
% 1.22/1.61 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.22/1.61 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.22/1.61 ), X ), ~( 'c_lessequals'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 'c_Int_OPls', Y,
% 1.22/1.61 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.22/1.61 ), Y ), 'c_Suc'( Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.22/1.61 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Int_Onat'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_Int_Oint' ) ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.22/1.61 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.22/1.61 Z, 'c_Suc'( T ), 'tc_nat' ), 'tc_nat', X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.61 ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.22/1.61 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'(
% 1.22/1.61 'tc_nat' ), 'tc_nat' ) ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.22/1.61 [ =( X, 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.22/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.22/1.61 'tc_nat' ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.22/1.61 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.22/1.61 'tc_nat' ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.22/1.61 ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.22/1.61 ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.22/1.61 ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.22/1.61 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.22/1.61 ],
% 1.22/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.22/1.61 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.22/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.22/1.61 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.22/1.61 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.22/1.61 , ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.22/1.61 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.22/1.61 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.61 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.22/1.61 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.22/1.61 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.22/1.61 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.22/1.61 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.22/1.61 ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.22/1.61 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.22/1.61 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.61 X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.22/1.61 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.22/1.61 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.22/1.61 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.22/1.61 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.61 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.22/1.61 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.22/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.22/1.61 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.22/1.61 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.22/1.61 ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.61 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.22/1.61 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.61 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.22/1.61 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.61 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.22/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.22/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.22/1.61 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.22/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.22/1.61 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.22/1.61 , ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.61 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.22/1.61 , 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.22/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.22/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.22/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.61 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.22/1.61 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Y ), T ), Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.22/1.61 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.22/1.61 Y ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.61 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ), T ) ), U ), W, X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ), W, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.61 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), U ) ), W ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.61 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ), X ) ) ],
% 1.22/1.61 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y
% 1.22/1.61 , X, 'tc_nat' ) ), Z ) ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z
% 1.22/1.61 ) ), T ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 ), Y ), Y, X ) ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.22/1.61 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.61 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.22/1.61 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 1.22/1.61 'tc_nat' ), ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.22/1.61 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 1.22/1.61 X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.22/1.61 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.22/1.61 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ) ), T ), U, 'tc_nat'
% 1.22/1.61 ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.22/1.61 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), T ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ), 'tc_nat' ) ),
% 1.22/1.61 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.22/1.61 ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ) ), Y ) ), Z ), U, 'tc_nat'
% 1.22/1.61 ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.22/1.61 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), T ) ), U ), 'tc_nat' )
% 1.22/1.61 , ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), X ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ), 'tc_nat' ) ),
% 1.22/1.61 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ),
% 1.22/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.22/1.61 ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.22/1.61 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ) ), Y ) ), U ), 'tc_nat' )
% 1.22/1.61 ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.22/1.61 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 1.22/1.61 ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.22/1.61 , Z ) ],
% 1.22/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.22/1.61 , Z ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.22/1.61 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.22/1.61 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.22/1.61 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.22/1.61 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.22/1.61 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.22/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.22/1.61 , X ) ), Z ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.61 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.61 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.22/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.22/1.61 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.22/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.61 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.61 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.61 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.22/1.61 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.61 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.22/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.61 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.22/1.61 ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.22/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.22/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.61 ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.22/1.61 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.22/1.61 , X ) ), Z ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( X, 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.22/1.61 'tc_nat' ), 'tc_nat' ) ) ],
% 1.22/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.22/1.61 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ),
% 1.22/1.61 'c_HOL_Ominus__class_Ominus'( Y, 'c_Divides_Odiv__class_Omod'( Y, X,
% 1.22/1.61 'tc_nat' ), 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.61 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.22/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.22/1.61 ) ), Z ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.61 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.22/1.61 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.22/1.61 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~(
% 1.22/1.61 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.22/1.61 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.22/1.61 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.22/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.22/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.62 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.22/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.22/1.62 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.22/1.62 ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.62 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 1.22/1.62 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.22/1.62 X ) ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.22/1.62 , Y, X ) ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.22/1.62 , X ) ) ],
% 1.22/1.62 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.22/1.62 , Y, X ) ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.22/1.62 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.22/1.62 [ ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.22/1.62 ), Y ), X ), 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), X, 'tc_nat' ), Y ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.22/1.62 , X ), Y ), 'tc_nat' ) ],
% 1.22/1.62 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.22/1.62 , X ), Y ), 'tc_nat' ) ],
% 1.22/1.62 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.22/1.62 , Y ), X ), 'tc_nat' ) ],
% 1.22/1.62 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.22/1.62 , X ), Y ), 'tc_nat' ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.22/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.22/1.62 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.22/1.62 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.22/1.62 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.22/1.62 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.22/1.62 X ), Z, X ) ) ],
% 1.22/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.22/1.62 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.22/1.62 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.62 , X ) ) ],
% 1.22/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.62 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.22/1.62 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.22/1.62 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.22/1.62 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.22/1.62 T, X ) ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.22/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.22/1.62 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.22/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.22/1.62 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.22/1.62 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.22/1.62 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.22/1.62 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.22/1.62 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.22/1.62 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.22/1.62 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.22/1.62 , X ) ) ],
% 1.22/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.62 , X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.62 X ), X ) ) ],
% 1.22/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.22/1.62 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Y ), X ), ~(
% 1.22/1.62 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.22/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.22/1.62 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ), ~( 'c_lessequals'(
% 1.22/1.62 X, Y, 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y, hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y,
% 1.22/1.62 X, 'tc_nat' ) ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.22/1.62 [ =( 'c_Int_Onat'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint'
% 1.22/1.62 ) ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ],
% 1.22/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.22/1.62 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ),
% 1.22/1.62 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.62 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat'
% 1.22/1.62 ) ) ],
% 1.22/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.22/1.62 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ),
% 1.22/1.62 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.62 'tc_nat' ), X ), Y ), Z, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 1.22/1.62 ) ) ],
% 1.22/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.22/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 1.22/1.62 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.22/1.62 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.22/1.62 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.22/1.62 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.22/1.62 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.22/1.62 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.22/1.62 , T ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.22/1.62 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.22/1.62 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.22/1.62 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.22/1.62 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.22/1.62 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.22/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.62 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.22/1.62 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.22/1.62 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.22/1.62 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.62 ) ) ],
% 1.22/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.22/1.62 'c_Finite__Set_Osetsum'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.22/1.62 'tc_bool' ) ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.22/1.62 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.62 'c_Suc'( Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.22/1.62 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.62 ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.62 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.22/1.62 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.62 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.22/1.62 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.22/1.62 ) ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.62 'c_Int_OBit1'( Y ), X ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), 'c_Int_Oiszero'(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ) ],
% 1.22/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.62 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.22/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.62 'c_Int_OPls', X ) ), Y ) ],
% 1.22/1.62 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.22/1.62 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.22/1.62 ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y
% 1.22/1.62 ), X ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.22/1.62 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.22/1.62 Y ), X ), X ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.22/1.62 , X ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.22/1.62 , X ), ~( 'c_lessequals'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint'
% 1.22/1.62 ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ), 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.22/1.62 , X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.22/1.62 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.22/1.62 , X ), ~( 'c_lessequals'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint'
% 1.22/1.62 ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.22/1.62 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.22/1.62 , X ) ) ],
% 1.22/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.22/1.62 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.62 'tc_nat' ) ) ) ],
% 1.22/1.62 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.22/1.62 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.22/1.62 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.62 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.22/1.62 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.62 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.22/1.62 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.22/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.22/1.62 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.22/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.22/1.62 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.22/1.62 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.22/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.22/1.62 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.22/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.62 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.22/1.62 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.62 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.22/1.62 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.22/1.62 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.22/1.62 ) ) ],
% 1.22/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.62 'c_Suc'( X ), 'tc_nat' ) ],
% 1.22/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.62 'c_Suc'( X ), 'tc_nat' ) ],
% 1.22/1.62 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 1.22/1.62 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.22/1.62 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.22/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.22/1.62 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.22/1.62 ), Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.62 X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.62 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.22/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.22/1.62 , Y ) ) ],
% 1.22/1.62 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ), ~(
% 1.22/1.62 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.22/1.62 [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.22/1.62 'c_Int_OPls', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ) ) ],
% 1.22/1.62 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.22/1.62 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.22/1.62 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.22/1.62 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.22/1.62 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.22/1.62 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.22/1.62 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.22/1.62 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.22/1.62 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.22/1.62 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.22/1.62 [ 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.22/1.62 'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.22/1.62 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ), ~(
% 1.22/1.62 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.22/1.62 [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.22/1.62 'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ) ) ],
% 1.22/1.62 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.22/1.62 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.22/1.62 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ), Y, 'tc_nat'
% 1.22/1.62 ) ) ],
% 1.22/1.62 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.22/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.62 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.22/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.22/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.62 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.22/1.62 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.22/1.62 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.22/1.62 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.22/1.62 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.22/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.22/1.62 , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.22/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.22/1.62 , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.22/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.62 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.22/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.22/1.62 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.22/1.62 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.22/1.62 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Int_Onat'(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_Int_Oint' ) ) ) ],
% 1.22/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.22/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.22/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.62 X ), Y ), Y ) ) ],
% 1.22/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ) ],
% 1.22/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.22/1.62 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.22/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.22/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 1.22/1.62 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.22/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.62 'tc_nat' ), X ), X ) ) ],
% 1.22/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.22/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.62 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.22/1.62 'tc_nat' ) ) ],
% 1.22/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.22/1.62 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.22/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.22/1.62 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.62 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.22/1.62 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.22/1.62 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'c_Suc'(
% 1.22/1.62 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.22/1.62 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.22/1.62 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( X
% 1.22/1.62 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.22/1.62 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.22/1.62 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.22/1.62 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.22/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.22/1.62 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.22/1.62 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.22/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.22/1.62 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ),
% 1.22/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.22/1.62 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.22/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.22/1.62 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.22/1.62 ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.22/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.22/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.22/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.22/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.22/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.22/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.22/1.62 'c_lessequals'( Z, Y, X ) ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), =( 'c_Orderings_Obot__class_Obot'(
% 1.22/1.62 'tc_fun'( X, 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.22/1.62 Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.22/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.22/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ) ) ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.22/1.62 [ =( 'c_SetInterval_Oord__class_OatMost'( 'c_Suc'( X ), 'tc_nat' ),
% 1.22/1.62 'c_Set_Oinsert'( 'c_Suc'( X ), 'c_SetInterval_Oord__class_OatMost'( X,
% 1.22/1.62 'tc_nat' ), 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), X ), X ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.22/1.62 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.22/1.62 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.22/1.62 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.22/1.62 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.22/1.62 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.22/1.62 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.22/1.62 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.62 , 'tc_nat' ), 'tc_nat' ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.22/1.62 Z, X ) ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.22/1.62 Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.22/1.62 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.22/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.22/1.62 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.22/1.62 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.22/1.62 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.22/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 1.22/1.62 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.22/1.62 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.22/1.62 ],
% 1.22/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.22/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.22/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.22/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.22/1.62 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.22/1.62 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.22/1.62 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.22/1.62 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.22/1.62 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.62 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.62 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.22/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.62 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.62 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.22/1.62 ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.62 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.22/1.62 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.22/1.62 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.22/1.62 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.62 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.62 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.22/1.62 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ), =( Z,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.22/1.62 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.22/1.62 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.22/1.62 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.22/1.62 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.22/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.62 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.22/1.62 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.22/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.22/1.62 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.22/1.62 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.22/1.62 X ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.22/1.62 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.22/1.62 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.22/1.62 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.22/1.62 , X ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.62 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.22/1.62 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.62 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.22/1.62 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.22/1.62 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.62 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.62 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.22/1.62 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.22/1.62 ],
% 1.22/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.62 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.22/1.62 , Z ), Y ), 'tc_nat' ) ) ],
% 1.22/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.62 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.22/1.62 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.22/1.62 ],
% 1.22/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.22/1.62 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.22/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.22/1.62 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.22/1.62 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.22/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.22/1.62 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.22/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.22/1.62 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.22/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.22/1.62 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.22/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.22/1.62 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.22/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.22/1.62 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.22/1.62 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.22/1.62 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( Z, Y,
% 1.22/1.62 'tc_Int_Oint' ) ), ~( 'c_lessequals'( X, Z, 'tc_Int_Oint' ) ) ],
% 1.22/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 1.22/1.62 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.22/1.62 [ 'c_lessequals'( X, X, 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.22/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.22/1.62 , X ) ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.22/1.62 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.22/1.62 , X ) ) ],
% 1.22/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.22/1.62 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.22/1.62 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.22/1.62 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.22/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.22/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.22/1.62 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.22/1.62 ) ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.22/1.62 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.22/1.62 ) ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.22/1.62 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.22/1.62 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.22/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.22/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.22/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.22/1.62 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X,
% 1.22/1.62 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.22/1.62 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.62 , X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.62 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.22/1.62 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.62 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.22/1.62 'c_SetInterval_Oord__class_OatMost'( Y, X ),
% 1.22/1.62 'c_SetInterval_Oord__class_OatMost'( Z, X ) ) ), =( Y, Z ) ],
% 1.22/1.62 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.62 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.62 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.22/1.62 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.22/1.62 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.62 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.22/1.62 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.22/1.62 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.22/1.62 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.22/1.62 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.22/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.22/1.62 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.22/1.62 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.22/1.62 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.22/1.62 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.22/1.62 ) ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ),
% 1.22/1.62 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.62 ) ],
% 1.22/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.22/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~(
% 1.22/1.62 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.22/1.62 'tc_nat' ), 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.22/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.22/1.62 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.22/1.62 'tc_nat' ), 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.22/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.62 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.22/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.22/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.22/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), =( Y,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.22/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.22/1.62 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.22/1.62 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Z ), Y ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.22/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ),
% 1.22/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.22/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.22/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.22/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.22/1.62 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.62 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.22/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.62 ), =( 'c_HOL_Oinverse__class_Odivide'( Y, U, X ),
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.22/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.22/1.62 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.62 X, 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.62 'tc_nat' ), X ), 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ), Y,
% 1.22/1.62 'tc_nat' ) ],
% 1.22/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.62 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.22/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.22/1.62 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.22/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.22/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.22/1.62 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.22/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.22/1.62 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y, X ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.22/1.62 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.22/1.62 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.22/1.62 'c_lessequals'( Z, Y, X ) ],
% 1.22/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), 'c_lessequals'( Y, X,
% 1.22/1.62 'tc_Int_Oint' ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.22/1.62 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.22/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.22/1.62 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.22/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.62 ) ) ],
% 1.22/1.62 [ =( 'c_Int_Onat'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.22/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_Int_Oint' ) ), 'c_Suc'( 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.22/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.22/1.62 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.22/1.62 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.22/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'tc_nat' ) ) ],
% 1.22/1.62 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.22/1.62 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.22/1.62 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.22/1.62 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.22/1.62 ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.22/1.62 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.22/1.62 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.22/1.62 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.62 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.22/1.62 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.22/1.62 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.62 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), X ), X ) ],
% 1.22/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.22/1.62 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.62 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.22/1.62 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X
% 1.22/1.62 ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.22/1.62 ), Y ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.22/1.62 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.22/1.62 ), Y ) ],
% 1.22/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.22/1.62 ) ) ],
% 1.22/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.62 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.22/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.22/1.62 , Y ) ],
% 1.22/1.62 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X,
% 1.22/1.62 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.22/1.62 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.22/1.62 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.22/1.62 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ), 'c_lessequals'( X
% 1.22/1.62 , 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.22/1.62 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.22/1.62 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.22/1.62 [ =( 'c_Suc'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.62 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.22/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.62 'tc_nat' ) ) ],
% 1.22/1.62 [ =( 'c_Suc'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.22/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.22/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ) ), =( X,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.62 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.62 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.22/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.22/1.62 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.62 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.22/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.62 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.62 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.22/1.62 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.22/1.62 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.22/1.62 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, 'c_Suc'( Y ),
% 1.22/1.62 'tc_nat' ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_nat', 'tc_bool'
% 1.22/1.62 ) ) ), 'c_lessequals'( X, Y, 'tc_nat' ) ],
% 1.22/1.62 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, 'c_Suc'( Y ),
% 1.22/1.62 'tc_nat' ), 'c_Set_Oinsert'( Y,
% 1.22/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( X, Y, 'tc_nat' ), 'tc_nat'
% 1.22/1.62 ) ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.22/1.62 [ =( 'c_SetInterval_Oord__class_OatMost'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.62 'tc_nat' ), 'tc_nat' ), 'c_Set_Oinsert'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.62 'tc_nat' ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_nat', 'tc_bool'
% 1.22/1.62 ) ), 'tc_nat' ) ) ],
% 1.22/1.62 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.22/1.62 , 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.62 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.22/1.62 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.22/1.62 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.22/1.62 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.22/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.22/1.62 ) ), =( 'c_Finite__Set_Osetsum'( Y,
% 1.22/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_nat' ), 'tc_nat', X ),
% 1.22/1.62 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ =( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.22/1.62 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.22/1.62 , X, Z, U, W, V0 ) ) ],
% 1.22/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.22/1.62 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.62 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.22/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.22/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.22/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.22/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.22/1.62 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.62 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.22/1.62 ) ],
% 1.22/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.22/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.22/1.62 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.22/1.62 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.22/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.22/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.22/1.62 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.22/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.22/1.62 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.22/1.62 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.22/1.62 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.62 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.22/1.62 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.22/1.62 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.62 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.22/1.62 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.22/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.22/1.62 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.62 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.22/1.62 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.22/1.62 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.22/1.62 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.22/1.62 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.22/1.62 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.22/1.62 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.22/1.62 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.22/1.62 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ],
% 1.22/1.62 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X,
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.22/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_nat', 'tc_bool' ) ) ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.22/1.62 'c_Set_Oinsert'( Y, Z, X ) ) ) ],
% 1.22/1.62 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.22/1.62 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.22/1.62 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.22/1.62 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.22/1.62 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.22/1.62 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.22/1.62 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.22/1.62 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.22/1.62 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.22/1.62 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.22/1.62 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP( 'c_Set_Oinsert'( Z,
% 1.22/1.62 X, T ), Y ) ) ) ],
% 1.22/1.62 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 1.22/1.62 'c_Set_Oinsert'( X, Y, Z ) ) ],
% 1.22/1.62 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.22/1.62 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.22/1.62 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.22/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.22/1.62 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 1.22/1.62 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.22/1.62 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.22/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.22/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.22/1.62 'tc_nat' ), 'c_Suc'( 'c_Suc'( 'c_Suc'( 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ), 'tc_nat' ) ) ],
% 1.22/1.62 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.22/1.62 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.22/1.62 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.22/1.62 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.22/1.62 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.22/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.22/1.62 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.22/1.62 ) ],
% 1.22/1.62 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.22/1.62 'tc_nat' ) ) ],
% 1.22/1.62 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'( 'c_Suc'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.22/1.62 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.22/1.62 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.22/1.62 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.22/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.22/1.62 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.22/1.62 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( X, T ) ],
% 1.22/1.62 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.22/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.22/1.62 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.22/1.62 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( X, T ) ],
% 1.22/1.62 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.22/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.22/1.62 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.22/1.62 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ],
% 1.22/1.62 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.22/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.22/1.62 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.22/1.62 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( Y, U ) ],
% 1.22/1.62 [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.22/1.62 ) ), Y ) ) ) ],
% 1.22/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.22/1.62 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.22/1.62 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, 'c_Suc'( X ),
% 1.22/1.62 'tc_nat' ), 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.22/1.62 'tc_nat', 'tc_bool' ) ), 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.22/1.62 'tc_fun'( Z, 'tc_bool' ) ) ) ) ],
% 1.22/1.62 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.22/1.62 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.22/1.62 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.22/1.62 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, Z, T ), T ),
% 1.22/1.62 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, Z, T ), T ) ) ],
% 1.22/1.62 [ =( 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.22/1.62 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.22/1.62 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.22/1.62 [ ~( =( 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 1.22/1.62 , 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'(
% 1.22/1.62 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), =( X, Z ) ],
% 1.22/1.62 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), T ) ), ~( hBOOL( hAPP( Y, T )
% 1.22/1.62 ) ) ],
% 1.22/1.62 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.22/1.62 [ ~( =( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.22/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( 'c_Suc'( 'c_Suc'(
% 1.22/1.62 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ), 'tc_nat' ),
% 1.22/1.62 'c_Set_Oinsert'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Set_Oinsert'(
% 1.22/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Set_Oinsert'(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Set_Oinsert'(
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.22/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.22/1.62 'tc_nat', 'tc_bool' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) )
% 1.22/1.62 ) ],
% 1.22/1.62 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.22/1.62 'class_Orderings_Opreorder'( Y ) ) ],
% 1.22/1.62 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.22/1.62 'class_Orderings_Oorder'( Y ) ) ],
% 1.22/1.62 [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Obot'(
% 1.22/1.62 Y ) ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.22/1.62 ],
% 1.22/1.62 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.22/1.62 ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.22/1.62 ],
% 1.22/1.62 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.22/1.62 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.22/1.62 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.22/1.62 [ 'class_Orderings_Obot'( 'tc_bool' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.22/1.62 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.22/1.62 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.22/1.62 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.22/1.62 ],
% 1.22/1.62 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.22/1.62 ],
% 1.22/1.62 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.22/1.62 ,
% 1.22/1.62 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.22/1.62 [ 'c_fequal'( X, X, Y ) ],
% 1.22/1.62 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.22/1.62 ] .
% 1.22/1.62
% 1.22/1.62
% 1.22/1.62 percentage equality = 0.221480, percentage horn = 0.810317
% 1.22/1.62 This is a problem with some equality
% 1.22/1.62
% 1.22/1.62
% 1.22/1.62
% 1.22/1.62 Options Used:
% 1.22/1.62
% 1.22/1.62 useres = 1
% 1.22/1.62 useparamod = 1
% 1.22/1.62 useeqrefl = 1
% 1.22/1.62 useeqfact = 1
% 1.22/1.62 usefactor = 1
% 1.22/1.62 usesimpsplitting = 0
% 1.22/1.62 usesimpdemod = 5
% 1.22/1.62 usesimpres = 3
% 1.22/1.62
% 1.22/1.62 resimpinuse = 1000
% 1.22/1.62 resimpclauses = 20000
% 1.22/1.62 substype = eqrewr
% 1.22/1.62 backwardsubs = 1
% 1.22/1.62 selectoldest = 5
% 1.22/1.62
% 1.22/1.62 litorderings [0] = split
% 1.22/1.62 litorderings [1] = extend the termordering, first sorting on arguments
% 1.22/1.62
% 1.22/1.62 termordering = kbo
% 1.22/1.62
% 1.22/1.62 litapriori = 0
% 1.22/1.62 termapriori = 1
% 1.22/1.62 litaposteriori = 0
% 1.22/1.62 termaposteriori = 0
% 1.22/1.62 demodaposteriori = 0
% 1.43/1.79 ordereqreflfact = 0
% 1.43/1.79
% 1.43/1.79 litselect = negord
% 1.43/1.79
% 1.43/1.79 maxweight = 15
% 1.43/1.79 maxdepth = 30000
% 1.43/1.79 maxlength = 115
% 1.43/1.79 maxnrvars = 195
% 1.43/1.79 excuselevel = 1
% 1.43/1.79 increasemaxweight = 1
% 1.43/1.79
% 1.43/1.79 maxselected = 10000000
% 1.43/1.79 maxnrclauses = 10000000
% 1.43/1.79
% 1.43/1.79 showgenerated = 0
% 1.43/1.79 showkept = 0
% 1.43/1.79 showselected = 0
% 1.43/1.79 showdeleted = 0
% 1.43/1.79 showresimp = 1
% 1.43/1.79 showstatus = 2000
% 1.43/1.79
% 1.43/1.79 prologoutput = 1
% 1.43/1.79 nrgoals = 5000000
% 1.43/1.79 totalproof = 1
% 1.43/1.79
% 1.43/1.79 Symbols occurring in the translation:
% 1.43/1.79
% 1.43/1.79 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.43/1.79 . [1, 2] (w:1, o:138, a:1, s:1, b:0),
% 1.43/1.79 ! [4, 1] (w:0, o:65, a:1, s:1, b:0),
% 1.43/1.79 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.43/1.79 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.43/1.79 'tc_nat' [40, 0] (w:1, o:15, a:1, s:1, b:0),
% 1.43/1.79 'c_HOL_Oplus__class_Oplus' [41, 1] (w:1, o:71, a:1, s:1, b:0),
% 1.43/1.79 hAPP [42, 2] (w:1, o:163, a:1, s:1, b:0),
% 1.43/1.79 'c_Suc' [44, 1] (w:1, o:72, a:1, s:1, b:0),
% 1.43/1.79 'c_HOL_Oord__class_Oless' [45, 3] (w:1, o:170, a:1, s:1, b:0),
% 1.43/1.79 'c_HOL_Ominus__class_Ominus' [49, 3] (w:1, o:171, a:1, s:1, b:0),
% 1.43/1.79 'c_lessequals' [50, 3] (w:1, o:172, a:1, s:1, b:0),
% 1.43/1.79 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [52, 1]
% 1.43/1.79 (w:1, o:73, a:1, s:1, b:0),
% 1.43/1.79 'class_OrderedGroup_Ocomm__monoid__add' [53, 1] (w:1, o:74, a:1, s:1
% 1.43/1.79 , b:0),
% 1.43/1.79 'c_HOL_Ozero__class_Ozero' [57, 1] (w:1, o:75, a:1, s:1, b:0),
% 1.43/1.79 'class_Ring__and__Field_Oordered__field' [61, 1] (w:1, o:77, a:1, s:1
% 1.43/1.79 , b:0),
% 1.43/1.79 'class_Ring__and__Field_Odivision__by__zero' [62, 1] (w:1, o:80, a:1
% 1.43/1.79 , s:1, b:0),
% 1.43/1.79 'c_HOL_Oinverse__class_Odivide' [63, 3] (w:1, o:173, a:1, s:1, b:0),
% 1.43/1.79
% 1.43/1.79 'class_Ring__and__Field_Opordered__ring' [64, 1] (w:1, o:87, a:1, s:1
% 1.43/1.79 , b:0),
% 1.43/1.79 'c_HOL_Otimes__class_Otimes' [65, 1] (w:1, o:88, a:1, s:1, b:0),
% 1.43/1.79 'class_Ring__and__Field_Oring' [68, 1] (w:1, o:89, a:1, s:1, b:0),
% 1.43/1.79 'class_Int_Onumber' [69, 1] (w:1, o:90, a:1, s:1, b:0),
% 1.43/1.79 'c_Int_Onumber__class_Onumber__of' [71, 2] (w:1, o:165, a:1, s:1, b:0
% 1.43/1.79 ),
% 1.43/1.79 'class_Ring__and__Field_Oordered__ring__strict' [72, 1] (w:1, o:81
% 1.43/1.79 , a:1, s:1, b:0),
% 1.43/1.79 'c_Divides_Odiv__class_Omod' [73, 3] (w:1, o:174, a:1, s:1, b:0),
% 1.43/1.79 'class_Ring__and__Field_Oordered__idom' [74, 1] (w:1, o:82, a:1, s:1
% 1.43/1.79 , b:0),
% 1.43/1.79 'c_Parity_Oeven__odd__class_Oeven' [76, 2] (w:1, o:166, a:1, s:1, b:0
% 1.43/1.79 ),
% 1.43/1.79 'c_Power_Opower__class_Opower' [77, 1] (w:1, o:92, a:1, s:1, b:0),
% 1.43/1.79 'c_Divides_Odiv__class_Odiv' [78, 3] (w:1, o:175, a:1, s:1, b:0),
% 1.43/1.79 'class_Ring__and__Field_Oordered__semiring' [79, 1] (w:1, o:83, a:1
% 1.43/1.79 , s:1, b:0),
% 1.43/1.79 'class_Ring__and__Field_Oordered__semiring__strict' [80, 1] (w:1, o:
% 1.43/1.79 84, a:1, s:1, b:0),
% 1.43/1.79 hBOOL [82, 1] (w:1, o:93, a:1, s:1, b:0),
% 1.43/1.79 'class_Ring__and__Field_Ocomm__semiring__1' [83, 1] (w:1, o:78, a:1
% 1.43/1.79 , s:1, b:0),
% 1.43/1.79 'class_OrderedGroup_Oab__group__add' [87, 1] (w:1, o:94, a:1, s:1, b:
% 1.43/1.79 0),
% 1.43/1.79 'c_SetInterval_Oord__class_OatLeastLessThan' [89, 3] (w:1, o:176, a:1
% 1.43/1.79 , s:1, b:0),
% 1.43/1.79 'c_Finite__Set_Osetsum' [90, 4] (w:1, o:179, a:1, s:1, b:0),
% 1.43/1.79 'class_OrderedGroup_Opordered__comm__monoid__add' [91, 1] (w:1, o:95
% 1.43/1.79 , a:1, s:1, b:0),
% 1.43/1.79 'tc_Int_Oint' [92, 0] (w:1, o:48, a:1, s:1, b:0),
% 1.43/1.79 'class_RealVector_Oreal__normed__field' [93, 1] (w:1, o:96, a:1, s:1
% 1.43/1.79 , b:0),
% 1.43/1.79 'class_Ring__and__Field_Ofield' [95, 1] (w:1, o:97, a:1, s:1, b:0),
% 1.43/1.79 'class_OrderedGroup_Olordered__ab__group__add' [96, 1] (w:1, o:98, a:
% 1.43/1.79 1, s:1, b:0),
% 1.43/1.79 'class_Ring__and__Field_Oordered__semidom' [97, 1] (w:1, o:85, a:1
% 1.43/1.79 , s:1, b:0),
% 1.43/1.79 'c_HOL_Oinverse__class_Oinverse' [98, 2] (w:1, o:164, a:1, s:1, b:0)
% 1.43/1.79 ,
% 1.43/1.79 'c_HOL_Oone__class_Oone' [99, 1] (w:1, o:70, a:1, s:1, b:0),
% 1.43/1.79 'class_Int_Onumber__ring' [100, 1] (w:1, o:99, a:1, s:1, b:0),
% 1.43/1.79 'class_Divides_Osemiring__div' [101, 1] (w:1, o:101, a:1, s:1, b:0),
% 1.43/1.79
% 1.43/1.79 'class_Ring__and__Field_Oidom' [102, 1] (w:1, o:102, a:1, s:1, b:0),
% 1.43/1.79
% 1.43/1.79 'class_OrderedGroup_Ogroup__add' [103, 1] (w:1, o:103, a:1, s:1, b:0)
% 1.43/1.79 ,
% 1.43/1.79 'class_Ring__and__Field_Odivision__ring' [104, 1] (w:1, o:104, a:1
% 10.63/11.08 , s:1, b:0),
% 10.63/11.08 'class_OrderedGroup_Omonoid__mult' [105, 1] (w:1, o:105, a:1, s:1, b:
% 10.63/11.08 0),
% 10.63/11.08 'class_Power_Opower' [106, 1] (w:1, o:120, a:1, s:1, b:0),
% 10.63/11.08 'class_Orderings_Oorder' [107, 1] (w:1, o:106, a:1, s:1, b:0),
% 10.63/11.08 'class_Orderings_Opreorder' [108, 1] (w:1, o:107, a:1, s:1, b:0),
% 10.63/11.08 'class_OrderedGroup_Oab__semigroup__add' [109, 1] (w:1, o:108, a:1
% 10.63/11.08 , s:1, b:0),
% 10.63/11.08 'class_Orderings_Olinorder' [110, 1] (w:1, o:109, a:1, s:1, b:0),
% 10.63/11.08 'class_Ring__and__Field_Osemiring' [115, 1] (w:1, o:123, a:1, s:1, b:
% 10.63/11.08 0),
% 10.63/11.08 'class_OrderedGroup_Opordered__ab__semigroup__add' [121, 1] (w:1, o:
% 10.63/11.08 110, a:1, s:1, b:0),
% 10.63/11.08 'class_OrderedGroup_Oab__semigroup__idem__mult' [122, 1] (w:1, o:111
% 10.63/11.08 , a:1, s:1, b:0),
% 10.63/11.08 'class_Ring__and__Field_Omult__mono1' [124, 1] (w:1, o:124, a:1, s:1
% 10.63/11.08 , b:0),
% 10.63/11.08 'class_Ring__and__Field_Omult__mono' [125, 1] (w:1, o:125, a:1, s:1
% 10.63/11.08 , b:0),
% 10.63/11.08 'class_RealVector_Oreal__normed__algebra' [126, 1] (w:1, o:126, a:1
% 10.63/11.08 , s:1, b:0),
% 10.63/11.08 'c_Groebner__Basis_Ogb__semiring' [129, 6] (w:1, o:180, a:1, s:1, b:0
% 10.63/11.08 ),
% 10.63/11.08 'class_Ring__and__Field_Oordered__comm__semiring__strict' [130, 1]
% 10.63/11.08 (w:1, o:86, a:1, s:1, b:0),
% 10.63/11.08 'c_Int_Onat' [131, 1] (w:1, o:127, a:1, s:1, b:0),
% 10.63/11.08 'c_SetInterval_Oord__class_OatMost' [132, 2] (w:1, o:167, a:1, s:1
% 10.63/11.08 , b:0),
% 10.63/11.08 'class_OrderedGroup_Opordered__ab__group__add' [133, 1] (w:1, o:112
% 10.63/11.08 , a:1, s:1, b:0),
% 10.63/11.08 'class_OrderedGroup_Ocomm__monoid__mult' [134, 1] (w:1, o:113, a:1
% 10.63/11.08 , s:1, b:0),
% 10.63/11.08 'class_Ring__and__Field_Opordered__cancel__semiring' [135, 1] (w:1
% 10.63/11.08 , o:128, a:1, s:1, b:0),
% 10.63/11.08 'class_OrderedGroup_Oab__semigroup__mult' [136, 1] (w:1, o:114, a:1
% 10.63/11.08 , s:1, b:0),
% 10.63/11.08 'class_Ring__and__Field_Ocomm__semiring' [137, 1] (w:1, o:79, a:1, s:
% 10.63/11.08 1, b:0),
% 10.63/11.08 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [138, 1]
% 10.63/11.08 (w:1, o:115, a:1, s:1, b:0),
% 10.63/11.08 'class_Ring__and__Field_Osemiring__1' [139, 1] (w:1, o:130, a:1, s:1
% 10.63/11.08 , b:0),
% 10.63/11.08 'c_Int_Oiszero' [140, 2] (w:1, o:168, a:1, s:1, b:0),
% 10.63/11.08 'class_Ring__and__Field_Oring__no__zero__divisors' [141, 1] (w:1, o:
% 10.63/11.08 121, a:1, s:1, b:0),
% 10.63/11.08 'class_Ring__and__Field_Omult__zero' [142, 1] (w:1, o:131, a:1, s:1
% 10.63/11.08 , b:0),
% 10.63/11.08 'class_Ring__and__Field_Oring__1__no__zero__divisors' [143, 1] (w:1
% 10.63/11.08 , o:122, a:1, s:1, b:0),
% 10.63/11.08 'class_Ring__and__Field_Ozero__neq__one' [144, 1] (w:1, o:132, a:1
% 10.63/11.08 , s:1, b:0),
% 10.63/11.08 'class_Ring__and__Field_Ono__zero__divisors' [145, 1] (w:1, o:76, a:1
% 10.63/11.08 , s:1, b:0),
% 10.63/11.08 'class_OrderedGroup_Omonoid__add' [146, 1] (w:1, o:116, a:1, s:1, b:0
% 10.63/11.08 ),
% 10.63/11.08 'class_Ring__and__Field_Opordered__semiring' [147, 1] (w:1, o:133, a:
% 10.63/11.08 1, s:1, b:0),
% 10.63/11.08 'class_Divides_Oring__div' [153, 1] (w:1, o:100, a:1, s:1, b:0),
% 10.63/11.08 'class_OrderedGroup_Ocancel__ab__semigroup__add' [154, 1] (w:1, o:117
% 10.63/11.08 , a:1, s:1, b:0),
% 10.63/11.08 'class_OrderedGroup_Ocancel__semigroup__add' [155, 1] (w:1, o:118, a:
% 10.63/11.08 1, s:1, b:0),
% 10.63/11.08 'class_Orderings_Obot' [156, 1] (w:1, o:119, a:1, s:1, b:0),
% 10.63/11.08 'c_Orderings_Obot__class_Obot' [157, 1] (w:1, o:91, a:1, s:1, b:0),
% 10.63/11.08 'class_RealVector_Oreal__field' [159, 1] (w:1, o:134, a:1, s:1, b:0)
% 10.63/11.08 ,
% 10.63/11.08 'c_Int_OBit1' [162, 1] (w:1, o:136, a:1, s:1, b:0),
% 10.63/11.08 'c_Int_OPls' [164, 0] (w:1, o:55, a:1, s:1, b:0),
% 10.63/11.08 'c_Int_OBit0' [165, 1] (w:1, o:135, a:1, s:1, b:0),
% 10.63/11.08 'class_Ring__and__Field_Osemiring__0' [167, 1] (w:1, o:129, a:1, s:1
% 10.63/11.08 , b:0),
% 10.63/11.08 'tc_bool' [169, 0] (w:1, o:57, a:1, s:1, b:0),
% 10.63/11.08 'tc_fun' [170, 2] (w:1, o:169, a:1, s:1, b:0),
% 10.63/11.08 'class_Int_Oring__char__0' [171, 1] (w:1, o:137, a:1, s:1, b:0),
% 10.63/11.08 'c_Set_Oinsert' [172, 3] (w:1, o:177, a:1, s:1, b:0),
% 10.63/11.08 'c_fequal' [178, 3] (w:1, o:178, a:1, s:1, b:0).
% 10.63/11.08
% 10.63/11.08
% 10.63/11.08 Starting Search:
% 10.63/11.08
% 10.63/11.08 Resimplifying inuse:
% 10.63/11.08 Done
% 10.63/11.08
% 10.63/11.08
% 10.63/11.08 Intermediate Status:
% 10.63/11.08 Generated: 4261
% 10.63/11.08 Kept: 2005
% 10.63/11.08 Inuse: 188
% 10.63/11.08 Deleted: 8
% 10.63/11.08 Deletedinuse: 0
% 10.63/11.08
% 10.63/11.08 Resimplifying inuse:
% 10.63/11.08 Done
% 10.63/11.08
% 10.63/11.08 Resimplifying inuse:
% 10.63/11.08 Done
% 10.63/11.08
% 10.63/11.08
% 10.63/11.08 Intermediate Status:
% 10.63/11.08 Generated: 12412
% 10.63/11.08 Kept: 5003
% 10.63/11.08 Inuse: 291
% 10.63/11.08 Deleted: 15
% 10.63/11.08 Deletedinuse: 3
% 10.63/11.08
% 10.63/11.08 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07
% 39.65/40.07 Intermediate Status:
% 39.65/40.07 Generated: 18895
% 39.65/40.07 Kept: 7027
% 39.65/40.07 Inuse: 452
% 39.65/40.07 Deleted: 27
% 39.65/40.07 Deletedinuse: 3
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07
% 39.65/40.07 Intermediate Status:
% 39.65/40.07 Generated: 27796
% 39.65/40.07 Kept: 10011
% 39.65/40.07 Inuse: 589
% 39.65/40.07 Deleted: 35
% 39.65/40.07 Deletedinuse: 5
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07
% 39.65/40.07 Intermediate Status:
% 39.65/40.07 Generated: 38074
% 39.65/40.07 Kept: 12395
% 39.65/40.07 Inuse: 659
% 39.65/40.07 Deleted: 37
% 39.65/40.07 Deletedinuse: 5
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07
% 39.65/40.07 Intermediate Status:
% 39.65/40.07 Generated: 46851
% 39.65/40.07 Kept: 14457
% 39.65/40.07 Inuse: 688
% 39.65/40.07 Deleted: 39
% 39.65/40.07 Deletedinuse: 6
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07
% 39.65/40.07 Intermediate Status:
% 39.65/40.07 Generated: 54795
% 39.65/40.07 Kept: 16915
% 39.65/40.07 Inuse: 723
% 39.65/40.07 Deleted: 39
% 39.65/40.07 Deletedinuse: 6
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07
% 39.65/40.07 Intermediate Status:
% 39.65/40.07 Generated: 62457
% 39.65/40.07 Kept: 18916
% 39.65/40.07 Inuse: 791
% 39.65/40.07 Deleted: 45
% 39.65/40.07 Deletedinuse: 6
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07 Resimplifying clauses:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07
% 39.65/40.07 Intermediate Status:
% 39.65/40.07 Generated: 75776
% 39.65/40.07 Kept: 21046
% 39.65/40.07 Inuse: 802
% 39.65/40.07 Deleted: 600
% 39.65/40.07 Deletedinuse: 6
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07
% 39.65/40.07 Intermediate Status:
% 39.65/40.07 Generated: 90720
% 39.65/40.07 Kept: 24646
% 39.65/40.07 Inuse: 812
% 39.65/40.07 Deleted: 600
% 39.65/40.07 Deletedinuse: 6
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07
% 39.65/40.07 Intermediate Status:
% 39.65/40.07 Generated: 105137
% 39.65/40.07 Kept: 27446
% 39.65/40.07 Inuse: 822
% 39.65/40.07 Deleted: 600
% 39.65/40.07 Deletedinuse: 6
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07
% 39.65/40.07 Intermediate Status:
% 39.65/40.07 Generated: 113768
% 39.65/40.07 Kept: 29461
% 39.65/40.07 Inuse: 869
% 39.65/40.07 Deleted: 600
% 39.65/40.07 Deletedinuse: 6
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07
% 39.65/40.07 Intermediate Status:
% 39.65/40.07 Generated: 123133
% 39.65/40.07 Kept: 31609
% 39.65/40.07 Inuse: 922
% 39.65/40.07 Deleted: 600
% 39.65/40.07 Deletedinuse: 6
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07
% 39.65/40.07 Intermediate Status:
% 39.65/40.07 Generated: 133513
% 39.65/40.07 Kept: 34303
% 39.65/40.07 Inuse: 956
% 39.65/40.07 Deleted: 611
% 39.65/40.07 Deletedinuse: 16
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.07 Done
% 39.65/40.07
% 39.65/40.07 Resimplifying inuse:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08
% 39.65/40.08 Intermediate Status:
% 39.65/40.08 Generated: 142025
% 39.65/40.08 Kept: 36471
% 39.65/40.08 Inuse: 991
% 39.65/40.08 Deleted: 612
% 39.65/40.08 Deletedinuse: 17
% 39.65/40.08
% 39.65/40.08 Resimplifying inuse:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08
% 39.65/40.08 Intermediate Status:
% 39.65/40.08 Generated: 162419
% 39.65/40.08 Kept: 39166
% 39.65/40.08 Inuse: 1006
% 39.65/40.08 Deleted: 612
% 39.65/40.08 Deletedinuse: 17
% 39.65/40.08
% 39.65/40.08 Resimplifying inuse:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08
% 39.65/40.08 Intermediate Status:
% 39.65/40.08 Generated: 181820
% 39.65/40.08 Kept: 41391
% 39.65/40.08 Inuse: 1011
% 39.65/40.08 Deleted: 612
% 39.65/40.08 Deletedinuse: 17
% 39.65/40.08
% 39.65/40.08 Resimplifying inuse:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08 Resimplifying clauses:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08 Resimplifying inuse:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08
% 39.65/40.08 Intermediate Status:
% 39.65/40.08 Generated: 192969
% 39.65/40.08 Kept: 44145
% 39.65/40.08 Inuse: 1021
% 39.65/40.08 Deleted: 1053
% 39.65/40.08 Deletedinuse: 17
% 39.65/40.08
% 39.65/40.08 Resimplifying inuse:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08 Resimplifying inuse:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08
% 39.65/40.08 Intermediate Status:
% 39.65/40.08 Generated: 201320
% 39.65/40.08 Kept: 46252
% 39.65/40.08 Inuse: 1041
% 39.65/40.08 Deleted: 1054
% 39.65/40.08 Deletedinuse: 18
% 39.65/40.08
% 39.65/40.08 Resimplifying inuse:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08
% 39.65/40.08 Intermediate Status:
% 39.65/40.08 Generated: 210525
% 39.65/40.08 Kept: 48695
% 39.65/40.08 Inuse: 1061
% 39.65/40.08 Deleted: 1054
% 39.65/40.08 Deletedinuse: 18
% 39.65/40.08
% 39.65/40.08 Resimplifying inuse:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08 Resimplifying inuse:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08
% 39.65/40.08 Intermediate Status:
% 39.65/40.08 Generated: 219600
% 39.65/40.08 Kept: 50716
% 39.65/40.08 Inuse: 1100
% 39.65/40.08 Deleted: 1056
% 39.65/40.08 Deletedinuse: 18
% 39.65/40.08
% 39.65/40.08 Resimplifying inuse:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08 Resimplifying inuse:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08
% 39.65/40.08 Intermediate Status:
% 39.65/40.08 Generated: 229233
% 39.65/40.08 Kept: 52751
% 39.65/40.08 Inuse: 1139
% 39.65/40.08 Deleted: 1056
% 39.65/40.08 Deletedinuse: 18
% 39.65/40.08
% 39.65/40.08 Resimplifying inuse:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08
% 39.65/40.08 Intermediate Status:
% 39.65/40.08 Generated: 239189
% 39.65/40.08 Kept: 55027
% 39.65/40.08 Inuse: 1159
% 39.65/40.08 Deleted: 1060
% 39.65/40.08 Deletedinuse: 22
% 39.65/40.08
% 39.65/40.08 Resimplifying inuse:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08 Resimplifying inuse:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08
% 39.65/40.08 Intermediate Status:
% 39.65/40.08 Generated: 248393
% 39.65/40.08 Kept: 57167
% 39.65/40.08 Inuse: 1179
% 39.65/40.08 Deleted: 1064
% 39.65/40.08 Deletedinuse: 26
% 39.65/40.08
% 39.65/40.08 Resimplifying inuse:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08
% 39.65/40.08 Intermediate Status:
% 39.65/40.08 Generated: 258417
% 39.65/40.08 Kept: 59272
% 39.65/40.08 Inuse: 1199
% 39.65/40.08 Deleted: 1064
% 39.65/40.08 Deletedinuse: 26
% 39.65/40.08
% 39.65/40.08 Resimplifying inuse:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08 Resimplifying inuse:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08
% 39.65/40.08 Intermediate Status:
% 39.65/40.08 Generated: 268410
% 39.65/40.08 Kept: 61318
% 39.65/40.08 Inuse: 1244
% 39.65/40.08 Deleted: 1065
% 39.65/40.08 Deletedinuse: 27
% 39.65/40.08
% 39.65/40.08 Resimplifying clauses:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08 Resimplifying inuse:
% 39.65/40.08 Done
% 39.65/40.08
% 39.65/40.08
% 39.65/40.08 Intermediate Status:
% 39.65/40.08 Generated: 278702
% 39.65/40.08 Kept: 63720
% 134.54/134.91 Inuse: 1269
% 134.54/134.91 Deleted: 1759
% 134.54/134.91 Deletedinuse: 27
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 287095
% 134.54/134.91 Kept: 65754
% 134.54/134.91 Inuse: 1284
% 134.54/134.91 Deleted: 1759
% 134.54/134.91 Deletedinuse: 27
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 304558
% 134.54/134.91 Kept: 67904
% 134.54/134.91 Inuse: 1304
% 134.54/134.91 Deleted: 1760
% 134.54/134.91 Deletedinuse: 28
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 314844
% 134.54/134.91 Kept: 70369
% 134.54/134.91 Inuse: 1328
% 134.54/134.91 Deleted: 1760
% 134.54/134.91 Deletedinuse: 28
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 322568
% 134.54/134.91 Kept: 72511
% 134.54/134.91 Inuse: 1334
% 134.54/134.91 Deleted: 1760
% 134.54/134.91 Deletedinuse: 28
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 332190
% 134.54/134.91 Kept: 74659
% 134.54/134.91 Inuse: 1364
% 134.54/134.91 Deleted: 1760
% 134.54/134.91 Deletedinuse: 28
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 356291
% 134.54/134.91 Kept: 80541
% 134.54/134.91 Inuse: 1398
% 134.54/134.91 Deleted: 1763
% 134.54/134.91 Deletedinuse: 29
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91 Resimplifying clauses:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 365349
% 134.54/134.91 Kept: 82634
% 134.54/134.91 Inuse: 1427
% 134.54/134.91 Deleted: 2055
% 134.54/134.91 Deletedinuse: 29
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 375356
% 134.54/134.91 Kept: 84888
% 134.54/134.91 Inuse: 1437
% 134.54/134.91 Deleted: 2055
% 134.54/134.91 Deletedinuse: 29
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 395019
% 134.54/134.91 Kept: 88020
% 134.54/134.91 Inuse: 1467
% 134.54/134.91 Deleted: 2055
% 134.54/134.91 Deletedinuse: 29
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 402621
% 134.54/134.91 Kept: 90054
% 134.54/134.91 Inuse: 1491
% 134.54/134.91 Deleted: 2057
% 134.54/134.91 Deletedinuse: 30
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 420504
% 134.54/134.91 Kept: 94720
% 134.54/134.91 Inuse: 1511
% 134.54/134.91 Deleted: 2057
% 134.54/134.91 Deletedinuse: 30
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 434488
% 134.54/134.91 Kept: 100783
% 134.54/134.91 Inuse: 1516
% 134.54/134.91 Deleted: 2057
% 134.54/134.91 Deletedinuse: 30
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 447646
% 134.54/134.91 Kept: 104062
% 134.54/134.91 Inuse: 1521
% 134.54/134.91 Deleted: 2057
% 134.54/134.91 Deletedinuse: 30
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91 Resimplifying clauses:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 457857
% 134.54/134.91 Kept: 106141
% 134.54/134.91 Inuse: 1551
% 134.54/134.91 Deleted: 2455
% 134.54/134.91 Deletedinuse: 30
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 471237
% 134.54/134.91 Kept: 108800
% 134.54/134.91 Inuse: 1571
% 134.54/134.91 Deleted: 2455
% 134.54/134.91 Deletedinuse: 30
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 482846
% 134.54/134.91 Kept: 111006
% 134.54/134.91 Inuse: 1606
% 134.54/134.91 Deleted: 2457
% 134.54/134.91 Deletedinuse: 32
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 493880
% 134.54/134.91 Kept: 113409
% 134.54/134.91 Inuse: 1636
% 134.54/134.91 Deleted: 2457
% 134.54/134.91 Deletedinuse: 32
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 505342
% 134.54/134.91 Kept: 115995
% 134.54/134.91 Inuse: 1651
% 134.54/134.91 Deleted: 2457
% 134.54/134.91 Deletedinuse: 32
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 515220
% 134.54/134.91 Kept: 118161
% 134.54/134.91 Inuse: 1681
% 134.54/134.91 Deleted: 2458
% 134.54/134.91 Deletedinuse: 33
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 526806
% 134.54/134.91 Kept: 120715
% 134.54/134.91 Inuse: 1700
% 134.54/134.91 Deleted: 2462
% 134.54/134.91 Deletedinuse: 36
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 537554
% 134.54/134.91 Kept: 122962
% 134.54/134.91 Inuse: 1730
% 134.54/134.91 Deleted: 2464
% 134.54/134.91 Deletedinuse: 38
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91 Resimplifying clauses:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 566143
% 134.54/134.91 Kept: 129164
% 134.54/134.91 Inuse: 1763
% 134.54/134.91 Deleted: 4951
% 134.54/134.91 Deletedinuse: 38
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 574350
% 134.54/134.91 Kept: 131603
% 134.54/134.91 Inuse: 1785
% 134.54/134.91 Deleted: 4952
% 134.54/134.91 Deletedinuse: 39
% 134.54/134.91
% 134.54/134.91 Resimplifying inuse:
% 134.54/134.91 Done
% 134.54/134.91
% 134.54/134.91
% 134.54/134.91 Intermediate Status:
% 134.54/134.91 Generated: 583660
% 134.54/134.91 Kept: 134568
% 134.54/134.91 Inuse: 1795
% 134.54/134.91 Deleted: 4952
% 134.54/134.91 Deletedinuse: 39
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 592143
% 242.45/242.91 Kept: 139706
% 242.45/242.91 Inuse: 1800
% 242.45/242.91 Deleted: 4952
% 242.45/242.91 Deletedinuse: 39
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 604302
% 242.45/242.91 Kept: 143971
% 242.45/242.91 Inuse: 1817
% 242.45/242.91 Deleted: 4952
% 242.45/242.91 Deletedinuse: 39
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91 Resimplifying clauses:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 624299
% 242.45/242.91 Kept: 147840
% 242.45/242.91 Inuse: 1855
% 242.45/242.91 Deleted: 5140
% 242.45/242.91 Deletedinuse: 39
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 691696
% 242.45/242.91 Kept: 151490
% 242.45/242.91 Inuse: 1865
% 242.45/242.91 Deleted: 5140
% 242.45/242.91 Deletedinuse: 39
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 700870
% 242.45/242.91 Kept: 153583
% 242.45/242.91 Inuse: 1870
% 242.45/242.91 Deleted: 5140
% 242.45/242.91 Deletedinuse: 39
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 710202
% 242.45/242.91 Kept: 155668
% 242.45/242.91 Inuse: 1875
% 242.45/242.91 Deleted: 5140
% 242.45/242.91 Deletedinuse: 39
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 736025
% 242.45/242.91 Kept: 159506
% 242.45/242.91 Inuse: 1880
% 242.45/242.91 Deleted: 5140
% 242.45/242.91 Deletedinuse: 39
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 762413
% 242.45/242.91 Kept: 163351
% 242.45/242.91 Inuse: 1885
% 242.45/242.91 Deleted: 5140
% 242.45/242.91 Deletedinuse: 39
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 775560
% 242.45/242.91 Kept: 166018
% 242.45/242.91 Inuse: 1900
% 242.45/242.91 Deleted: 5140
% 242.45/242.91 Deletedinuse: 39
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91 Resimplifying clauses:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 792104
% 242.45/242.91 Kept: 168937
% 242.45/242.91 Inuse: 1925
% 242.45/242.91 Deleted: 5510
% 242.45/242.91 Deletedinuse: 41
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 800906
% 242.45/242.91 Kept: 172810
% 242.45/242.91 Inuse: 1931
% 242.45/242.91 Deleted: 5510
% 242.45/242.91 Deletedinuse: 41
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 819372
% 242.45/242.91 Kept: 179227
% 242.45/242.91 Inuse: 1940
% 242.45/242.91 Deleted: 5510
% 242.45/242.91 Deletedinuse: 41
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 847669
% 242.45/242.91 Kept: 185209
% 242.45/242.91 Inuse: 1943
% 242.45/242.91 Deleted: 5512
% 242.45/242.91 Deletedinuse: 41
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 862343
% 242.45/242.91 Kept: 188676
% 242.45/242.91 Inuse: 1944
% 242.45/242.91 Deleted: 5517
% 242.45/242.91 Deletedinuse: 42
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91 Resimplifying clauses:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 872072
% 242.45/242.91 Kept: 190794
% 242.45/242.91 Inuse: 1969
% 242.45/242.91 Deleted: 5699
% 242.45/242.91 Deletedinuse: 42
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 905286
% 242.45/242.91 Kept: 196386
% 242.45/242.91 Inuse: 1989
% 242.45/242.91 Deleted: 5699
% 242.45/242.91 Deletedinuse: 42
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 916000
% 242.45/242.91 Kept: 198574
% 242.45/242.91 Inuse: 2013
% 242.45/242.91 Deleted: 5700
% 242.45/242.91 Deletedinuse: 42
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 927107
% 242.45/242.91 Kept: 200597
% 242.45/242.91 Inuse: 2030
% 242.45/242.91 Deleted: 5700
% 242.45/242.91 Deletedinuse: 42
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 937970
% 242.45/242.91 Kept: 202955
% 242.45/242.91 Inuse: 2033
% 242.45/242.91 Deleted: 5700
% 242.45/242.91 Deletedinuse: 42
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 975776
% 242.45/242.91 Kept: 207472
% 242.45/242.91 Inuse: 2038
% 242.45/242.91 Deleted: 5700
% 242.45/242.91 Deletedinuse: 42
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91 Resimplifying clauses:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 991895
% 242.45/242.91 Kept: 209493
% 242.45/242.91 Inuse: 2057
% 242.45/242.91 Deleted: 5993
% 242.45/242.91 Deletedinuse: 42
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 1011110
% 242.45/242.91 Kept: 212610
% 242.45/242.91 Inuse: 2063
% 242.45/242.91 Deleted: 5993
% 242.45/242.91 Deletedinuse: 42
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 1024370
% 242.45/242.91 Kept: 215124
% 242.45/242.91 Inuse: 2068
% 242.45/242.91 Deleted: 5993
% 242.45/242.91 Deletedinuse: 42
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 1035094
% 242.45/242.91 Kept: 217402
% 242.45/242.91 Inuse: 2083
% 242.45/242.91 Deleted: 5993
% 242.45/242.91 Deletedinuse: 42
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 1045755
% 242.45/242.91 Kept: 219495
% 242.45/242.91 Inuse: 2098
% 242.45/242.91 Deleted: 5993
% 242.45/242.91 Deletedinuse: 42
% 242.45/242.91
% 242.45/242.91 Resimplifying inuse:
% 242.45/242.91 Done
% 242.45/242.91
% 242.45/242.91
% 242.45/242.91 Intermediate Status:
% 242.45/242.91 Generated: 1056315
% 242.45/242.91 Kept: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------