TSTP Solution File: ALG336-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : ALG336-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n029.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 : Thu Jul 14 12:10:22 EDT 2022
% Result : Timeout 300.01s 300.45s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG336-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Tue Jun 7 22:52:35 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.18/1.59 *** allocated 10000 integers for termspace/termends
% 1.18/1.59 *** allocated 10000 integers for clauses
% 1.18/1.59 *** allocated 10000 integers for justifications
% 1.18/1.59 *** allocated 15000 integers for termspace/termends
% 1.18/1.59 *** allocated 22500 integers for termspace/termends
% 1.18/1.59 *** allocated 33750 integers for termspace/termends
% 1.18/1.59 *** allocated 50625 integers for termspace/termends
% 1.18/1.59 Bliksem 1.12
% 1.18/1.59
% 1.18/1.59
% 1.18/1.59 Automatic Strategy Selection
% 1.18/1.59
% 1.18/1.59 Clauses:
% 1.18/1.59 [
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.18/1.59 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.18/1.59 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.18/1.59 , Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.18/1.59 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.18/1.59 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.18/1.59 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 1.18/1.59 'tc_nat' ), 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z
% 1.18/1.59 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' )
% 1.18/1.59 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.18/1.59 , Z, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.18/1.59 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.18/1.59 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.59 , Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 1.18/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 , X ) ) ],
% 1.18/1.59 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), T, X ),
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.18/1.59 , T, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), X ) ), =( Z
% 1.18/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.18/1.59 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.18/1.59 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'(
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' )
% 1.18/1.59 , 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.18/1.59 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.18/1.59 , X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.18/1.59 , X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.18/1.59 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.18/1.59 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ), Z ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.18/1.59 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 , X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.59 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 , X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 , X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 , X ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.18/1.59 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 1.18/1.59 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ), ~( 'c_lessequals'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, 'c_Int_OPls',
% 1.18/1.59 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.59 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.18/1.59 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ],
% 1.18/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.18/1.59 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.18/1.59 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.18/1.59 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.18/1.59 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.59 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.59 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.59 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.59 ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.59 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.59 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.59 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.18/1.59 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.59 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.59 ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.59 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.59 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.18/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.18/1.59 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.59 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.59 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.18/1.59 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.18/1.59 X ) ],
% 1.18/1.59 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'(
% 1.18/1.59 'tc_nat' ), X, 'tc_nat' ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.59 ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.59 ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( T, U, X ), X ),
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( U, T, X ) ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.59 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.18/1.59 ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.59 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.18/1.59 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.18/1.59 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 1.18/1.59 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( X
% 1.18/1.59 , 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat'
% 1.18/1.59 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.59 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.59 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.18/1.59 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 1.18/1.59 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.18/1.59 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Odiv'( Y, Z,
% 1.18/1.59 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 1.18/1.59 'tc_nat' ), 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.59 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.18/1.59 X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.59 X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.59 , Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.18/1.59 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 1.18/1.59 , 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.59 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.59 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.18/1.59 X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.59 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.59 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.18/1.59 X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.18/1.59 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.18/1.59 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_Int_Oint' ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_Int_Oint' ), 'tc_Int_Oint' ), ~(
% 1.18/1.59 'c_lessequals'( Y, Z, 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ],
% 1.18/1.59 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.18/1.59 'tc_nat' ), 'tc_nat' ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.18/1.59 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( T, X ), X ) ), ~(
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 1.18/1.59 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.59 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) )
% 1.18/1.59 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.18/1.59 , 'tc_nat' ) ) ],
% 1.18/1.59 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.18/1.59 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.18/1.59 ), =( Z, Y ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.18/1.59 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.18/1.59 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.18/1.59 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.18/1.59 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.18/1.59 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_Int_Oint' ) ), ~(
% 1.18/1.59 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.18/1.59 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 1.18/1.59 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.18/1.59 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.18/1.59 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.18/1.59 , T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.59 ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.18/1.59 , Z, X ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.59 ), ~( 'c_lessequals'( T, Y, X ) ) ],
% 1.18/1.59 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.59 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T )
% 1.18/1.59 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.59 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.18/1.59 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.18/1.59 ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.18/1.59 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.59 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =(
% 1.18/1.59 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.18/1.59 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.18/1.59 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 1.18/1.59 X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.18/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.18/1.59 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.18/1.59 Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.18/1.59 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.18/1.59 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.18/1.59 Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.18/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.18/1.59 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.18/1.59 X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.18/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.18/1.59 Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.18/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.18/1.59 X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ), T, X ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Nat_Osemiring__1__class_Oof__nat'( X
% 1.18/1.59 , 'tc_Int_Oint' ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' ), Z,
% 1.18/1.59 'tc_Int_Oint' ), 'tc_Int_Oint' ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.18/1.59 'tc_nat' ), 'tc_Int_Oint' ), Z, 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_Onat'( Y ), 'tc_nat' ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( X,
% 1.18/1.59 'tc_Int_Oint' ), Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( X,
% 1.18/1.59 'tc_Int_Oint' ), Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.18/1.59 'c_Int_Onat'( Y ), 'tc_nat' ) ) ],
% 1.18/1.59 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'c_Int_Onat'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint' ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.18/1.59 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 1.18/1.59 , 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.18/1.59 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.18/1.59 , 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.18/1.59 Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z
% 1.18/1.59 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.18/1.59 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oone__class_Oone'(
% 1.18/1.59 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.18/1.59 T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X ) ),
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.59 , Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.18/1.59 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 1.18/1.59 ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), T, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.59 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 , X ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.18/1.59 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.18/1.59 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.18/1.59 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Z,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ), X ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.18/1.59 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.18/1.59 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.18/1.59 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.18/1.59 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 1.18/1.59 , X ), W, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( Z, W, X ), X ) ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.18/1.59 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Z,
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( U, W, X ), X ), T, X ), X ) ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ],
% 1.18/1.59 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y,
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z, X ),
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z, X ),
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Y ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( Z, Y, X ), X ),
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( Z, Y, X ), X ), Z ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.18/1.59 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), =( X, Y ), ~(
% 1.18/1.59 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.18/1.59 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.18/1.59 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.18/1.59 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.18/1.59 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.18/1.59 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.18/1.59 ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.59 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.18/1.59 Y, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.18/1.59 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.18/1.59 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.59 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.18/1.59 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.59 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.59 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.18/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.59 Y, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.59 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.59 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.18/1.59 , X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X ) ],
% 1.18/1.59 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Odiv'(
% 1.18/1.59 Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.18/1.59 X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Odiv'(
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.18/1.59 X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), X ) ), ~(
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.59 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.18/1.59 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.59 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.59 ), X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.59 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.59 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.59 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.59 ), X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.18/1.59 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.18/1.59 T, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.18/1.59 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.18/1.59 X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.18/1.59 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.18/1.59 T, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.18/1.59 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.18/1.59 X ), T, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.18/1.59 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.59 T, X ), X ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.18/1.59 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.18/1.59 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.18/1.59 X ), T, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.18/1.59 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.18/1.59 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), =( Y, X ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ],
% 1.18/1.59 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 1.18/1.59 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 1.18/1.59 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y, X ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.18/1.59 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.18/1.59 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.18/1.59 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.18/1.59 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_RealDef_Oreal' ) ), ~(
% 1.18/1.59 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.18/1.59 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.59 , Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.18/1.59 , X ) ) ), =( Y, Z ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.18/1.59 , X ) ) ), =( Y, Z ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ), Z ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 1.18/1.59 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( T, X ), X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.18/1.59 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.18/1.59 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint' )
% 1.18/1.59 , 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ), 'tc_Int_Oint' )
% 1.18/1.59 , ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ), 'tc_Int_Oint' ) )
% 1.18/1.59 ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, Z, 'tc_Int_Oint' ),
% 1.18/1.59 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~( 'c_lessequals'( Y, Z
% 1.18/1.59 , 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.59 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.59 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.18/1.59 ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.59 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 1.18/1.59 , X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 1.18/1.59 , X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 Z, Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.18/1.59 , X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.18/1.59 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.18/1.59 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_Int_Opred'( X ), Y, 'tc_Int_Oint' ), ~(
% 1.18/1.59 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_Int_Opred'( X ), Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.59 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~(
% 1.18/1.59 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.18/1.59 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.18/1.59 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.18/1.59 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.18/1.59 ), X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.18/1.59 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.18/1.59 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.18/1.59 Z, T, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.18/1.59 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat'
% 1.18/1.59 ), 'tc_nat' ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.18/1.59 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.59 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.18/1.59 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.59 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.18/1.59 'tc_Int_Oint' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.18/1.59 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint' ), X ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.59 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.59 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.59 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.59 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.18/1.59 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_Osucc'( X ), 'tc_nat' ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.18/1.59 'c_Power_Opower__class_Opower'( Y, T, X ), X ),
% 1.18/1.59 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.18/1.59 'tc_nat' ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 1.18/1.59 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.59 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.59 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.59 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.18/1.59 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.59 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.18/1.59 , Z, X ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.18/1.59 , T, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.18/1.59 , Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.18/1.59 , T, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.18/1.59 , Z, X ), X ) ) ],
% 1.18/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.18/1.59 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.18/1.59 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.18/1.59 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.18/1.59 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.18/1.59 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.18/1.59 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.18/1.59 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.18/1.59 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.18/1.59 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.18/1.59 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.18/1.59 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.18/1.59 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.18/1.59 'tc_nat' ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.59 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X ), X ) )
% 1.18/1.59 ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.59 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.59 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.59 Y, X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.59 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.18/1.59 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ), T, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 1.18/1.59 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.59 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 1.18/1.59 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.18/1.59 , X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.18/1.59 , X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.18/1.59 , X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.18/1.59 , X ) ) ],
% 1.18/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.18/1.59 , X ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.59 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.59 , T, X ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 1.18/1.59 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Z, Y, X ),
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.18/1.59 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.59 [ =( 'c_Int_Osucc'( 'c_Int_Opred'( X ) ), X ) ],
% 1.18/1.59 [ ~( 'class_HOL_Oeq'( X ) ), 'c_HOL_Oeq__class_Oeq'( Y, Y, X ) ],
% 1.18/1.59 [ 'c_HOL_Oeq__class_Oeq'( X, X, 'tc_Int_Oint' ) ],
% 1.18/1.59 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.59 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( 'c_Divides_Odiv__class_Odiv'( Y
% 1.18/1.59 , X, 'tc_nat' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.18/1.59 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.18/1.59 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 1.18/1.59 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.18/1.59 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.18/1.59 X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.18/1.59 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.18/1.59 X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.18/1.59 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.18/1.59 X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.18/1.59 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.18/1.59 X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 Y, Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 Y, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 1.18/1.59 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 1.18/1.59 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.18/1.59 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.18/1.59 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.18/1.59 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.18/1.59 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.18/1.59 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.18/1.59 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.18/1.59 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.18/1.59 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.18/1.59 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.18/1.59 'c_Power_Opower__class_Opower'( T, 'c_Suc'( Z ), X ) ) ), =( Y, T ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.18/1.59 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( X, Z, 'tc_nat'
% 1.18/1.59 ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ),
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ), 'tc_nat' ), Z, 'tc_nat' )
% 1.18/1.59 , 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.18/1.59 , X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.18/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.18/1.59 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.59 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.18/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.18/1.59 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.18/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.18/1.59 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.18/1.59 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.18/1.59 , X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.18/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.59 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.18/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.59 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 Y, T, X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.18/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.59 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 Y, T, X ), Z, X ) ) ],
% 1.18/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.18/1.59 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' )
% 1.18/1.59 , 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.18/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.18/1.59 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.18/1.59 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.18/1.59 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.18/1.59 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.18/1.59 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.18/1.59 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.18/1.59 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' )
% 1.18/1.59 , 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.18/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.18/1.59 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.18/1.59 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.18/1.59 Y, 'tc_nat' ), 'tc_nat' ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.18/1.59 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.18/1.59 Y, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.18/1.59 'tc_nat' ) ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.18/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.18/1.59 'tc_nat' ), 'tc_nat' ) ],
% 1.18/1.59 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.18/1.59 'tc_nat' ), 'tc_nat' ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.18/1.59 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.18/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), 'c_Suc'( 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.18/1.59 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.59 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 1.18/1.59 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.18/1.59 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 1.18/1.59 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.18/1.59 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.18/1.59 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.18/1.59 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.18/1.59 Y, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.18/1.59 Z, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.18/1.59 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), Z
% 1.18/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), X
% 1.18/1.59 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.59 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.59 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.59 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.18/1.59 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.18/1.59 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.18/1.59 [ ~( =( 'c_Nat_Osemiring__1__class_Oof__nat'( X, 'tc_Int_Oint' ),
% 1.18/1.59 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' ) ) ), =( X, Y ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( =( 'c_Nat_Osemiring__1__class_Oof__nat'( X, 'tc_Int_Oint' ),
% 1.18/1.59 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' ) ) ), =( X, Y ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.59 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.59 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ), X ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.59 , 'tc_nat' ), 'tc_nat' ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.59 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.59 , 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ), 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.18/1.59 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) )
% 1.18/1.59 ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_OPls'
% 1.18/1.59 , Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.18/1.59 ), X ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.59 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.59 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.18/1.59 ), =( 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.59 Y, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ),
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ),
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.59 , T, X ), X ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( X
% 1.18/1.59 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.18/1.59 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.18/1.59 ), 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.18/1.59 , T, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.18/1.59 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.18/1.59 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.18/1.59 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.18/1.59 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.18/1.59 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.18/1.59 W, X ), X ), ~( 'c_lessequals'( T, 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.18/1.59 , X ), W, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.18/1.59 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U, X ), W, X ), X ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 T, U, X ), Y, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.18/1.59 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.18/1.59 W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 1.18/1.59 , X ), T, X ), W, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.18/1.60 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.18/1.60 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.18/1.60 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 1.18/1.60 ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.18/1.60 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.18/1.60 ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 1.18/1.60 Y, 'tc_nat' ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.18/1.60 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 1.18/1.60 ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.18/1.60 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.60 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 1.18/1.60 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.60 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.18/1.60 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oabs__class_Oabs'(
% 1.18/1.60 Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ),
% 1.18/1.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.18/1.60 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.18/1.60 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.18/1.60 X, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.18/1.60 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.18/1.60 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Odiv'(
% 1.18/1.60 X, 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.18/1.60 ), 'tc_nat' ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' )
% 1.18/1.60 ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Z, Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.18/1.60 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.18/1.60 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Y, T, X ),
% 1.18/1.60 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.18/1.60 , X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 1.18/1.60 ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.18/1.60 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.60 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.18/1.60 , X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.18/1.60 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 1.18/1.60 , X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 1.18/1.60 , X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.60 , Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.60 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.60 ), X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.60 ), X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.60 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.60 ), X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.60 ), X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.60 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.18/1.60 ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.60 , X ), X ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.18/1.60 ],
% 1.18/1.60 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.18/1.60 , X, 'tc_nat' ), X ) ],
% 1.18/1.60 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.18/1.60 ), 'tc_nat' ), X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.18/1.60 , Y, X ), X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.18/1.60 , Z, X ), X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.18/1.60 , Z, X ), X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.18/1.60 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.18/1.60 ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.60 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 1.18/1.60 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), Y, X ), Z, X ) ) ],
% 1.18/1.60 [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'(
% 1.18/1.60 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.18/1.60 [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.18/1.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.60 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.18/1.60 ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.60 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.18/1.60 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.60 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.18/1.60 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.18/1.60 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.18/1.60 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.18/1.60 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.18/1.60 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.60 X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.18/1.60 'tc_nat' ), X, 'tc_nat' ) ],
% 1.18/1.60 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.60 X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 1.18/1.60 'tc_nat' ), X, 'tc_nat' ) ],
% 1.18/1.60 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.18/1.60 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), Z, X ) ), =( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.18/1.60 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Z,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), T, X ) ), =( T,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 1.18/1.60 X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), X ) ), =( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.60 ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.18/1.60 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.18/1.60 'tc_Int_Oint' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ),
% 1.18/1.60 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.18/1.60 'tc_Int_Oint' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ),
% 1.18/1.60 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.18/1.60 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.18/1.60 ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.60 Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.60 Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, T
% 1.18/1.60 , X ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, Z
% 1.18/1.60 , X ), 'c_Divides_Odiv__class_Odiv'( T, Z, X ), X ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.60 Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.60 Z, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.18/1.60 , X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.18/1.60 , X ), Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 1.18/1.60 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.18/1.60 , T, X ), X ), T, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.60 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.18/1.60 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.60 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.60 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y, X ), ~( 'c_lessequals'( Z,
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.18/1.60 ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.18/1.60 'c_lessequals'( Y, Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.18/1.60 'c_lessequals'( Y, Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.18/1.60 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ],
% 1.18/1.60 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 1.18/1.60 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.60 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.18/1.60 X ) ) ), =( Z, T ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.18/1.60 X ) ) ), =( Z, T ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.18/1.60 X ) ) ), =( Y, T ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.18/1.60 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.60 ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.18/1.60 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.18/1.60 , X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.18/1.60 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Z
% 1.18/1.60 , X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ), =( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.60 ) ],
% 1.18/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), T, X ), X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_Int_Oint' ), X ), T, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.60 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.60 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.60 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.18/1.60 , X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.18/1.60 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.60 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.18/1.60 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), =( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.18/1.60 Z, 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.18/1.60 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.60 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 1.18/1.60 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.60 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.60 ), X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 1.18/1.60 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.18/1.60 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.60 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.18/1.60 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.18/1.60 'tc_Int_Oint' ), X ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.18/1.60 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.18/1.60 , 'c_Int_Onumber__class_Onumber__of'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.18/1.60 'tc_Int_Oint' ), 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls'
% 1.18/1.60 , 'tc_Int_Oint' ), 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.18/1.60 'tc_Int_Oint' ) ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.18/1.60 'tc_Int_Oint' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ),
% 1.18/1.60 'tc_Int_Oint' ), 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_Int_Oint' ), 'tc_Int_Oint' ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.18/1.60 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.18/1.60 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.60 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.60 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.18/1.60 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.60 ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.60 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T
% 1.18/1.60 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.60 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.60 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.18/1.60 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.18/1.60 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 X ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_Int_Onat'( X ), 'c_Int_Onat'( Y ), 'tc_nat'
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 1.18/1.60 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.18/1.60 , X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.60 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.60 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ), X ), ~(
% 1.18/1.60 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.60 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.60 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.18/1.60 X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X
% 1.18/1.60 ), X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 1.18/1.60 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.60 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.60 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T
% 1.18/1.60 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_Opred'( Y ), X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.60 , X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 1.18/1.60 ), Y ) ],
% 1.18/1.60 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.18/1.60 ), X ), Y ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.60 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.60 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T
% 1.18/1.60 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.18/1.60 ), X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.18/1.60 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.18/1.60 Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.60 'c_Suc'( Z ), X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.60 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.18/1.60 ), X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.18/1.60 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.18/1.60 , Y, X ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.18/1.60 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.18/1.60 , Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.18/1.60 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.18/1.60 , T, X ), X ), T, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), T, X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.18/1.60 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.60 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.18/1.60 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.18/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.18/1.60 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.60 , 'tc_nat' ), 'tc_nat' ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.18/1.60 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.18/1.60 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.18/1.60 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.18/1.60 'tc_Int_Oint' ), Z, 'tc_Int_Oint' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_Int_Oint' ), 'tc_Int_Oint' ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.18/1.60 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.18/1.60 'tc_Int_Oint' ), 'tc_Int_Oint' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_Int_Oint' ), 'tc_Int_Oint' ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.18/1.60 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.18/1.60 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.18/1.60 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.18/1.60 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.18/1.60 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.18/1.60 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.18/1.60 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.60 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X
% 1.18/1.60 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.18/1.60 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.18/1.60 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.18/1.60 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.18/1.60 Y, T, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.18/1.60 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.18/1.60 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.18/1.60 Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X )
% 1.18/1.60 , 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.18/1.60 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat' ) ), 'tc_nat' ) )
% 1.18/1.60 ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( X,
% 1.18/1.60 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), 'tc_Int_Oint' ),
% 1.18/1.60 'tc_Int_Oint' ), 'tc_Int_Oint' ) ],
% 1.18/1.60 [ ~( =( 'c_Nat_Osemiring__1__class_Oof__nat'( X, 'tc_Int_Oint' ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ) ) ), =( X,
% 1.18/1.60 'c_Int_Onat'( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ) ) )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.18/1.60 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.18/1.60 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.18/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.18/1.60 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.18/1.60 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.18/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.18/1.60 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.18/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.18/1.60 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.18/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.18/1.60 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.18/1.60 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.60 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.60 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.18/1.60 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.18/1.60 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.18/1.60 ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.60 ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.18/1.60 ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.60 ), X ) ) ],
% 1.18/1.60 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.18/1.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.18/1.60 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.18/1.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.18/1.60 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.60 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.18/1.60 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.18/1.60 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.18/1.60 ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.18/1.60 , T, X ) ) ), =( Z, T ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.18/1.60 , T, X ) ) ), =( Y, Z ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.18/1.60 X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Z
% 1.18/1.60 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.60 , T, X ), X ) ) ],
% 1.18/1.60 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.60 'tc_nat' ) ), =( Y, Z ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.60 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.60 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.60 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.18/1.60 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.60 X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.18/1.60 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.60 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.18/1.60 , T, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.60 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.18/1.60 , Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 1.18/1.60 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.60 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.18/1.60 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 X ), T, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 1.18/1.60 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.60 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.18/1.60 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.18/1.60 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.60 Z, X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.60 Y, Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.18/1.60 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.60 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.18/1.60 ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.18/1.60 ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.18/1.60 'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.18/1.60 ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.60 'c_Suc'( X ), 'tc_nat' ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.60 'c_Suc'( X ), 'tc_nat' ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.60 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.60 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.18/1.60 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.60 , Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.18/1.60 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.18/1.60 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 1.18/1.60 [ =( 'c_Suc'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Odiv'(
% 1.18/1.60 X, 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.18/1.60 ), 'tc_nat' ) ), X ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.18/1.60 ), 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.18/1.60 ), 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z
% 1.18/1.60 ), X ), 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), X ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.18/1.60 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.18/1.60 , X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.18/1.60 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.18/1.60 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 'tc_nat' ) ), Y, 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat'
% 1.18/1.60 ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 'tc_nat' ) ), Y, 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.18/1.60 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.60 X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.18/1.60 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.60 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.60 ) ],
% 1.18/1.60 [ ~( 'class_RealVector_Oreal__field'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.18/1.60 , U, X ), X ), W, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Z, U, X ), W, X ), X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Y, T, X ), W, X ), U, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.18/1.60 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.18/1.60 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.18/1.60 ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.18/1.60 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.60 ), X ), X ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.18/1.60 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.18/1.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.18/1.60 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, U,
% 1.18/1.60 X ), X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Y, T, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ), X ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.60 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.18/1.60 , ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.18/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.18/1.60 'tc_nat' ), Y, 'tc_nat' ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.18/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.18/1.60 'tc_nat' ), X, 'tc_nat' ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.18/1.60 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.18/1.60 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.60 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.18/1.60 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.60 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.18/1.60 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.18/1.60 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ],
% 1.18/1.60 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.60 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.18/1.60 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.18/1.60 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.18/1.60 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.18/1.60 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z
% 1.18/1.60 , X ), 'c_Power_Opower__class_Opower'( Y, Z, X ) ), ~(
% 1.18/1.60 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.60 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.18/1.60 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.18/1.60 , X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.18/1.60 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.18/1.60 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.18/1.60 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.18/1.60 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.18/1.60 , X ), W, X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 1.18/1.60 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), T, X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y, X )
% 1.18/1.60 , X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ), X ), T, X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Z, T, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 Y, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), T, X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.60 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.60 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.60 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'( Z,
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.60 , X ), X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.60 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.18/1.60 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.18/1.60 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 1.18/1.60 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.18/1.60 'tc_nat' ) ) ],
% 1.18/1.60 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 1.18/1.60 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X,
% 1.18/1.60 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.60 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.60 ), X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.60 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.60 ), X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.18/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), T, X ), X ),
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_Int_Oint' ), X ), T, X ) ) ],
% 1.18/1.60 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 X, Y, 'tc_nat' ) ), X, 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) )
% 1.18/1.60 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 1.18/1.60 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.18/1.60 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.60 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.18/1.60 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.18/1.60 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.18/1.60 [ =( 'c_Int_Onat'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_Int_Oint' ) ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.60 [ =( 'c_Int_Onat'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.18/1.60 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_Int_Oint' ) ), 'c_Suc'( 'c_Suc'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.18/1.60 ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.60 ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.18/1.60 X ) ) ],
% 1.18/1.60 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 X, T, 'tc_nat' ) ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_Int_Oint' ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.18/1.60 X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.18/1.60 X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 1.18/1.60 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z
% 1.18/1.60 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'(
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ), Z, X
% 1.18/1.60 ), 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.18/1.60 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.60 'c_lessequals'( Z, Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.18/1.60 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.60 'c_lessequals'( Z, Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.18/1.60 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.18/1.60 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 1.18/1.60 X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.18/1.60 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.18/1.60 , T, X ), X ), T, X ) ) ],
% 1.18/1.60 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.18/1.60 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.18/1.60 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Z, 'c_Divides_Odiv__class_Odiv'( Y, T, X ), X
% 1.18/1.60 ) ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( T, 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), X
% 1.18/1.60 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.18/1.60 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.60 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.18/1.60 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.18/1.60 , Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.18/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.18/1.60 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.60 , Z, X ) ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.18/1.60 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z,
% 1.18/1.60 Y, 'tc_nat' ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.18/1.60 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.18/1.60 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.18/1.60 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.18/1.60 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.18/1.60 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.60 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 1.18/1.60 ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.60 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.18/1.60 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.18/1.60 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.18/1.60 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.60 ) ), =( Y, Z ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.60 ) ), =( Y, Z ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.60 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.18/1.60 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.18/1.60 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.18/1.60 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.18/1.60 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.18/1.60 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.18/1.60 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.18/1.60 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.18/1.60 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.18/1.60 , U, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.18/1.60 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.60 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.60 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.18/1.60 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.60 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.60 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.18/1.60 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.60 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.18/1.60 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.60 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.60 , X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), T
% 1.18/1.60 , X ), 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.18/1.60 X ), Z, X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 1.18/1.60 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 1.18/1.60 'tc_nat' ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 1.18/1.60 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 1.18/1.60 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 1.18/1.60 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.60 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.18/1.60 , 'c_Power_Opower__class_Opower'( Y, Z, X ) ), ~(
% 1.18/1.60 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.60 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.60 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.60 , 'tc_nat' ), 'tc_nat' ), 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 X ), X ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Z,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'(
% 1.18/1.60 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.18/1.60 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.18/1.60 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.18/1.60 ), X ), ~( 'c_lessequals'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 'c_Int_OPls', Y,
% 1.18/1.60 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.60 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 1.18/1.60 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.60 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.60 ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.60 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.60 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 T, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.60 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X
% 1.18/1.60 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( T, Y, X ), X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.18/1.60 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.18/1.60 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.18/1.60 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.18/1.60 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.60 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.18/1.60 , Y, 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.18/1.60 'tc_Int_Oint' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.18/1.60 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.18/1.60 T, Z, X ) ) ), =( Y, T ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.18/1.60 , Z ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.18/1.60 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.18/1.60 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.18/1.60 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.18/1.60 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ),
% 1.18/1.60 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_Osucc'( X ), 'tc_nat' ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.18/1.60 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_Suc'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_Osucc'( Y ), X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.60 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.60 ), X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 Y, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), T, X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.60 , X ), X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.60 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.60 ), X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.60 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.60 , X ), X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.18/1.60 , T, X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 Y, T, X ), Z, X ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.18/1.60 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.18/1.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y, X )
% 1.18/1.60 , X ), Z ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 1.18/1.60 , X ), Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.60 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.18/1.60 'tc_nat' ), Z, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z
% 1.18/1.60 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.18/1.60 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 X ), T, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.18/1.60 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.18/1.60 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.18/1.60 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.60 'tc_nat' ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.18/1.60 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.18/1.60 'tc_nat' ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.18/1.60 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.18/1.60 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.18/1.60 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.18/1.60 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.18/1.60 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.60 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.18/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.18/1.60 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.18/1.60 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.60 , Z, X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.18/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.18/1.60 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.60 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X
% 1.18/1.60 ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.18/1.60 ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.60 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ),
% 1.18/1.60 ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X
% 1.18/1.60 ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.18/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.60 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.60 , T, X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.18/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.60 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.60 , T, X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.18/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.60 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.18/1.60 Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.60 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ) ), =( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.60 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.18/1.60 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.18/1.60 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.60 , T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), T, X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.60 , T, X ), Z, X ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.60 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.60 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.18/1.60 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.60 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.60 , T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.60 , T, X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.18/1.60 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 1.18/1.60 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 1.18/1.60 W, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 1.18/1.60 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 1.18/1.60 , X ), T, X ), W, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 1.18/1.60 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 1.18/1.60 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 1.18/1.60 W, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 1.18/1.60 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.18/1.60 , X ), W, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.60 , X ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.60 , X ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 1.18/1.60 , X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.18/1.60 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 1.18/1.60 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 1.18/1.60 Z, X ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.60 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.18/1.60 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 'tc_nat' ), 'tc_nat' ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.60 ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.60 ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Power_Opower__class_Opower'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.18/1.60 T, X ), 'c_Divides_Odiv__class_Odiv'( 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.60 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.18/1.60 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.18/1.60 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.18/1.60 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.18/1.60 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), Y,
% 1.18/1.60 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.18/1.60 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 1.18/1.60 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 1.18/1.60 , T ), =( X, Z ) ],
% 1.18/1.60 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.18/1.60 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 1.18/1.60 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 1.18/1.60 , T ), =( X, Z ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.60 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.18/1.60 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.60 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.18/1.60 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 1.18/1.60 , X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.18/1.60 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.18/1.60 Y, X ), Z, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.60 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.18/1.60 Y, X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.18/1.60 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.18/1.60 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.18/1.60 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.18/1.60 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.18/1.60 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.18/1.60 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( =( X, 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.18/1.60 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.18/1.60 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 1.18/1.60 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 1.18/1.60 X ), Z, X ) ) ],
% 1.18/1.60 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 'tc_nat' ), 'tc_nat' ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.60 , X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.60 , Z, X ), Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Int_Onat'(
% 1.18/1.60 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 'tc_nat' ), 'tc_Int_Oint' ) ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.60 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.18/1.60 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.18/1.60 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.60 ) ],
% 1.18/1.60 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 1.18/1.60 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.60 'tc_nat' ), X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.18/1.60 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.18/1.60 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.18/1.60 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'(
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ),
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 1.18/1.60 ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X
% 1.18/1.60 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X
% 1.18/1.60 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) )
% 1.18/1.60 ],
% 1.18/1.60 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.18/1.60 X ) ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 1.18/1.60 , X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.60 ), X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Int_Oiszero'( Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ 'c_HOL_Oeq__class_Oeq'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.18/1.60 'tc_Int_Oint' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ),
% 1.18/1.60 'tc_Int_Oint' ), ~( 'c_HOL_Oeq__class_Oeq'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ 'c_HOL_Oeq__class_Oeq'( X, Y, 'tc_Int_Oint' ), ~(
% 1.18/1.60 'c_HOL_Oeq__class_Oeq'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.18/1.60 'tc_Int_Oint' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ),
% 1.18/1.60 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ),
% 1.18/1.60 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) )
% 1.18/1.60 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.18/1.60 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 Y, X, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.18/1.60 , Y, 'tc_nat' ) ) ],
% 1.18/1.60 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'( Y,
% 1.18/1.60 X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.60 X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.18/1.60 Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.18/1.60 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.18/1.60 ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.18/1.60 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.18/1.60 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.18/1.60 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.18/1.60 , Y, X ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.18/1.60 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.18/1.60 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.60 'tc_nat' ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.18/1.60 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.18/1.60 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.18/1.60 'tc_nat' ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Nat_Osemiring__1__class_Oof__nat'( X
% 1.18/1.60 , 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint'
% 1.18/1.60 ), 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Nat_Osemiring__1__class_Oof__nat'( X
% 1.18/1.60 , 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint'
% 1.18/1.60 ), 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X,
% 1.18/1.60 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' ), 'tc_Int_Oint' )
% 1.18/1.60 , 'tc_Int_Oint' ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.18/1.60 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.18/1.60 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), Y,
% 1.18/1.60 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.60 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.60 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.60 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.18/1.60 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.18/1.60 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.18/1.60 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.18/1.60 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), =( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 1.18/1.60 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.18/1.60 ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.18/1.60 , X ), X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.18/1.60 , X ), X ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.60 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.18/1.60 ],
% 1.18/1.60 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.18/1.60 ), 'tc_nat' ), X ) ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.18/1.60 , X, 'tc_nat' ), X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~( 'c_lessequals'( Y,
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.18/1.60 ), Y ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.18/1.60 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 1.18/1.60 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.18/1.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.18/1.60 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 1.18/1.60 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.18/1.60 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.18/1.60 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.18/1.60 , Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.18/1.60 ), Y ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.18/1.60 ), Y ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.18/1.60 ), Y ) ],
% 1.18/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.18/1.60 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.18/1.60 X ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.18/1.60 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.18/1.60 'tc_Int_Oint' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_Int_Oint' ),
% 1.18/1.60 'tc_Int_Oint' ), ~( 'c_lessequals'( Y, T, 'tc_Int_Oint' ) ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( X, Z, 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.18/1.60 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.18/1.60 , X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.18/1.60 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.18/1.60 , X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.18/1.60 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.60 , X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.18/1.60 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.60 , X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.18/1.60 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.18/1.60 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.60 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.18/1.60 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.18/1.60 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 1.18/1.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.18/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.18/1.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.60 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.18/1.60 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.60 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.18/1.60 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.60 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.18/1.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.60 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.60 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.60 , X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.18/1.60 ), X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.60 , X ), 'c_Int_Onumber__class_Onumber__of'( 'c_HOL_Oplus__class_Oplus'( Y
% 1.18/1.60 , 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint' ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.60 , X ), 'c_Int_Onumber__class_Onumber__of'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.60 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.18/1.60 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint' ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.60 , X ), ~( 'c_lessequals'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint'
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, 'c_Int_OBit1'(
% 1.18/1.60 'c_Int_OPls' ), 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.60 , X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y,
% 1.18/1.60 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.60 , X ), ~( 'c_lessequals'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint'
% 1.18/1.60 ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 'c_Int_OBit1'(
% 1.18/1.60 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.60 , X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.60 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.60 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), X ), X ) ],
% 1.18/1.60 [ 'c_HOL_Oeq__class_Oeq'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.18/1.60 'tc_Int_Oint' ), ~( 'c_HOL_Oeq__class_Oeq'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ 'c_HOL_Oeq__class_Oeq'( X, Y, 'tc_Int_Oint' ), ~(
% 1.18/1.60 'c_HOL_Oeq__class_Oeq'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.18/1.60 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.18/1.60 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.60 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.18/1.60 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.60 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.18/1.60 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.18/1.60 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.18/1.60 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.18/1.60 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit1'( X ),
% 1.18/1.60 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit1'( X ),
% 1.18/1.60 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.18/1.60 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OPls', 'tc_Int_Oint' ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OPls',
% 1.18/1.60 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ 'c_HOL_Oeq__class_Oeq'( 'c_Int_OPls', 'c_Int_OPls', 'tc_Int_Oint' ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.18/1.60 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Int_OPls', 'tc_Int_Oint' ), X )
% 1.18/1.60 ],
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_OPls', X, 'tc_Int_Oint' ), X ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Int_OPls', 'tc_Int_Oint' ), X ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.18/1.60 ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.60 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.18/1.60 ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.60 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.18/1.60 , X ) ) ],
% 1.18/1.60 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.18/1.60 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_Int_Oint' ) ) ],
% 1.18/1.60 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.18/1.60 , Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.18/1.60 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.60 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.60 ), X ) ],
% 1.18/1.60 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.18/1.60 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.60 X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.60 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.18/1.60 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.18/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.18/1.60 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.18/1.60 X ), Z, X ) ) ],
% 1.18/1.60 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.18/1.61 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.61 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.61 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.61 , X ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.18/1.61 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.18/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.18/1.61 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.18/1.61 , Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( Z, Y, X ), X ), Z ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), Z ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.61 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.18/1.61 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.18/1.61 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.18/1.61 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.61 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.18/1.61 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.61 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.18/1.61 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.61 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.61 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.18/1.61 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.18/1.61 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.61 [ ~( 'class_HOL_Oeq'( X ) ), =( Y, Z ), ~( 'c_HOL_Oeq__class_Oeq'( Y, Z
% 1.18/1.61 , X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), X ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.18/1.61 , X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.61 , X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( X,
% 1.18/1.61 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' )
% 1.18/1.61 , 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( X,
% 1.18/1.61 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' )
% 1.18/1.61 , 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( X,
% 1.18/1.61 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' )
% 1.18/1.61 , 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( X,
% 1.18/1.61 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' )
% 1.18/1.61 , 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.18/1.61 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.18/1.61 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.18/1.61 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z,
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.61 ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.61 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.18/1.61 [ =( 'c_Int_Onat'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint'
% 1.18/1.61 ) ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ],
% 1.18/1.61 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.18/1.61 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.61 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.18/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 1.18/1.61 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.18/1.61 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.18/1.61 , Z, 'tc_nat' ) ) ],
% 1.18/1.61 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.61 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.18/1.61 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.61 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.61 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.61 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.18/1.61 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.61 , 'tc_nat' ), X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.18/1.61 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 1.18/1.61 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.18/1.61 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.18/1.61 ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( T ), X ),
% 1.18/1.61 'c_Power_Opower__class_Opower'( Z, 'c_Suc'( T ), X ), X ) ) ],
% 1.18/1.61 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.61 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( T,
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( Y, U, 'tc_nat' ), 'tc_nat' ) ) ), =(
% 1.18/1.61 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.18/1.61 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.18/1.61 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.61 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.18/1.61 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.18/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.61 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.18/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.61 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.18/1.61 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.18/1.61 Y, T, X ) ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X
% 1.18/1.61 ), Y, X ) ), =( Z, T ) ],
% 1.18/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.18/1.61 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.61 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.18/1.61 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.18/1.61 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_Divides_Osemiring__div'( X )
% 1.18/1.61 ), =( 'c_Divides_Odiv__class_Omod'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 Y, X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.18/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_Divides_Osemiring__div'( X )
% 1.18/1.61 ), ~( =( 'c_Divides_Odiv__class_Omod'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.61 , 'tc_nat' ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.18/1.61 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.61 , 'tc_nat' ), 'tc_nat' ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.61 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.61 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.61 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.18/1.61 ), X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.18/1.61 Y, X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.18/1.61 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.18/1.61 X ), X ) ) ],
% 1.18/1.61 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.61 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y
% 1.18/1.61 , Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X
% 1.18/1.61 ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z
% 1.18/1.61 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_Power_Opower__class_Opower'( Y
% 1.18/1.61 , Z, X ), X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.18/1.61 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y,
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( T, X )
% 1.18/1.61 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.61 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ),
% 1.18/1.61 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ),
% 1.18/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.18/1.61 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.18/1.61 ) ), X, 'tc_nat' ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 1.18/1.61 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.18/1.61 ) ), X, 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.61 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 1.18/1.61 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 Y, 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.61 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.61 Z, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'(
% 1.18/1.61 Z, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), 'c_Int_Oiszero'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.18/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.61 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 1.18/1.61 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 1.18/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.18/1.61 ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.18/1.61 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.18/1.61 ) ],
% 1.18/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), 'c_Suc'( 'c_Suc'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.18/1.61 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 1.18/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.18/1.61 ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.61 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.61 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.61 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.18/1.61 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.61 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.18/1.61 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.18/1.61 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.18/1.61 X ), T, X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.18/1.61 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.18/1.61 X ), T, X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.61 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 1.18/1.61 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ),
% 1.18/1.61 'tc_Int_Oint' ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ),
% 1.18/1.61 'tc_Int_Oint' ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y )
% 1.18/1.61 , 'tc_Int_Oint' ), 'c_Int_OBit0'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.18/1.61 'c_Int_Osucc'( Y ), 'tc_Int_Oint' ) ) ) ],
% 1.18/1.61 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y
% 1.18/1.61 ), 'tc_Int_Oint' ), 'c_Int_OBit1'( 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.61 'c_Int_Opred'( X ), Y, 'tc_Int_Oint' ) ) ) ],
% 1.18/1.61 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.18/1.61 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.61 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.18/1.61 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.61 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.18/1.61 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.18/1.61 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.18/1.61 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.18/1.61 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y )
% 1.18/1.61 , 'tc_Int_Oint' ), 'c_Int_OBit0'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.18/1.61 'tc_Int_Oint' ) ) ) ],
% 1.18/1.61 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y
% 1.18/1.61 ), 'tc_Int_Oint' ), 'c_Int_OBit0'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.18/1.61 'tc_Int_Oint' ) ) ) ],
% 1.18/1.61 [ =( 'c_Int_OBit0'( X ), 'c_HOL_Oplus__class_Oplus'( X, X, 'tc_Int_Oint'
% 1.18/1.61 ) ) ],
% 1.18/1.61 [ 'c_HOL_Oeq__class_Oeq'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.18/1.61 'tc_Int_Oint' ), ~( 'c_HOL_Oeq__class_Oeq'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'c_HOL_Oeq__class_Oeq'( X, Y, 'tc_Int_Oint' ), ~(
% 1.18/1.61 'c_HOL_Oeq__class_Oeq'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.18/1.61 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.18/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.18/1.61 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.61 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.61 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.18/1.61 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.18/1.61 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.18/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.18/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X
% 1.18/1.61 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.18/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.18/1.61 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.18/1.61 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.18/1.61 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.61 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.18/1.61 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.61 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.18/1.61 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.18/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.18/1.61 , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.18/1.61 , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 1.18/1.61 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, Z, X ), T, X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.18/1.61 X ), Y ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.18/1.61 X ), Y ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.18/1.61 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 1.18/1.61 Y, Z, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.18/1.61 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.61 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.18/1.61 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.18/1.61 Y, X ), Z, X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.61 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.61 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.61 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.61 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.18/1.61 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.61 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.18/1.61 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.61 ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.61 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.18/1.61 Z, T, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.18/1.61 , T, X ), 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 Z, T, 'tc_nat' ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.61 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 1.18/1.61 , 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X
% 1.18/1.61 ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.18/1.61 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.18/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.18/1.61 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.18/1.61 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.18/1.61 , 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.18/1.61 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.18/1.61 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.18/1.61 , 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X,
% 1.18/1.61 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.18/1.61 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.18/1.61 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ), 'c_lessequals'( X
% 1.18/1.61 , 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.18/1.61 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.18/1.61 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.18/1.61 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.18/1.61 , ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.61 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' )
% 1.18/1.61 ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.61 , 'tc_nat' ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.18/1.61 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.18/1.61 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.61 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.61 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.18/1.61 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.61 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.61 'c_HOL_Oone__class_Oone'( X ), X ), 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), Y, 'tc_nat' ) ), X ),
% 1.18/1.61 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'(
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' )
% 1.18/1.61 ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.61 'c_Suc'( 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' )
% 1.18/1.61 ), X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.61 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.61 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), X ), X ), X ) ) ],
% 1.18/1.61 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.18/1.61 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'(
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' )
% 1.18/1.61 ), 'tc_nat' ) ) ],
% 1.18/1.61 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.18/1.61 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.61 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'( 'c_Suc'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.18/1.61 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Int_Onat'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_Int_Oint' ) ) ) ],
% 1.18/1.61 [ =( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.18/1.61 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.18/1.61 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ) ), X ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.18/1.61 Y, Z, X ), X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Z,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ) ), X ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.61 'c_HOL_Oone__class_Oone'( X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), Y, 'tc_nat' ), X ),
% 1.18/1.61 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' )
% 1.18/1.61 , X ), X ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 X ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ), X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), X ), =( Z,
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), X ), =( Y,
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.18/1.61 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), X )
% 1.18/1.61 ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.18/1.61 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.18/1.61 ) ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit1'( Y ), X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.61 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.18/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), 'c_Int_Oiszero'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ) ],
% 1.18/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), Y, X ), Y ) ],
% 1.18/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'( Y
% 1.18/1.61 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ), Y ) ],
% 1.18/1.61 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.18/1.61 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.18/1.61 ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y
% 1.18/1.61 ), X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.18/1.61 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.18/1.61 Y ), X ), X ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.61 , X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.61 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), X ), Y, X ), 'c_HOL_Oplus__class_Oplus'( Y, Y, X ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 Y, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), X ), X ), 'c_HOL_Oplus__class_Oplus'( Y, Y, X ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.18/1.61 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), Y, X ), Z, X ), X )
% 1.18/1.61 ) ],
% 1.18/1.61 [ ~( 'c_HOL_Oeq__class_Oeq'( 'c_Int_OPls', 'c_Int_OBit1'( X ),
% 1.18/1.61 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ =( 'c_Int_Osucc'( 'c_Int_OPls' ), 'c_Int_OBit1'( 'c_Int_OPls' ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ ~( 'c_HOL_Oeq__class_Oeq'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.18/1.61 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ), ~(
% 1.18/1.61 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.61 'c_Int_OPls', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.61 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.61 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.18/1.61 ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.61 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.61 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.18/1.61 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.18/1.61 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.18/1.61 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.18/1.61 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.18/1.61 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.61 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.18/1.61 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.18/1.61 X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.61 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.18/1.61 Z, T, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.18/1.61 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'(
% 1.18/1.61 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.18/1.61 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.18/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 1.18/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.61 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.61 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.18/1.61 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.18/1.61 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.18/1.61 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.61 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.18/1.61 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.61 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.61 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.18/1.61 , X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.61 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.61 ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.18/1.61 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.18/1.61 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 1.18/1.61 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.18/1.61 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.61 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Power_Opower__class_Opower'(
% 1.18/1.61 Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.61 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.18/1.61 'tc_Int_Oint' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_Int_Oint' ),
% 1.18/1.61 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_Int_Oint' ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.18/1.61 ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.18/1.61 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.61 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.18/1.61 X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.61 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 Z, T, X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 Z, T, X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.61 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.18/1.61 X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.61 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 Y, T, X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 Y, T, X ) ) ],
% 1.18/1.61 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.18/1.61 [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( Z, Y,
% 1.18/1.61 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( X, Z, 'tc_RealDef_Oreal' ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'c_lessequals'( X, X, 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( Z, Y,
% 1.18/1.61 'tc_Int_Oint' ) ), ~( 'c_lessequals'( X, Z, 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_lessequals'( X, X, 'tc_Int_Oint' ) ],
% 1.18/1.61 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.18/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.18/1.61 , X ) ) ],
% 1.18/1.61 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.18/1.61 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.18/1.61 , X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.61 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 1.18/1.61 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.18/1.61 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.18/1.61 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.18/1.61 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.18/1.61 ) ) ],
% 1.18/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.18/1.61 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.18/1.61 ) ) ],
% 1.18/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.18/1.61 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.61 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.18/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.18/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.18/1.61 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( Y, X,
% 1.18/1.61 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.61 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.18/1.61 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.61 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.61 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.61 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.18/1.61 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.18/1.61 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.61 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 1.18/1.61 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.61 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 1.18/1.61 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.61 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.18/1.61 , X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 1.18/1.61 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.61 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.61 ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.61 ), X ), Z, X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.18/1.61 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.18/1.61 , Y, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.61 ) ],
% 1.18/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 1.18/1.61 , X ), X ), Y ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.61 ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.18/1.61 , Y, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.18/1.61 , T, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.18/1.61 , T, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.18/1.61 , Y, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.18/1.61 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.18/1.61 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.61 , 'tc_nat' ), X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.18/1.61 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.61 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~( 'c_Int_Oiszero'(
% 1.18/1.61 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.61 'tc_nat' ), X ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Z, Y, X
% 1.18/1.61 ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.18/1.61 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.18/1.61 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.18/1.61 ), X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.18/1.61 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.18/1.61 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.61 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.18/1.61 ), X ) ) ],
% 1.18/1.61 [ =( X, 'c_Int_Onat'( 'c_Nat_Osemiring__1__class_Oof__nat'( X,
% 1.18/1.61 'tc_Int_Oint' ) ) ) ],
% 1.18/1.61 [ =( 'c_Int_Onat'( 'c_Nat_Osemiring__1__class_Oof__nat'( X,
% 1.18/1.61 'tc_Int_Oint' ) ), X ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.61 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.61 ), =( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.18/1.61 , U, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( U,
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.18/1.61 , U, X ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.18/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.61 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 1.18/1.61 , X ) ) ],
% 1.18/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.61 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 1.18/1.61 , X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.18/1.61 ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.18/1.61 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.18/1.61 ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.18/1.61 Y, X ), X ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y, X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.61 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( Y,
% 1.18/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.18/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.18/1.61 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ),
% 1.18/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.61 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 1.18/1.61 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.18/1.61 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.18/1.61 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 1.18/1.61 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.61 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.18/1.61 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.18/1.61 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.18/1.61 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.18/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.18/1.61 'c_lessequals'( Z, Y, X ) ],
% 1.18/1.61 [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), 'c_lessequals'( Y, X,
% 1.18/1.61 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.18/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 1.18/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 1.18/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.18/1.61 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 1.18/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 1.18/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 1.18/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.18/1.61 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), 'c_lessequals'( Y, X,
% 1.18/1.61 'tc_Int_Oint' ) ],
% 1.18/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.18/1.61 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.18/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.18/1.61 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.18/1.61 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.18/1.61 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.18/1.61 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ =( 'c_Int_Osucc'( 'c_Int_OBit1'( X ) ), 'c_Int_OBit0'( 'c_Int_Osucc'(
% 1.18/1.61 X ) ) ) ],
% 1.18/1.61 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y )
% 1.18/1.61 , 'tc_Int_Oint' ), 'c_Int_OBit1'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.18/1.61 'tc_Int_Oint' ) ) ) ],
% 1.18/1.61 [ =( 'c_Int_Osucc'( 'c_Int_OBit0'( X ) ), 'c_Int_OBit1'( X ) ) ],
% 1.18/1.61 [ ~( 'c_HOL_Oeq__class_Oeq'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.18/1.61 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.18/1.61 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.61 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.18/1.61 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.61 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ =( 'c_Int_Opred'( 'c_Int_OBit1'( X ) ), 'c_Int_OBit0'( X ) ) ],
% 1.18/1.61 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y
% 1.18/1.61 ), 'tc_Int_Oint' ), 'c_Int_OBit1'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.18/1.61 'tc_Int_Oint' ) ) ) ],
% 1.18/1.61 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y )
% 1.18/1.61 , 'tc_Int_Oint' ), 'c_Int_OBit1'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.18/1.61 'tc_Int_Oint' ) ) ) ],
% 1.18/1.61 [ ~( 'c_HOL_Oeq__class_Oeq'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ),
% 1.18/1.61 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ =( 'c_Int_Opred'( 'c_Int_OBit0'( X ) ), 'c_Int_OBit1'( 'c_Int_Opred'(
% 1.18/1.61 X ) ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.18/1.61 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.18/1.61 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.18/1.61 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.18/1.61 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y
% 1.18/1.61 ), 'tc_Int_Oint' ), 'c_Int_OBit0'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.18/1.61 'tc_Int_Oint' ) ) ) ],
% 1.18/1.61 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.18/1.61 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.61 'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.18/1.61 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X,
% 1.18/1.61 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.18/1.61 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_HOL_Oeq__class_Oeq'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.18/1.61 'tc_Int_Oint' ), ~( 'c_HOL_Oeq__class_Oeq'( 'c_Int_OPls', X,
% 1.18/1.61 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_HOL_Oeq__class_Oeq'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.18/1.61 'c_HOL_Oeq__class_Oeq'( 'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' )
% 1.18/1.61 ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.18/1.61 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.18/1.61 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.18/1.61 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ), ~(
% 1.18/1.61 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.61 'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.18/1.61 'tc_Int_Oint' ), 'c_Int_OBit0'( 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.61 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ) ],
% 1.18/1.61 [ 'c_HOL_Oeq__class_Oeq'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.18/1.61 'tc_Int_Oint' ), ~( 'c_HOL_Oeq__class_Oeq'( X, 'c_Int_OPls',
% 1.18/1.61 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_HOL_Oeq__class_Oeq'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.18/1.61 'c_HOL_Oeq__class_Oeq'( 'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' )
% 1.18/1.61 ) ],
% 1.18/1.61 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.18/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.18/1.61 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.18/1.61 ) ],
% 1.18/1.61 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Int_Onat'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_Int_Oint' ) ) ) ],
% 1.18/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X, X,
% 1.18/1.61 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.18/1.61 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.18/1.61 [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ), ~(
% 1.18/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.18/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.18/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' )
% 1.18/1.61 ) ],
% 1.18/1.61 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.18/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.18/1.61 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' )
% 1.18/1.61 , 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.18/1.61 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.18/1.61 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.18/1.61 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_Int_Oint' ) ) ],
% 1.18/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.18/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ), 'tc_nat' ) ],
% 1.18/1.61 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.18/1.61 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.61 [ =( 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.18/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.18/1.61 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 1.18/1.61 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.18/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.18/1.61 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.18/1.61 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( X, X, 'tc_nat' ) ) ],
% 1.18/1.61 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' )
% 1.18/1.61 , 'c_HOL_Oplus__class_Oplus'( X, X, 'tc_nat' ) ) ],
% 1.18/1.61 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.18/1.61 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.18/1.61 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.18/1.61 ), ~( =( 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.61 ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.61 ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.18/1.61 ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.18/1.61 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.18/1.61 ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.61 ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.61 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' )
% 1.18/1.61 , X ), 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ), X ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.18/1.61 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ), =( Y
% 1.18/1.61 , Z ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), =(
% 1.18/1.61 Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.61 [ =( 'c_Power_Opower__class_Opower'(
% 1.18/1.61 'c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt'( 'v_z' ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_Complex_Ocomplex' ), 'v_z' ), ~(
% 1.18/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 1.18/1.61 'v_x____', 'tc_RealDef_Oreal' ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.61 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.18/1.61 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X
% 1.18/1.61 ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.61 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.18/1.61 ), Y ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.61 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.18/1.61 ), Y ) ],
% 1.18/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.18/1.61 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.61 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.18/1.61 ) ],
% 1.18/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.18/1.61 ) ) ],
% 1.18/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), Y
% 1.18/1.61 , X ), Y ) ],
% 1.18/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 Y, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.18/1.61 , X ), Y ) ],
% 1.18/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.18/1.61 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.18/1.61 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), X ), Y, X ), Z, X ), X ) ) ],
% 1.18/1.61 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.18/1.61 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.18/1.61 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.18/1.61 'tc_nat' ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit1'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y
% 1.18/1.61 , X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.18/1.61 Y, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.18/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.61 ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ), X ),
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.18/1.61 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.18/1.61 'c_HOL_Otimes__class_Otimes'( Y, Y, X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.18/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ],
% 1.18/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.61 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y,
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_Power_Opower__class_Opower'( Y
% 1.18/1.61 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ],
% 1.18/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.18/1.61 X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.61 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.18/1.61 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.18/1.61 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.18/1.61 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.18/1.61 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.18/1.61 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.18/1.61 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.18/1.61 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.18/1.61 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.18/1.61 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.18/1.61 [ =( 'c_Power_Opower__class_Opower'( 'c_NthRoot_Osqrt'(
% 1.18/1.61 'c_HOL_Ouminus__class_Ouminus'( 'v_x____', 'tc_RealDef_Oreal' ) ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_RealDef_Oreal' ),
% 1.18/1.61 'c_HOL_Ouminus__class_Ouminus'( 'v_x____', 'tc_RealDef_Oreal' ) ) ],
% 1.18/1.61 [ =( 'v_z', 'c_Complex_Ocomplex_OComplex'( 'v_x____', 'v_y____' ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ =( 'v_y____', 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 1.18/1.61 'c_HOL_Ouminus__class_Ouminus'( 'v_x____', 'tc_RealDef_Oreal' ),
% 1.18/1.61 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ ~( =( 'c_Power_Opower__class_Opower'(
% 1.18/1.61 'c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt'( 'v_z' ),
% 1.18/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_Complex_Ocomplex' ), 'v_z' ) ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.18/1.61 ],
% 1.18/1.61 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.18/1.61 ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.18/1.61 ],
% 1.18/1.61 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_HOL_Oeq'( 'tc_nat' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.18/1.61 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.18/1.61 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.18/1.61 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.18/1.61 ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.18/1.61 ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Nat_Osemiring__char__0'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Odvd'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_HOL_Oeq'( 'tc_Int_Oint' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.18/1.61 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.18/1.61 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.18/1.61 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.18/1.61 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.18/1.61 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.18/1.61 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_RealDef_Oreal'
% 1.18/1.61 ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 1.18/1.61 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'(
% 1.18/1.61 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_RealDef_Oreal'
% 1.18/1.61 ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_RealDef_Oreal'
% 1.18/1.61 ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_RealDef_Oreal' )
% 1.18/1.61 ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_RealDef_Oreal' )
% 1.18/1.61 ],
% 1.18/1.61 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_RealDef_Oreal' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_RealDef_Oreal' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_RealDef_Oreal' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_RealDef_Oreal' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_RealDef_Oreal' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_RealDef_Oreal' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_RealDef_Oreal' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_RealDef_Oreal' ) ]
% 1.18/1.61 ,
% 1.18/1.61 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oordered__field'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_RealVector_Oreal__normed__field'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Oab__group__add'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Omult__zero'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Omult__mono'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Osemiring'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Omonoid__add'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_OrderedGroup_Ogroup__add'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oring__1'( 'tc_RealDef_Oreal' ) ],
% 1.18/1.61 [ 'class_Ring__and__Field_Oabs__if'( 'tc_RealDef_Oreal' ) ],
% 1.22/1.61 [ 'class_RealVector_Oreal__field'( 'tc_RealDef_Oreal' ) ],
% 1.22/1.61 [ 'class_Ring__and__Field_Ofield'( 'tc_RealDef_Oreal' ) ],
% 1.22/1.61 [ 'class_Ring__and__Field_Oring'( 'tc_RealDef_Oreal' ) ],
% 1.22/1.61 [ 'class_Ring__and__Field_Oidom'( 'tc_RealDef_Oreal' ) ],
% 1.22/1.61 [ 'class_Nat_Osemiring__char__0'( 'tc_RealDef_Oreal' ) ],
% 1.22/1.61 [ 'class_Ring__and__Field_Odvd'( 'tc_RealDef_Oreal' ) ],
% 1.22/1.61 [ 'class_Orderings_Opreorder'( 'tc_RealDef_Oreal' ) ],
% 1.22/1.61 [ 'class_Orderings_Olinorder'( 'tc_RealDef_Oreal' ) ],
% 1.22/1.61 [ 'class_Orderings_Oorder'( 'tc_RealDef_Oreal' ) ],
% 1.22/1.61 [ 'class_Int_Oring__char__0'( 'tc_RealDef_Oreal' ) ],
% 1.22/1.61 [ 'class_Int_Onumber__ring'( 'tc_RealDef_Oreal' ) ],
% 1.22/1.61 [ 'class_Power_Opower'( 'tc_RealDef_Oreal' ) ],
% 1.22/1.61 [ 'class_Int_Onumber'( 'tc_RealDef_Oreal' ) ],
% 1.22/1.61 [ 'class_HOL_Oeq'( 'tc_RealDef_Oreal' ) ],
% 1.22/1.61 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.22/1.61 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.22/1.61 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.22/1.61 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.22/1.61 ],
% 1.22/1.61 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.22/1.61 ],
% 1.22/1.61 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.22/1.61 ],
% 1.22/1.61 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_Complex_Ocomplex' ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_RealVector_Oreal__field'( 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_Nat_Osemiring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_Ring__and__Field_Odvd'( 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ],
% 1.22/1.61 [ 'class_HOL_Oeq'( 'tc_Complex_Ocomplex' ) ]
% 1.22/1.61 ] .
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 percentage equality = 0.211214, percentage horn = 0.849528
% 1.22/1.61 This is a problem with some equality
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 Options Used:
% 1.22/1.61
% 1.22/1.61 useres = 1
% 1.22/1.61 useparamod = 1
% 1.22/1.61 useeqrefl = 1
% 1.22/1.61 useeqfact = 1
% 1.22/1.61 usefactor = 1
% 1.22/1.61 usesimpsplitting = 0
% 1.22/1.61 usesimpdemod = 5
% 1.22/1.61 usesimpres = 3
% 1.22/1.61
% 1.22/1.61 resimpinuse = 1000
% 1.22/1.61 resimpclauses = 20000
% 1.22/1.61 substype = eqrewr
% 1.22/1.61 backwardsubs = 1
% 1.22/1.61 selectoldest = 5
% 1.22/1.61
% 1.22/1.61 litorderings [0] = split
% 1.22/1.61 litorderings [1] = extend the termordering, first sorting on arguments
% 1.22/1.61
% 1.22/1.61 termordering = kbo
% 1.22/1.61
% 1.22/1.61 litapriori = 0
% 1.22/1.61 termapriori = 1
% 1.22/1.61 litaposteriori = 0
% 1.22/1.61 termaposteriori = 0
% 1.22/1.61 demodaposteriori = 0
% 1.22/1.61 ordereqreflfact = 0
% 1.22/1.61
% 1.22/1.61 litselect = negord
% 1.22/1.61
% 1.22/1.61 maxweight = 15
% 1.22/1.61 maxdepth = 30000
% 1.22/1.61 maxlength = 115
% 1.22/1.61 maxnrvars = 195
% 1.22/1.61 excuselevel = 1
% 1.22/1.61 increasemaxweight = 1
% 1.22/1.61
% 1.22/1.61 maxselected = 10000000
% 1.22/1.61 maxnrclauses = 10000000
% 1.22/1.61
% 1.22/1.61 showgenerated = 0
% 1.22/1.61 showkept = 0
% 1.22/1.61 showselected = 0
% 1.22/1.61 showdeleted = 0
% 1.22/1.61 showresimp = 1
% 1.22/1.61 showstatus = 2000
% 1.22/1.61
% 1.22/1.61 prologoutput = 1
% 1.22/1.61 nrgoals = 5000000
% 1.22/1.61 totalproof = 1
% 1.22/1.61
% 1.22/1.61 Symbols occurring in the translation:
% 1.22/1.61
% 1.22/1.61 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.22/1.61 . [1, 2] (w:1, o:147, a:1, s:1, b:0),
% 1.22/1.61 ! [4, 1] (w:0, o:63, a:1, s:1, b:0),
% 1.22/1.61 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.22/1.61 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.22/1.61 'class_Ring__and__Field_Omult__mono' [40, 1] (w:1, o:69, a:1, s:1, b:
% 1.22/1.61 0),
% 1.22/1.61 'c_HOL_Otimes__class_Otimes' [43, 3] (w:1, o:180, a:1, s:1, b:0),
% 1.22/1.61 'c_lessequals' [45, 3] (w:1, o:181, a:1, s:1, b:0),
% 1.22/1.61 'c_HOL_Ozero__class_Ozero' [46, 1] (w:1, o:70, a:1, s:1, b:0),
% 1.22/1.62 'class_Ring__and__Field_Omult__mono1' [47, 1] (w:1, o:71, a:1, s:1
% 1.22/1.62 , b:0),
% 1.22/1.62 'tc_nat' [49, 0] (w:1, o:17, a:1, s:1, b:0),
% 1.22/1.62 'c_Divides_Odiv__class_Omod' [50, 3] (w:1, o:182, a:1, s:1, b:0),
% 1.22/1.62 'c_HOL_Oplus__class_Oplus' [52, 3] (w:1, o:184, a:1, s:1, b:0),
% 1.22/1.62 'c_HOL_Oord__class_Oless' [53, 3] (w:1, o:183, a:1, s:1, b:0),
% 1.22/1.62 'class_Ring__and__Field_Ofield' [54, 1] (w:1, o:72, a:1, s:1, b:0),
% 1.22/1.62 'class_Ring__and__Field_Odivision__by__zero' [55, 1] (w:1, o:77, a:1
% 1.22/1.62 , s:1, b:0),
% 1.22/1.62 'c_HOL_Oinverse__class_Odivide' [56, 3] (w:1, o:185, a:1, s:1, b:0),
% 1.22/1.62
% 1.22/1.62 'c_HOL_Oinverse__class_Oinverse' [57, 2] (w:1, o:172, a:1, s:1, b:0)
% 1.22/1.62 ,
% 1.22/1.62 'class_Ring__and__Field_Oordered__semidom' [58, 1] (w:1, o:81, a:1
% 1.22/1.62 , s:1, b:0),
% 1.22/1.62 'c_Power_Opower__class_Opower' [60, 3] (w:1, o:186, a:1, s:1, b:0),
% 1.22/1.62 'c_HOL_Oone__class_Oone' [61, 1] (w:1, o:82, a:1, s:1, b:0),
% 1.22/1.62 'class_Ring__and__Field_Oordered__field' [62, 1] (w:1, o:83, a:1, s:1
% 1.22/1.62 , b:0),
% 1.22/1.62 'class_RealVector_Oreal__normed__field' [63, 1] (w:1, o:84, a:1, s:1
% 1.22/1.62 , b:0),
% 1.22/1.62 'c_HOL_Ominus__class_Ominus' [64, 3] (w:1, o:187, a:1, s:1, b:0),
% 1.22/1.62 'c_HOL_Ouminus__class_Ouminus' [66, 2] (w:1, o:173, a:1, s:1, b:0),
% 1.22/1.62 'c_Divides_Odiv__class_Odiv' [68, 3] (w:1, o:188, a:1, s:1, b:0),
% 1.22/1.62 'class_Ring__and__Field_Ocomm__semiring__1' [69, 1] (w:1, o:75, a:1
% 1.22/1.62 , s:1, b:0),
% 1.22/1.62 'c_Ring__and__Field_Odvd__class_Odvd' [70, 3] (w:1, o:189, a:1, s:1
% 1.22/1.62 , b:0),
% 1.22/1.62 'class_OrderedGroup_Ogroup__add' [71, 1] (w:1, o:86, a:1, s:1, b:0),
% 1.22/1.62
% 1.22/1.62 'class_OrderedGroup_Opordered__ab__group__add__abs' [72, 1] (w:1, o:
% 1.22/1.62 88, a:1, s:1, b:0),
% 1.22/1.62 'c_HOL_Oabs__class_Oabs' [73, 2] (w:1, o:174, a:1, s:1, b:0),
% 1.22/1.62 'class_Ring__and__Field_Oordered__semiring__strict' [74, 1] (w:1, o:
% 1.22/1.62 89, a:1, s:1, b:0),
% 1.22/1.62 'class_Ring__and__Field_Oordered__ring__strict' [75, 1] (w:1, o:80
% 1.22/1.62 , a:1, s:1, b:0),
% 1.22/1.62 'class_Divides_Osemiring__div' [76, 1] (w:1, o:91, a:1, s:1, b:0),
% 1.22/1.62 'class_Ring__and__Field_Oordered__idom' [77, 1] (w:1, o:92, a:1, s:1
% 1.22/1.62 , b:0),
% 1.22/1.62 'class_Int_Onumber__ring' [78, 1] (w:1, o:94, a:1, s:1, b:0),
% 1.22/1.62 'c_Int_Onumber__class_Onumber__of' [80, 2] (w:1, o:175, a:1, s:1, b:0
% 1.22/1.62 ),
% 1.22/1.62 'c_Int_OPls' [81, 0] (w:1, o:33, a:1, s:1, b:0),
% 1.22/1.62 'tc_Int_Oint' [82, 0] (w:1, o:34, a:1, s:1, b:0),
% 1.22/1.62 'c_Suc' [83, 1] (w:1, o:95, a:1, s:1, b:0),
% 1.22/1.62 'c_Parity_Oeven__odd__class_Oeven' [84, 2] (w:1, o:176, a:1, s:1, b:0
% 1.22/1.62 ),
% 1.22/1.62 'class_Ring__and__Field_Osemiring__0' [85, 1] (w:1, o:100, a:1, s:1
% 1.22/1.62 , b:0),
% 1.22/1.62 'class_Power_Opower' [86, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.22/1.62 'class_Ring__and__Field_Ozero__neq__one' [87, 1] (w:1, o:122, a:1, s:
% 1.22/1.62 1, b:0),
% 1.22/1.62 'class_Ring__and__Field_Ono__zero__divisors' [88, 1] (w:1, o:79, a:1
% 1.22/1.62 , s:1, b:0),
% 1.22/1.62 'class_Ring__and__Field_Omult__zero' [89, 1] (w:1, o:78, a:1, s:1, b:
% 1.22/1.62 0),
% 1.22/1.62 'class_Int_Onumber' [90, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.22/1.62 'class_OrderedGroup_Opordered__ab__group__add' [93, 1] (w:1, o:101
% 1.22/1.62 , a:1, s:1, b:0),
% 7.19/7.54 'class_OrderedGroup_Oab__semigroup__idem__mult' [96, 1] (w:1, o:102
% 7.19/7.54 , a:1, s:1, b:0),
% 7.19/7.54 'class_OrderedGroup_Olordered__ab__group__add' [99, 1] (w:1, o:103
% 7.19/7.54 , a:1, s:1, b:0),
% 7.19/7.54 'class_Ring__and__Field_Oring' [100, 1] (w:1, o:96, a:1, s:1, b:0),
% 7.19/7.54 'class_Ring__and__Field_Opordered__ring__abs' [101, 1] (w:1, o:126
% 7.19/7.54 , a:1, s:1, b:0),
% 7.19/7.54 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [102, 1]
% 7.19/7.54 (w:1, o:104, a:1, s:1, b:0),
% 7.19/7.54 'class_OrderedGroup_Opordered__ab__semigroup__add' [103, 1] (w:1, o:
% 7.19/7.54 105, a:1, s:1, b:0),
% 7.19/7.54 'class_Ring__and__Field_Oidom' [106, 1] (w:1, o:127, a:1, s:1, b:0),
% 7.19/7.54
% 7.19/7.54 'class_Orderings_Olinorder' [107, 1] (w:1, o:106, a:1, s:1, b:0),
% 7.19/7.54 'class_Orderings_Oorder' [108, 1] (w:1, o:107, a:1, s:1, b:0),
% 7.19/7.54 'class_Ring__and__Field_Opordered__ring' [109, 1] (w:1, o:128, a:1
% 7.19/7.54 , s:1, b:0),
% 7.19/7.54 'class_Ring__and__Field_Odivision__ring' [111, 1] (w:1, o:129, a:1
% 7.19/7.54 , s:1, b:0),
% 7.19/7.54 'c_Nat_Osemiring__1__class_Oof__nat' [112, 2] (w:1, o:177, a:1, s:1
% 7.19/7.54 , b:0),
% 7.19/7.54 'c_Int_Onat' [113, 1] (w:1, o:130, a:1, s:1, b:0),
% 7.19/7.54 'class_Ring__and__Field_Osemiring__1' [114, 1] (w:1, o:131, a:1, s:1
% 7.19/7.54 , b:0),
% 7.19/7.54 'class_Ring__and__Field_Odvd' [117, 1] (w:1, o:132, a:1, s:1, b:0),
% 7.19/7.54 'class_Ring__and__Field_Ocomm__ring' [118, 1] (w:1, o:73, a:1, s:1
% 7.19/7.54 , b:0),
% 7.19/7.54 'class_Ring__and__Field_Opordered__cancel__semiring' [121, 1] (w:1
% 7.19/7.54 , o:133, a:1, s:1, b:0),
% 7.19/7.54 'class_Divides_Oring__div' [122, 1] (w:1, o:90, a:1, s:1, b:0),
% 7.19/7.54 'class_OrderedGroup_Oab__semigroup__mult' [123, 1] (w:1, o:108, a:1
% 7.19/7.54 , s:1, b:0),
% 7.19/7.54 'class_RealVector_Oreal__normed__algebra' [128, 1] (w:1, o:134, a:1
% 7.19/7.54 , s:1, b:0),
% 7.19/7.54 'tc_RealDef_Oreal' [130, 0] (w:1, o:50, a:1, s:1, b:0),
% 7.19/7.54 'class_Lattices_Oboolean__algebra' [131, 1] (w:1, o:135, a:1, s:1, b:
% 7.19/7.54 0),
% 7.19/7.54 'class_OrderedGroup_Olordered__ab__group__add__abs' [132, 1] (w:1, o:
% 7.19/7.54 109, a:1, s:1, b:0),
% 7.19/7.54 'class_OrderedGroup_Opordered__comm__monoid__add' [134, 1] (w:1, o:
% 7.19/7.54 110, a:1, s:1, b:0),
% 7.19/7.54 'c_Int_Opred' [135, 1] (w:1, o:136, a:1, s:1, b:0),
% 7.19/7.54 'class_Ring__and__Field_Oring__no__zero__divisors' [136, 1] (w:1, o:
% 7.19/7.54 97, a:1, s:1, b:0),
% 7.19/7.54 'c_Int_Osucc' [138, 1] (w:1, o:137, a:1, s:1, b:0),
% 7.19/7.54 'class_Ring__and__Field_Ocomm__ring__1' [140, 1] (w:1, o:74, a:1, s:1
% 7.19/7.54 , b:0),
% 7.19/7.54 'class_OrderedGroup_Oab__group__add' [141, 1] (w:1, o:111, a:1, s:1
% 7.19/7.54 , b:0),
% 7.19/7.54 'class_Ring__and__Field_Oabs__if' [142, 1] (w:1, o:138, a:1, s:1, b:0
% 7.19/7.54 ),
% 7.19/7.54 'class_Ring__and__Field_Oordered__semiring' [143, 1] (w:1, o:124, a:1
% 7.19/7.54 , s:1, b:0),
% 7.19/7.54 'class_Ring__and__Field_Ocomm__semiring' [146, 1] (w:1, o:76, a:1, s:
% 7.19/7.54 1, b:0),
% 7.19/7.54 'class_OrderedGroup_Oordered__ab__group__add' [147, 1] (w:1, o:87, a:
% 7.19/7.54 1, s:1, b:0),
% 7.19/7.54 'class_HOL_Oeq' [148, 1] (w:1, o:93, a:1, s:1, b:0),
% 7.19/7.54 'c_HOL_Oeq__class_Oeq' [149, 3] (w:1, o:190, a:1, s:1, b:0),
% 7.19/7.54 'class_Ring__and__Field_Opordered__semiring' [150, 1] (w:1, o:139, a:
% 7.19/7.54 1, s:1, b:0),
% 7.19/7.54 'class_Nat_Osemiring__char__0' [151, 1] (w:1, o:85, a:1, s:1, b:0),
% 7.19/7.54 'class_OrderedGroup_Ocomm__monoid__add' [153, 1] (w:1, o:112, a:1, s:
% 7.19/7.54 1, b:0),
% 7.19/7.54 'class_Ring__and__Field_Olordered__ring' [155, 1] (w:1, o:68, a:1, s:
% 7.19/7.54 1, b:0),
% 7.19/7.54 'c_Int_OBit0' [156, 1] (w:1, o:140, a:1, s:1, b:0),
% 7.19/7.54 'class_OrderedGroup_Omonoid__mult' [157, 1] (w:1, o:113, a:1, s:1, b:
% 7.19/7.54 0),
% 7.19/7.54 'class_OrderedGroup_Ocomm__monoid__mult' [158, 1] (w:1, o:114, a:1
% 7.19/7.54 , s:1, b:0),
% 7.19/7.54 'class_OrderedGroup_Ocancel__ab__semigroup__add' [159, 1] (w:1, o:115
% 7.19/7.54 , a:1, s:1, b:0),
% 7.19/7.54 'class_OrderedGroup_Ocancel__semigroup__add' [160, 1] (w:1, o:116, a:
% 7.19/7.54 1, s:1, b:0),
% 7.19/7.54 'class_Orderings_Opreorder' [161, 1] (w:1, o:117, a:1, s:1, b:0),
% 7.19/7.54 'class_OrderedGroup_Oab__semigroup__add' [165, 1] (w:1, o:118, a:1
% 7.19/7.54 , s:1, b:0),
% 7.19/7.54 'class_Ring__and__Field_Osemiring' [166, 1] (w:1, o:141, a:1, s:1, b:
% 7.19/7.54 0),
% 7.19/7.54 'class_RealVector_Oreal__field' [168, 1] (w:1, o:142, a:1, s:1, b:0)
% 7.19/7.54 ,
% 7.19/7.54 'c_Int_OBit1' [170, 1] (w:1, o:143, a:1, s:1, b:0),
% 7.19/7.54 'class_Ring__and__Field_Oring__1' [171, 1] (w:1, o:98, a:1, s:1, b:0)
% 34.02/34.39 ,
% 34.02/34.39 'class_Ring__and__Field_Oordered__comm__semiring__strict' [172, 1]
% 34.02/34.39 (w:1, o:125, a:1, s:1, b:0),
% 34.02/34.39 'c_Int_Oiszero' [174, 2] (w:1, o:178, a:1, s:1, b:0),
% 34.02/34.39 'class_OrderedGroup_Omonoid__add' [175, 1] (w:1, o:119, a:1, s:1, b:0
% 34.02/34.39 ),
% 34.02/34.39 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [176, 1]
% 34.02/34.39 (w:1, o:120, a:1, s:1, b:0),
% 34.02/34.39 'class_Ring__and__Field_Oring__1__no__zero__divisors' [182, 1] (w:1
% 34.02/34.39 , o:99, a:1, s:1, b:0),
% 34.02/34.39 'class_Int_Oring__char__0' [183, 1] (w:1, o:144, a:1, s:1, b:0),
% 34.02/34.39 'v_z' [184, 0] (w:1, o:60, a:1, s:1, b:0),
% 34.02/34.39 'c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt' [185, 1] (w:1, o:
% 34.02/34.39 145, a:1, s:1, b:0),
% 34.02/34.39 'tc_Complex_Ocomplex' [186, 0] (w:1, o:61, a:1, s:1, b:0),
% 34.02/34.39 'v_x____' [187, 0] (w:1, o:62, a:1, s:1, b:0),
% 34.02/34.39 'c_NthRoot_Osqrt' [188, 1] (w:1, o:146, a:1, s:1, b:0),
% 34.02/34.39 'v_y____' [189, 0] (w:1, o:59, a:1, s:1, b:0),
% 34.02/34.39 'c_Complex_Ocomplex_OComplex' [190, 2] (w:1, o:179, a:1, s:1, b:0).
% 34.02/34.39
% 34.02/34.39
% 34.02/34.39 Starting Search:
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39
% 34.02/34.39 Intermediate Status:
% 34.02/34.39 Generated: 3786
% 34.02/34.39 Kept: 2000
% 34.02/34.39 Inuse: 78
% 34.02/34.39 Deleted: 2
% 34.02/34.39 Deletedinuse: 0
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39
% 34.02/34.39 Intermediate Status:
% 34.02/34.39 Generated: 9011
% 34.02/34.39 Kept: 4219
% 34.02/34.39 Inuse: 288
% 34.02/34.39 Deleted: 16
% 34.02/34.39 Deletedinuse: 0
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39
% 34.02/34.39 Intermediate Status:
% 34.02/34.39 Generated: 16990
% 34.02/34.39 Kept: 6323
% 34.02/34.39 Inuse: 422
% 34.02/34.39 Deleted: 19
% 34.02/34.39 Deletedinuse: 0
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39
% 34.02/34.39 Intermediate Status:
% 34.02/34.39 Generated: 27005
% 34.02/34.39 Kept: 8675
% 34.02/34.39 Inuse: 442
% 34.02/34.39 Deleted: 19
% 34.02/34.39 Deletedinuse: 0
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39
% 34.02/34.39 Intermediate Status:
% 34.02/34.39 Generated: 40320
% 34.02/34.39 Kept: 10866
% 34.02/34.39 Inuse: 462
% 34.02/34.39 Deleted: 19
% 34.02/34.39 Deletedinuse: 0
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39
% 34.02/34.39 Intermediate Status:
% 34.02/34.39 Generated: 46869
% 34.02/34.39 Kept: 12868
% 34.02/34.39 Inuse: 499
% 34.02/34.39 Deleted: 21
% 34.02/34.39 Deletedinuse: 0
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39
% 34.02/34.39 Intermediate Status:
% 34.02/34.39 Generated: 56306
% 34.02/34.39 Kept: 15350
% 34.02/34.39 Inuse: 570
% 34.02/34.39 Deleted: 27
% 34.02/34.39 Deletedinuse: 1
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39
% 34.02/34.39 Intermediate Status:
% 34.02/34.39 Generated: 64337
% 34.02/34.39 Kept: 17901
% 34.02/34.39 Inuse: 594
% 34.02/34.39 Deleted: 28
% 34.02/34.39 Deletedinuse: 1
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39
% 34.02/34.39 Intermediate Status:
% 34.02/34.39 Generated: 89000
% 34.02/34.39 Kept: 20113
% 34.02/34.39 Inuse: 619
% 34.02/34.39 Deleted: 28
% 34.02/34.39 Deletedinuse: 1
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39 Resimplifying clauses:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39
% 34.02/34.39 Intermediate Status:
% 34.02/34.39 Generated: 99579
% 34.02/34.39 Kept: 22132
% 34.02/34.39 Inuse: 655
% 34.02/34.39 Deleted: 529
% 34.02/34.39 Deletedinuse: 1
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39
% 34.02/34.39 Intermediate Status:
% 34.02/34.39 Generated: 107248
% 34.02/34.39 Kept: 24561
% 34.02/34.39 Inuse: 675
% 34.02/34.39 Deleted: 530
% 34.02/34.39 Deletedinuse: 2
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39
% 34.02/34.39 Intermediate Status:
% 34.02/34.39 Generated: 112303
% 34.02/34.39 Kept: 26589
% 34.02/34.39 Inuse: 680
% 34.02/34.39 Deleted: 530
% 34.02/34.39 Deletedinuse: 2
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39
% 34.02/34.39 Intermediate Status:
% 34.02/34.39 Generated: 118172
% 34.02/34.39 Kept: 28595
% 34.02/34.39 Inuse: 690
% 34.02/34.39 Deleted: 530
% 34.02/34.39 Deletedinuse: 2
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39
% 34.02/34.39 Intermediate Status:
% 34.02/34.39 Generated: 136510
% 34.02/34.39 Kept: 32132
% 34.02/34.39 Inuse: 732
% 34.02/34.39 Deleted: 533
% 34.02/34.39 Deletedinuse: 2
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39
% 34.02/34.39 Intermediate Status:
% 34.02/34.39 Generated: 143438
% 34.02/34.39 Kept: 34150
% 34.02/34.39 Inuse: 755
% 34.02/34.39 Deleted: 536
% 34.02/34.39 Deletedinuse: 5
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39
% 34.02/34.39 Intermediate Status:
% 34.02/34.39 Generated: 157325
% 34.02/34.39 Kept: 36964
% 34.02/34.39 Inuse: 792
% 34.02/34.39 Deleted: 536
% 34.02/34.39 Deletedinuse: 5
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39
% 34.02/34.39 Intermediate Status:
% 34.02/34.39 Generated: 171590
% 34.02/34.39 Kept: 40187
% 34.02/34.39 Inuse: 807
% 34.02/34.39 Deleted: 536
% 34.02/34.39 Deletedinuse: 5
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39 Resimplifying clauses:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39
% 34.02/34.39 Intermediate Status:
% 34.02/34.39 Generated: 182386
% 34.02/34.39 Kept: 42685
% 34.02/34.39 Inuse: 817
% 34.02/34.39 Deleted: 746
% 34.02/34.39 Deletedinuse: 5
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39 Resimplifying inuse:
% 34.02/34.39 Done
% 34.02/34.39
% 34.02/34.39
% 34.02/34.39 Intermediate Status:
% 34.02/34.39 Generated: 190322
% 34.02/34.39 Kept: 44781
% 34.02/34.39 Inuse: 847
% 84.93/85.40 Deleted: 746
% 84.93/85.40 Deletedinuse: 5
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 198183
% 84.93/85.40 Kept: 46805
% 84.93/85.40 Inuse: 866
% 84.93/85.40 Deleted: 746
% 84.93/85.40 Deletedinuse: 5
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 207413
% 84.93/85.40 Kept: 49401
% 84.93/85.40 Inuse: 877
% 84.93/85.40 Deleted: 746
% 84.93/85.40 Deletedinuse: 5
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 216213
% 84.93/85.40 Kept: 51506
% 84.93/85.40 Inuse: 897
% 84.93/85.40 Deleted: 746
% 84.93/85.40 Deletedinuse: 5
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 225185
% 84.93/85.40 Kept: 53747
% 84.93/85.40 Inuse: 927
% 84.93/85.40 Deleted: 746
% 84.93/85.40 Deletedinuse: 5
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 233318
% 84.93/85.40 Kept: 55851
% 84.93/85.40 Inuse: 957
% 84.93/85.40 Deleted: 746
% 84.93/85.40 Deletedinuse: 5
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 242606
% 84.93/85.40 Kept: 57887
% 84.93/85.40 Inuse: 984
% 84.93/85.40 Deleted: 746
% 84.93/85.40 Deletedinuse: 5
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 259427
% 84.93/85.40 Kept: 61074
% 84.93/85.40 Inuse: 1007
% 84.93/85.40 Deleted: 746
% 84.93/85.40 Deletedinuse: 5
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying clauses:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 272187
% 84.93/85.40 Kept: 63101
% 84.93/85.40 Inuse: 1015
% 84.93/85.40 Deleted: 840
% 84.93/85.40 Deletedinuse: 5
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 286264
% 84.93/85.40 Kept: 65108
% 84.93/85.40 Inuse: 1025
% 84.93/85.40 Deleted: 840
% 84.93/85.40 Deletedinuse: 5
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 298053
% 84.93/85.40 Kept: 67143
% 84.93/85.40 Inuse: 1047
% 84.93/85.40 Deleted: 840
% 84.93/85.40 Deletedinuse: 5
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 310106
% 84.93/85.40 Kept: 70466
% 84.93/85.40 Inuse: 1057
% 84.93/85.40 Deleted: 844
% 84.93/85.40 Deletedinuse: 9
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 315557
% 84.93/85.40 Kept: 72720
% 84.93/85.40 Inuse: 1062
% 84.93/85.40 Deleted: 844
% 84.93/85.40 Deletedinuse: 9
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 325180
% 84.93/85.40 Kept: 74771
% 84.93/85.40 Inuse: 1080
% 84.93/85.40 Deleted: 844
% 84.93/85.40 Deletedinuse: 9
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 354264
% 84.93/85.40 Kept: 79034
% 84.93/85.40 Inuse: 1122
% 84.93/85.40 Deleted: 846
% 84.93/85.40 Deletedinuse: 11
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 364124
% 84.93/85.40 Kept: 81171
% 84.93/85.40 Inuse: 1141
% 84.93/85.40 Deleted: 847
% 84.93/85.40 Deletedinuse: 11
% 84.93/85.40
% 84.93/85.40 Resimplifying clauses:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 374814
% 84.93/85.40 Kept: 83186
% 84.93/85.40 Inuse: 1165
% 84.93/85.40 Deleted: 1295
% 84.93/85.40 Deletedinuse: 14
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 386728
% 84.93/85.40 Kept: 85216
% 84.93/85.40 Inuse: 1193
% 84.93/85.40 Deleted: 1295
% 84.93/85.40 Deletedinuse: 14
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 399213
% 84.93/85.40 Kept: 87487
% 84.93/85.40 Inuse: 1223
% 84.93/85.40 Deleted: 1301
% 84.93/85.40 Deletedinuse: 19
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 406802
% 84.93/85.40 Kept: 90150
% 84.93/85.40 Inuse: 1232
% 84.93/85.40 Deleted: 1302
% 84.93/85.40 Deletedinuse: 19
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 424415
% 84.93/85.40 Kept: 92810
% 84.93/85.40 Inuse: 1242
% 84.93/85.40 Deleted: 1302
% 84.93/85.40 Deletedinuse: 19
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 442943
% 84.93/85.40 Kept: 95656
% 84.93/85.40 Inuse: 1252
% 84.93/85.40 Deleted: 1302
% 84.93/85.40 Deletedinuse: 19
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 471834
% 84.93/85.40 Kept: 99338
% 84.93/85.40 Inuse: 1272
% 84.93/85.40 Deleted: 1302
% 84.93/85.40 Deletedinuse: 19
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 489168
% 84.93/85.40 Kept: 102279
% 84.93/85.40 Inuse: 1302
% 84.93/85.40 Deleted: 1302
% 84.93/85.40 Deletedinuse: 19
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying clauses:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 84.93/85.40 Done
% 84.93/85.40
% 84.93/85.40
% 84.93/85.40 Intermediate Status:
% 84.93/85.40 Generated: 504108
% 84.93/85.40 Kept: 105183
% 84.93/85.40 Inuse: 1312
% 84.93/85.40 Deleted: 1806
% 84.93/85.40 Deletedinuse: 21
% 84.93/85.40
% 84.93/85.40 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 522837
% 173.41/173.83 Kept: 107760
% 173.41/173.83 Inuse: 1326
% 173.41/173.83 Deleted: 1809
% 173.41/173.83 Deletedinuse: 23
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 544974
% 173.41/173.83 Kept: 110463
% 173.41/173.83 Inuse: 1336
% 173.41/173.83 Deleted: 1809
% 173.41/173.83 Deletedinuse: 23
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 558202
% 173.41/173.83 Kept: 112749
% 173.41/173.83 Inuse: 1356
% 173.41/173.83 Deleted: 1809
% 173.41/173.83 Deletedinuse: 23
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 570937
% 173.41/173.83 Kept: 114793
% 173.41/173.83 Inuse: 1376
% 173.41/173.83 Deleted: 1809
% 173.41/173.83 Deletedinuse: 23
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 584486
% 173.41/173.83 Kept: 116793
% 173.41/173.83 Inuse: 1404
% 173.41/173.83 Deleted: 1809
% 173.41/173.83 Deletedinuse: 23
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 595821
% 173.41/173.83 Kept: 119025
% 173.41/173.83 Inuse: 1426
% 173.41/173.83 Deleted: 1809
% 173.41/173.83 Deletedinuse: 23
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 609588
% 173.41/173.83 Kept: 121291
% 173.41/173.83 Inuse: 1451
% 173.41/173.83 Deleted: 1809
% 173.41/173.83 Deletedinuse: 23
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 640790
% 173.41/173.83 Kept: 124582
% 173.41/173.83 Inuse: 1466
% 173.41/173.83 Deleted: 1809
% 173.41/173.83 Deletedinuse: 23
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 Resimplifying clauses:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 651438
% 173.41/173.83 Kept: 126992
% 173.41/173.83 Inuse: 1486
% 173.41/173.83 Deleted: 2125
% 173.41/173.83 Deletedinuse: 23
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 661979
% 173.41/173.83 Kept: 129334
% 173.41/173.83 Inuse: 1496
% 173.41/173.83 Deleted: 2125
% 173.41/173.83 Deletedinuse: 23
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 670458
% 173.41/173.83 Kept: 133272
% 173.41/173.83 Inuse: 1501
% 173.41/173.83 Deleted: 2125
% 173.41/173.83 Deletedinuse: 23
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 684252
% 173.41/173.83 Kept: 136217
% 173.41/173.83 Inuse: 1505
% 173.41/173.83 Deleted: 2126
% 173.41/173.83 Deletedinuse: 23
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 701123
% 173.41/173.83 Kept: 140776
% 173.41/173.83 Inuse: 1510
% 173.41/173.83 Deleted: 2126
% 173.41/173.83 Deletedinuse: 23
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 710687
% 173.41/173.83 Kept: 143180
% 173.41/173.83 Inuse: 1530
% 173.41/173.83 Deleted: 2130
% 173.41/173.83 Deletedinuse: 27
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 Resimplifying clauses:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 720938
% 173.41/173.83 Kept: 145247
% 173.41/173.83 Inuse: 1547
% 173.41/173.83 Deleted: 2610
% 173.41/173.83 Deletedinuse: 27
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 731255
% 173.41/173.83 Kept: 148468
% 173.41/173.83 Inuse: 1557
% 173.41/173.83 Deleted: 2610
% 173.41/173.83 Deletedinuse: 27
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 737048
% 173.41/173.83 Kept: 150503
% 173.41/173.83 Inuse: 1568
% 173.41/173.83 Deleted: 2610
% 173.41/173.83 Deletedinuse: 27
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 742796
% 173.41/173.83 Kept: 152523
% 173.41/173.83 Inuse: 1579
% 173.41/173.83 Deleted: 2610
% 173.41/173.83 Deletedinuse: 27
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 751595
% 173.41/173.83 Kept: 154575
% 173.41/173.83 Inuse: 1597
% 173.41/173.83 Deleted: 2610
% 173.41/173.83 Deletedinuse: 27
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 760067
% 173.41/173.83 Kept: 156806
% 173.41/173.83 Inuse: 1615
% 173.41/173.83 Deleted: 2616
% 173.41/173.83 Deletedinuse: 33
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 768483
% 173.41/173.83 Kept: 159074
% 173.41/173.83 Inuse: 1635
% 173.41/173.83 Deleted: 2616
% 173.41/173.83 Deletedinuse: 33
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 777041
% 173.41/173.83 Kept: 161428
% 173.41/173.83 Inuse: 1655
% 173.41/173.83 Deleted: 2616
% 173.41/173.83 Deletedinuse: 33
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 787315
% 173.41/173.83 Kept: 163548
% 173.41/173.83 Inuse: 1675
% 173.41/173.83 Deleted: 2616
% 173.41/173.83 Deletedinuse: 33
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 Resimplifying clauses:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83
% 173.41/173.83 Intermediate Status:
% 173.41/173.83 Generated: 796522
% 173.41/173.83 Kept: 165713
% 173.41/173.83 Inuse: 1690
% 173.41/173.83 Deleted: 3453
% 173.41/173.83 Deletedinuse: 33
% 173.41/173.83
% 173.41/173.83 Resimplifying inuse:
% 173.41/173.83 Done
% 173.41/173.83
% 173.41/173.83 ResimCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------