TSTP Solution File: SWV631-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV631-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:27:17 EDT 2022
% Result : Timeout 300.06s 300.52s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV631-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : bliksem %s
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % DateTime : Wed Jun 15 02:29:48 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.15/1.51 *** allocated 10000 integers for termspace/termends
% 1.15/1.51 *** allocated 10000 integers for clauses
% 1.15/1.51 *** allocated 10000 integers for justifications
% 1.15/1.51 *** allocated 15000 integers for termspace/termends
% 1.15/1.51 *** allocated 22500 integers for termspace/termends
% 1.15/1.51 *** allocated 33750 integers for termspace/termends
% 1.15/1.51 *** allocated 50625 integers for termspace/termends
% 1.15/1.51 Bliksem 1.12
% 1.15/1.51
% 1.15/1.51
% 1.15/1.51 Automatic Strategy Selection
% 1.15/1.51
% 1.15/1.51 Clauses:
% 1.15/1.51 [
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.15/1.51 ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 1.15/1.51 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.15/1.51 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.51 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.51 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.15/1.51 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.51 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T )
% 1.15/1.51 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.15/1.51 , Z, X ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.15/1.51 ), ~( 'c_lessequals'( T, Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.15/1.51 , T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.15/1.51 ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.15/1.51 , Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.15/1.51 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.15/1.51 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.15/1.51 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.15/1.51 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.15/1.51 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 1.15/1.51 'tc_nat' ), 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z
% 1.15/1.51 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' )
% 1.15/1.51 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.15/1.51 , Z, 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.51 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.15/1.51 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.15/1.51 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.15/1.51 , Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 1.15/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 , X ) ) ],
% 1.15/1.51 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.15/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), T, X ),
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.15/1.51 , T, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), X ) ), =( Z
% 1.15/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.51 ) ) ],
% 1.15/1.51 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.15/1.51 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.15/1.51 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.51 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.51 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.15/1.51 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'(
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' )
% 1.15/1.51 , 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.15/1.51 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.15/1.51 , X ), Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.15/1.51 , X ), Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.15/1.51 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.15/1.51 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ), Z ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.15/1.51 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.15/1.51 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.15/1.51 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 , X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.51 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.15/1.51 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 , X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 , X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.51 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 , X ) ) ],
% 1.15/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.15/1.51 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 1.15/1.51 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.51 ), X ), ~( 'c_lessequals'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, 'c_Int_OPls',
% 1.15/1.51 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.15/1.51 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.15/1.51 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.51 X ) ) ],
% 1.15/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.15/1.51 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.51 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.15/1.51 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.15/1.51 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.15/1.51 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.15/1.51 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.15/1.51 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.15/1.51 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.15/1.51 ), X ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.51 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.51 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.15/1.51 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.51 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.15/1.51 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.51 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.15/1.51 ), X ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.51 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.51 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.15/1.51 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.15/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.15/1.51 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.15/1.51 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.51 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.15/1.51 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X
% 1.15/1.51 ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.15/1.51 X ) ],
% 1.15/1.51 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'(
% 1.15/1.51 'tc_nat' ), X, 'tc_nat' ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.51 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.15/1.51 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.15/1.51 ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.51 ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.15/1.51 ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.51 ) ) ],
% 1.15/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( T, U, X ), X ),
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), ~(
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( U, T, X ) ), ~(
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.15/1.51 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.51 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.15/1.51 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.51 ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.51 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.15/1.51 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.15/1.51 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.15/1.51 ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.15/1.51 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.15/1.51 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.15/1.51 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 1.15/1.51 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 1.15/1.51 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( X
% 1.15/1.51 , 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat'
% 1.15/1.51 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.15/1.51 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.15/1.51 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.15/1.51 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.15/1.51 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 1.15/1.51 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.15/1.51 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Odiv'( Y, Z,
% 1.15/1.51 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 1.15/1.51 'tc_nat' ), 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.51 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.15/1.51 X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.51 X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.15/1.51 , Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.15/1.51 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 1.15/1.51 , 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.15/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.15/1.51 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.15/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.15/1.51 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.15/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.15/1.51 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.15/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.15/1.51 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.15/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.15/1.51 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.15/1.51 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.15/1.51 ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.15/1.51 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.15/1.51 X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.15/1.51 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.15/1.51 ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.15/1.51 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.15/1.51 X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.15/1.51 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.15/1.51 ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.15/1.51 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.15/1.51 ) ],
% 1.15/1.51 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_Int_Oint' ),
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_Int_Oint' ), 'tc_Int_Oint' ), ~(
% 1.15/1.51 'c_lessequals'( Y, Z, 'tc_Int_Oint' ) ) ],
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ],
% 1.15/1.51 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.15/1.51 'tc_nat' ), 'tc_nat' ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.15/1.51 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.15/1.51 'c_HOL_Oabs__class_Oabs'( T, X ), X ) ), ~(
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 1.15/1.51 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.51 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.15/1.51 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.15/1.51 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =(
% 1.15/1.51 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.15/1.51 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.15/1.51 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.15/1.51 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 1.15/1.51 X ), Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.15/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.15/1.51 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.15/1.51 Z, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.15/1.51 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.15/1.51 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.15/1.51 Z, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.15/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.15/1.51 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.15/1.51 X ), Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.15/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.15/1.51 Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.51 X ), Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.15/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.15/1.51 X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.51 X ), T, X ) ) ],
% 1.15/1.51 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Nat_Osemiring__1__class_Oof__nat'( X
% 1.15/1.51 , 'tc_Int_Oint' ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.51 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' ), Z,
% 1.15/1.51 'tc_Int_Oint' ), 'tc_Int_Oint' ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.51 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.15/1.51 'tc_nat' ), 'tc_Int_Oint' ), Z, 'tc_Int_Oint' ) ) ],
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_Onat'( Y ), 'tc_nat' ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( X,
% 1.15/1.51 'tc_Int_Oint' ), Y, 'tc_Int_Oint' ) ) ],
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( X,
% 1.15/1.51 'tc_Int_Oint' ), Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.15/1.51 'c_Int_Onat'( Y ), 'tc_nat' ) ) ],
% 1.15/1.51 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'c_Int_Onat'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint' ) ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.51 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.51 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.15/1.51 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 1.15/1.51 , 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.15/1.51 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.15/1.51 , 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.15/1.51 Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z
% 1.15/1.51 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.15/1.51 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oone__class_Oone'(
% 1.15/1.51 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.15/1.51 T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X ) ),
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.51 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.51 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.15/1.51 , Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.15/1.51 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 1.15/1.51 ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.15/1.51 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), T, X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.15/1.51 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.51 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 , X ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.51 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.15/1.51 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.15/1.51 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.51 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.15/1.51 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Z,
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ), X ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.15/1.51 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.15/1.51 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.15/1.51 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.15/1.51 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.51 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.51 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.51 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.15/1.51 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.51 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.51 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.15/1.51 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 1.15/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.15/1.51 ) ) ],
% 1.15/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.15/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.15/1.51 ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.51 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 1.15/1.51 , X ), W, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( Z, W, X ), X ) ), ~(
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.15/1.51 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Z,
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( U, W, X ), X ), T, X ), X ) ), ~(
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ],
% 1.15/1.51 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.15/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y,
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z, X ),
% 1.15/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z, X ),
% 1.15/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Y ) ],
% 1.15/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( Z, Y, X ), X ),
% 1.15/1.51 'c_Divides_Odiv__class_Omod'( Z, Y, X ), X ), Z ) ],
% 1.15/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.15/1.51 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), =( X, Y ), ~(
% 1.15/1.51 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.15/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.15/1.51 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.15/1.51 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.15/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.15/1.51 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.15/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.15/1.51 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.15/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.15/1.51 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.15/1.51 ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.51 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.15/1.51 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.15/1.51 Y, X ), Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.51 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.15/1.51 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.15/1.51 Y, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.15/1.51 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.15/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.15/1.51 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.51 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.15/1.51 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.51 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.15/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.15/1.51 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.15/1.51 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.15/1.51 Y, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.15/1.51 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.15/1.51 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.15/1.51 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.15/1.51 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.15/1.51 , X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 1.15/1.51 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X ) ],
% 1.15/1.51 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Odiv'(
% 1.15/1.51 Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.15/1.51 X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Odiv'(
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.15/1.51 X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), X ) ), ~(
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.51 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.15/1.51 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.51 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.15/1.51 ), X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.15/1.51 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.15/1.51 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.15/1.51 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.15/1.51 ), X ), Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.15/1.51 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.15/1.51 T, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.15/1.51 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.15/1.51 X ), Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.15/1.51 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.15/1.51 T, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.15/1.51 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.15/1.51 X ), T, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.15/1.51 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.51 T, X ), X ) ) ],
% 1.15/1.51 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.15/1.51 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.15/1.51 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.15/1.51 X ), T, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.15/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.15/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.15/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.15/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.15/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.15/1.51 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.15/1.51 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.51 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.15/1.51 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.15/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.15/1.51 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) )
% 1.15/1.51 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.15/1.51 , 'tc_nat' ) ) ],
% 1.15/1.51 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.15/1.51 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.15/1.51 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.15/1.51 ), =( Z, Y ) ],
% 1.15/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.15/1.51 ) ],
% 1.15/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.15/1.51 ) ],
% 1.15/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.15/1.51 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.15/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.15/1.51 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.15/1.51 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.15/1.51 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.15/1.51 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_Int_Oint' ) ), ~(
% 1.15/1.51 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.15/1.51 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.15/1.51 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 1.15/1.51 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.15/1.51 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.15/1.51 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), =( Y, X ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ],
% 1.15/1.51 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 1.15/1.51 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 1.15/1.51 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y, X ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.15/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.15/1.51 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.15/1.51 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.15/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.15/1.51 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.15/1.51 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.15/1.51 , Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.51 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.15/1.51 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.51 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.15/1.51 Z, T, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.15/1.51 , X ) ) ), =( Y, Z ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.15/1.51 , X ) ) ), =( Y, Z ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ), Z ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 1.15/1.51 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.15/1.51 'c_HOL_Oabs__class_Oabs'( T, X ), X ), X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.15/1.51 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.15/1.51 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint' )
% 1.15/1.51 , 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ), 'tc_Int_Oint' )
% 1.15/1.51 , ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.15/1.51 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint' ),
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ), 'tc_Int_Oint' ) )
% 1.15/1.51 ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, Z, 'tc_Int_Oint' ),
% 1.15/1.51 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~( 'c_lessequals'( Y, Z
% 1.15/1.51 , 'tc_Int_Oint' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.51 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.15/1.51 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.15/1.51 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.15/1.51 ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.51 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.15/1.51 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.51 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.51 ), X ) ],
% 1.15/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 1.15/1.51 , X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 1.15/1.51 , X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 Z, Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.15/1.51 , X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.15/1.51 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.15/1.51 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.15/1.51 ) ) ],
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Int_Opred'( X ), Y, 'tc_Int_Oint' ), ~(
% 1.15/1.51 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.15/1.51 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_Int_Opred'( X ), Y, 'tc_Int_Oint' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.51 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~(
% 1.15/1.51 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.51 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~(
% 1.15/1.51 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.15/1.51 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.15/1.51 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.15/1.51 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.15/1.51 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.15/1.51 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.15/1.51 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.15/1.51 ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.15/1.51 ), X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.15/1.51 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.15/1.51 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.51 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.15/1.51 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.15/1.51 Z, T, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.15/1.51 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.51 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat'
% 1.15/1.51 ), 'tc_nat' ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.15/1.51 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.51 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.15/1.51 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.51 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.15/1.51 'tc_Int_Oint' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.15/1.51 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint' ), X ) ],
% 1.15/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.15/1.51 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.15/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.15/1.51 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.15/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.15/1.51 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.15/1.51 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.15/1.51 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.15/1.51 ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.15/1.51 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.51 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.15/1.51 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.15/1.51 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_Osucc'( X ), 'tc_nat' ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.15/1.51 'c_Power_Opower__class_Opower'( Y, T, X ), X ),
% 1.15/1.51 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.15/1.51 'tc_nat' ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 1.15/1.51 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.15/1.51 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.15/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.15/1.51 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.15/1.51 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.15/1.51 'tc_nat' ) ) ],
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.15/1.51 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.15/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 1.15/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X ), X ) )
% 1.15/1.51 ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.15/1.51 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.15/1.51 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.15/1.51 Y, X ), Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.15/1.51 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.15/1.51 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.51 X ), T, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 1.15/1.51 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.51 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 1.15/1.51 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.51 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.15/1.51 , X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.51 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.15/1.51 , X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.51 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.15/1.51 , X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.51 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.15/1.51 , X ) ) ],
% 1.15/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.15/1.51 , X ), X ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.15/1.51 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.15/1.51 , T, X ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.15/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.51 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.51 X ) ) ],
% 1.15/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 1.15/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Z, Y, X ),
% 1.15/1.51 'c_HOL_Oone__class_Oone'( X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.51 ) ) ],
% 1.15/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.15/1.51 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Oone__class_Oone'( X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.51 ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.15/1.51 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.15/1.51 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.15/1.51 [ =( 'c_Int_Osucc'( 'c_Int_Opred'( X ) ), X ) ],
% 1.15/1.51 [ ~( 'class_HOL_Oeq'( X ) ), 'c_HOL_Oeq__class_Oeq'( Y, Y, X ) ],
% 1.15/1.51 [ 'c_HOL_Oeq__class_Oeq'( X, X, 'tc_Int_Oint' ) ],
% 1.15/1.51 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.15/1.51 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( 'c_Divides_Odiv__class_Odiv'( Y
% 1.15/1.51 , X, 'tc_nat' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.15/1.51 ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.15/1.51 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.15/1.51 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.15/1.51 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.51 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 1.15/1.51 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.15/1.51 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.15/1.51 X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.15/1.51 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.15/1.51 X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.15/1.51 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.15/1.51 X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.15/1.51 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.15/1.51 X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 Y, Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 Y, Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 1.15/1.51 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.51 X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 1.15/1.51 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.51 X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.15/1.51 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.51 X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.15/1.51 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.15/1.51 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.15/1.51 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.15/1.51 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.15/1.51 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.15/1.51 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.15/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.15/1.51 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.15/1.51 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.15/1.51 'c_Power_Opower__class_Opower'( T, 'c_Suc'( Z ), X ) ) ), =( Y, T ), ~(
% 1.15/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.15/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.15/1.51 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( X, Z, 'tc_nat'
% 1.15/1.51 ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.51 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ),
% 1.15/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ), 'tc_nat' ), Z, 'tc_nat' )
% 1.15/1.51 , 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.15/1.51 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.15/1.51 , X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.15/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.15/1.51 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.15/1.51 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.15/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.15/1.51 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.15/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.15/1.51 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.15/1.51 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.15/1.51 , X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.15/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.15/1.51 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.15/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.51 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 Y, T, X ), Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.15/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.51 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 Y, T, X ), Z, X ) ) ],
% 1.15/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.15/1.51 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' )
% 1.15/1.51 , 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.15/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.15/1.51 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.15/1.51 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.15/1.51 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.15/1.51 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.15/1.51 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.15/1.51 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.15/1.51 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' )
% 1.15/1.51 , 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.15/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.15/1.51 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.15/1.51 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.15/1.51 Y, 'tc_nat' ), 'tc_nat' ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.15/1.51 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.15/1.51 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.15/1.51 Y, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.15/1.51 'tc_nat' ) ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.15/1.51 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.15/1.51 'tc_nat' ), 'tc_nat' ) ],
% 1.15/1.51 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.15/1.51 'tc_nat' ), 'tc_nat' ) ],
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.15/1.51 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.15/1.51 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.15/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), 'c_Suc'( 'c_Suc'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.15/1.51 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.51 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 1.15/1.51 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.15/1.51 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 1.15/1.51 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.15/1.51 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.15/1.51 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.15/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.15/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.15/1.51 ,
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.15/1.51 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.15/1.51 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.15/1.51 Y, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.15/1.51 Z, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 ) ],
% 1.15/1.51 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.15/1.51 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.15/1.51 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.15/1.51 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.51 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), Z
% 1.15/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.51 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), X
% 1.15/1.51 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.15/1.51 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), Z, X ) ), =( Z,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.15/1.51 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Z,
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), T, X ) ), =( T,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.51 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 1.15/1.51 X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.15/1.51 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.15/1.51 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.51 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.51 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 1.15/1.51 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), X ) ), =( Z,
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.15/1.51 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_Int_Oint' ) ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.51 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.15/1.51 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.15/1.51 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.15/1.51 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.15/1.51 ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.15/1.51 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.51 ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.15/1.51 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 1.15/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.15/1.51 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.15/1.51 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.15/1.51 ) ],
% 1.15/1.51 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.15/1.51 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.15/1.51 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.15/1.52 ) ],
% 1.15/1.52 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.15/1.52 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.15/1.52 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.15/1.52 ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.15/1.52 , Z, X ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.15/1.52 , T, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.15/1.52 , Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.15/1.52 , T, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.15/1.52 , Z, X ), X ) ) ],
% 1.15/1.52 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.15/1.52 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.15/1.52 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.15/1.52 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.15/1.52 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.15/1.52 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.15/1.52 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.15/1.52 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.15/1.52 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.15/1.52 [ ~( =( 'c_Nat_Osemiring__1__class_Oof__nat'( X, 'tc_Int_Oint' ),
% 1.15/1.52 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' ) ) ), =( X, Y ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( =( 'c_Nat_Osemiring__1__class_Oof__nat'( X, 'tc_Int_Oint' ),
% 1.15/1.52 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' ) ) ), =( X, Y ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.15/1.52 ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.52 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ), X ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.15/1.52 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.52 , 'tc_nat' ), 'tc_nat' ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.15/1.52 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.52 , 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 X ), 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.15/1.52 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_OPls'
% 1.15/1.52 , Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.15/1.52 ), X ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.15/1.52 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.52 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.15/1.52 ), =( 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.52 Y, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ),
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.15/1.52 , T, X ), X ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( X
% 1.15/1.52 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.15/1.52 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.15/1.52 ), 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.15/1.52 , T, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.15/1.52 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.15/1.52 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.15/1.52 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.15/1.52 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.15/1.52 W, X ), X ), ~( 'c_lessequals'( T, 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.15/1.52 , X ), W, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.15/1.52 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U, X ), W, X ), X ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 T, U, X ), Y, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.15/1.52 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.15/1.52 W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 1.15/1.52 , X ), T, X ), W, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.15/1.52 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.15/1.52 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.15/1.52 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 1.15/1.52 ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.15/1.52 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.15/1.52 ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 1.15/1.52 Y, 'tc_nat' ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.15/1.52 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 1.15/1.52 ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.15/1.52 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.15/1.52 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 1.15/1.52 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.15/1.52 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.15/1.52 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oabs__class_Oabs'(
% 1.15/1.52 Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ),
% 1.15/1.52 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.15/1.52 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.15/1.52 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.15/1.52 X, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.15/1.52 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.15/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Odiv'(
% 1.15/1.52 X, 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.15/1.52 ), 'tc_nat' ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' )
% 1.15/1.52 ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.52 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Z, Y, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.15/1.52 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.15/1.52 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Y, T, X ),
% 1.15/1.52 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.15/1.52 , X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 1.15/1.52 ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.15/1.52 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.15/1.52 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.15/1.52 , X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.15/1.52 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 1.15/1.52 , X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 1.15/1.52 , X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.15/1.52 , Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.15/1.52 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.15/1.52 ), X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.15/1.52 ), X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.52 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.15/1.52 ), X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.15/1.52 ), X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.15/1.52 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.15/1.52 ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ), X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.15/1.52 , X ), X ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.15/1.52 ],
% 1.15/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.15/1.52 , X, 'tc_nat' ), X ) ],
% 1.15/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.15/1.52 ), 'tc_nat' ), X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.15/1.52 , Y, X ), X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.15/1.52 , Z, X ), X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.15/1.52 , Z, X ), X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.15/1.52 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.15/1.52 ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.15/1.52 'tc_Int_Oint' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ),
% 1.15/1.52 'tc_Int_Oint' ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.15/1.52 'tc_Int_Oint' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ),
% 1.15/1.52 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.15/1.52 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.15/1.52 ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 1.15/1.52 Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.15/1.52 Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, T
% 1.15/1.52 , X ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, Z
% 1.15/1.52 , X ), 'c_Divides_Odiv__class_Odiv'( T, Z, X ), X ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.15/1.52 Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.15/1.52 Z, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.15/1.52 , X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.15/1.52 , X ), Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 1.15/1.52 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.15/1.52 , T, X ), X ), T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.15/1.52 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.15/1.52 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.15/1.52 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.52 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y, X ), ~( 'c_lessequals'( Z,
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.15/1.52 ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.15/1.52 'c_lessequals'( Y, Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.15/1.52 'c_lessequals'( Y, Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.15/1.52 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ],
% 1.15/1.52 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 1.15/1.52 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.15/1.52 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.15/1.52 X ) ) ), =( Z, T ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.15/1.52 X ) ) ), =( Z, T ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.15/1.52 X ) ) ), =( Y, T ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.15/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.15/1.52 ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.15/1.52 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.15/1.52 , X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.15/1.52 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Z
% 1.15/1.52 , X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ), =( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.52 ) ],
% 1.15/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), T, X ), X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_Int_Oint' ), X ), T, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.52 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.52 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.52 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.52 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.15/1.52 , X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.15/1.52 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.15/1.52 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.15/1.52 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), =( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.15/1.52 Z, 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.15/1.52 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.52 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 1.15/1.52 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.15/1.52 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.15/1.52 ), X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 1.15/1.52 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.15/1.52 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.52 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.15/1.52 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.15/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.15/1.52 'tc_Int_Oint' ), X ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.15/1.52 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.15/1.52 , 'c_Int_Onumber__class_Onumber__of'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.15/1.52 'tc_Int_Oint' ), 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls'
% 1.15/1.52 , 'tc_Int_Oint' ), 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.15/1.52 'tc_Int_Oint' ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.15/1.52 'tc_Int_Oint' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ),
% 1.15/1.52 'tc_Int_Oint' ), 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_Int_Oint' ), 'tc_Int_Oint' ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.15/1.52 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.15/1.52 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.15/1.52 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.15/1.52 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.15/1.52 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.15/1.52 ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.52 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T
% 1.15/1.52 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.15/1.52 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.15/1.52 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.15/1.52 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.15/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.15/1.52 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 X ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_Onat'( X ), 'c_Int_Onat'( Y ), 'tc_nat'
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 1.15/1.52 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.15/1.52 , X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.52 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.15/1.52 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ), X ), ~(
% 1.15/1.52 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.52 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.15/1.52 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 1.15/1.52 [ =( 'c_Suc'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Odiv'(
% 1.15/1.52 X, 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.15/1.52 ), 'tc_nat' ) ), X ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.15/1.52 ), 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.15/1.52 ), 'tc_nat' ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 1.15/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ), Y, X ), Z, X ) ) ],
% 1.15/1.52 [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'(
% 1.15/1.52 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.15/1.52 [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.15/1.52 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.15/1.52 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.15/1.52 ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.15/1.52 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.15/1.52 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.15/1.52 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.15/1.52 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.15/1.52 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.15/1.52 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.15/1.52 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.15/1.52 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.15/1.52 X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.15/1.52 'tc_nat' ), X, 'tc_nat' ) ],
% 1.15/1.52 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.15/1.52 X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 1.15/1.52 'tc_nat' ), X, 'tc_nat' ) ],
% 1.15/1.52 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.15/1.52 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.15/1.52 X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X
% 1.15/1.52 ), X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 1.15/1.52 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.15/1.52 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.52 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T
% 1.15/1.52 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_Opred'( Y ), X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ), X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.15/1.52 , X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 1.15/1.52 ), Y ) ],
% 1.15/1.52 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.15/1.52 ), X ), Y ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.15/1.52 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.52 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T
% 1.15/1.52 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.15/1.52 , T, X ), 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 Z, T, 'tc_nat' ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.15/1.52 ), X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.15/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.15/1.52 Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.52 'c_Suc'( Z ), X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.15/1.52 ), X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.15/1.52 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.15/1.52 , Y, X ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.15/1.52 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.15/1.52 , Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.15/1.52 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.15/1.52 , T, X ), X ), T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), T, X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.15/1.52 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.15/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.15/1.52 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.52 , 'tc_nat' ), 'tc_nat' ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.15/1.52 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.15/1.52 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.15/1.52 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.15/1.52 'tc_Int_Oint' ), Z, 'tc_Int_Oint' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_Int_Oint' ), 'tc_Int_Oint' ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.15/1.52 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.15/1.52 'tc_Int_Oint' ), 'tc_Int_Oint' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_Int_Oint' ), 'tc_Int_Oint' ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.15/1.52 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.15/1.52 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.15/1.52 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.15/1.52 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.15/1.52 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.15/1.52 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.15/1.52 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.15/1.52 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X
% 1.15/1.52 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.15/1.52 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.15/1.52 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.15/1.52 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.15/1.52 Y, T, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.15/1.52 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.15/1.52 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.15/1.52 Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X )
% 1.15/1.52 , 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.15/1.52 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat' ) ), 'tc_nat' ) )
% 1.15/1.52 ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( X,
% 1.15/1.52 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), 'tc_Int_Oint' ),
% 1.15/1.52 'tc_Int_Oint' ), 'tc_Int_Oint' ) ],
% 1.15/1.52 [ ~( =( 'c_Nat_Osemiring__1__class_Oof__nat'( X, 'tc_Int_Oint' ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ) ) ), =( X,
% 1.15/1.52 'c_Int_Onat'( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ) ) )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.15/1.52 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.15/1.52 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.15/1.52 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.15/1.52 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.15/1.52 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.15/1.52 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.15/1.52 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.15/1.52 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.15/1.52 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.15/1.52 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.15/1.52 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.15/1.52 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.15/1.52 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.15/1.52 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.15/1.52 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.15/1.52 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.15/1.52 ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.15/1.52 ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.15/1.52 ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.15/1.52 ), X ) ) ],
% 1.15/1.52 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.15/1.52 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.15/1.52 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.15/1.52 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.15/1.52 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.15/1.52 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.15/1.52 ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.15/1.52 , T, X ) ) ), =( Z, T ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.15/1.52 , T, X ) ) ), =( Y, Z ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.15/1.52 X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Z
% 1.15/1.52 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.15/1.52 , T, X ), X ) ) ],
% 1.15/1.52 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.15/1.52 'tc_nat' ) ), =( Y, Z ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.15/1.52 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 1.15/1.52 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.15/1.52 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.15/1.52 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.52 X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.52 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.15/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.15/1.52 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.15/1.52 , T, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z
% 1.15/1.52 ), X ), 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), X ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.15/1.52 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.15/1.52 , X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.15/1.52 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.15/1.52 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 'tc_nat' ) ), Y, 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat'
% 1.15/1.52 ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 'tc_nat' ) ), Y, 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.15/1.52 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.15/1.52 X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.15/1.52 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.15/1.52 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.15/1.52 ) ],
% 1.15/1.52 [ ~( 'class_RealVector_Oreal__field'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.15/1.52 , U, X ), X ), W, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Z, U, X ), W, X ), X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Y, T, X ), W, X ), U, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.15/1.52 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.15/1.52 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.15/1.52 ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.15/1.52 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.15/1.52 ), X ), X ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.15/1.52 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.15/1.52 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.15/1.52 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, U,
% 1.15/1.52 X ), X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Y, T, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ), X ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.15/1.52 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.15/1.52 , ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.15/1.52 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.15/1.52 'tc_nat' ), Y, 'tc_nat' ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.15/1.52 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.15/1.52 'tc_nat' ), X, 'tc_nat' ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.15/1.52 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.15/1.52 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.15/1.52 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.15/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.15/1.52 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.15/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.15/1.52 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ],
% 1.15/1.52 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 1.15/1.52 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.15/1.52 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.15/1.52 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.15/1.52 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.15/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z
% 1.15/1.52 , X ), 'c_Power_Opower__class_Opower'( Y, Z, X ) ), ~(
% 1.15/1.52 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.15/1.52 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.15/1.52 , X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.15/1.52 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.15/1.52 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.15/1.52 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.15/1.52 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.15/1.52 , X ), W, X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 1.15/1.52 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), T, X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y, X )
% 1.15/1.52 , X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ), X ), T, X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Z, T, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 Y, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), T, X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.15/1.52 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.52 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.15/1.52 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'( Z,
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.15/1.52 , X ), X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.15/1.52 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.15/1.52 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.15/1.52 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 1.15/1.52 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.15/1.52 'tc_nat' ) ) ],
% 1.15/1.52 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 1.15/1.52 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X,
% 1.15/1.52 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.52 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.15/1.52 ), X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.15/1.52 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.15/1.52 ), X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.15/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ominus__class_Ominus'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), T, X ), X ),
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_Int_Oint' ), X ), T, X ) ) ],
% 1.15/1.52 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 X, Y, 'tc_nat' ) ), X, 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) )
% 1.15/1.52 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 1.15/1.52 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.15/1.52 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.15/1.52 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.15/1.52 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.15/1.52 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.15/1.52 [ =( 'c_Int_Onat'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_Int_Oint' ) ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.52 [ =( 'c_Int_Onat'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.15/1.52 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_Int_Oint' ) ), 'c_Suc'( 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.15/1.52 ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.52 ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.15/1.52 X ) ) ],
% 1.15/1.52 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 X, T, 'tc_nat' ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_Int_Oint' ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_Int_Oint' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.15/1.52 X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.15/1.52 X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 1.15/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z
% 1.15/1.52 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'(
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ), Z, X
% 1.15/1.52 ), 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.15/1.52 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.15/1.52 'c_lessequals'( Z, Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.15/1.52 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.52 'c_lessequals'( Z, Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.15/1.52 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.15/1.52 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 1.15/1.52 X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.15/1.52 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.15/1.52 , T, X ), X ), T, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.15/1.52 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 1.15/1.52 Y, Z, X ), X ) ) ],
% 1.15/1.52 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.15/1.52 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.15/1.52 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Z, 'c_Divides_Odiv__class_Odiv'( Y, T, X ), X
% 1.15/1.52 ) ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( T, 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), X
% 1.15/1.52 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.15/1.52 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.15/1.52 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.15/1.52 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.15/1.52 , Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.15/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.15/1.52 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.52 , Z, X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.15/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.15/1.52 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.15/1.52 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.52 , Z, X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.15/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.15/1.52 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.15/1.52 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X
% 1.15/1.52 ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.15/1.52 ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.15/1.52 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ),
% 1.15/1.52 ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X
% 1.15/1.52 ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.15/1.52 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.15/1.52 , Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 1.15/1.52 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.52 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.15/1.52 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 X ), T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 1.15/1.52 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.52 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.15/1.52 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.15/1.52 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.15/1.52 Z, X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.52 Y, Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.15/1.52 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 1.15/1.52 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.15/1.52 ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.15/1.52 ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.15/1.52 'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.15/1.52 ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.15/1.52 'c_Suc'( X ), 'tc_nat' ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.15/1.52 'c_Suc'( X ), 'tc_nat' ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.15/1.52 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.15/1.52 , Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.15/1.52 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.15/1.52 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z,
% 1.15/1.52 Y, 'tc_nat' ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.15/1.52 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.15/1.52 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.15/1.52 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.15/1.52 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.15/1.52 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.15/1.52 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 1.15/1.52 ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.15/1.52 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.15/1.52 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.15/1.52 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.15/1.52 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.52 ) ), =( Y, Z ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.52 ) ), =( Y, Z ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.15/1.52 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.15/1.52 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.15/1.52 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.15/1.52 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.15/1.52 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.15/1.52 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.15/1.52 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.15/1.52 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.15/1.52 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.15/1.52 , U, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.15/1.52 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.15/1.52 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.15/1.52 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.15/1.52 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.52 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.15/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.15/1.52 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.52 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.15/1.52 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.52 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.52 , X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), T
% 1.15/1.52 , X ), 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.15/1.52 X ), Z, X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 1.15/1.52 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 1.15/1.52 'tc_nat' ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 1.15/1.52 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 1.15/1.52 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 1.15/1.52 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.15/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.15/1.52 , 'c_Power_Opower__class_Opower'( Y, Z, X ) ), ~(
% 1.15/1.52 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.15/1.52 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.52 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.15/1.52 , 'tc_nat' ), 'tc_nat' ), 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 X ), X ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Z,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'(
% 1.15/1.52 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.15/1.52 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.15/1.52 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.15/1.52 ), X ), ~( 'c_lessequals'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 'c_Int_OPls', Y,
% 1.15/1.52 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 1.15/1.52 , 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 1.15/1.52 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.15/1.52 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.15/1.52 ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.52 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.15/1.52 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 T, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.15/1.52 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.15/1.52 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X
% 1.15/1.52 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( T, Y, X ), X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.15/1.52 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.15/1.52 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.15/1.52 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.15/1.52 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.15/1.52 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.52 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.15/1.52 , Y, 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.15/1.52 'tc_Int_Oint' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.15/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.15/1.52 T, Z, X ) ) ), =( Y, T ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.15/1.52 , Z ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.15/1.52 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.15/1.52 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.15/1.52 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.15/1.52 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ),
% 1.15/1.52 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_Osucc'( X ), 'tc_nat' ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.15/1.52 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_Osucc'( Y ), X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.15/1.52 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.15/1.52 ), X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 Y, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), T, X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.52 , X ), X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.52 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.15/1.52 ), X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.15/1.52 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.15/1.52 , X ), X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.15/1.52 , T, X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 Y, T, X ), Z, X ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.15/1.52 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.15/1.52 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y, X )
% 1.15/1.52 , X ), Z ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 1.15/1.52 , X ), Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.15/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.52 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.52 , T, X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.15/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.52 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.52 , T, X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.15/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.15/1.52 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.15/1.52 Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.15/1.52 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ) ), =( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.52 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.15/1.52 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.15/1.52 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.15/1.52 , T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), T, X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.15/1.52 , T, X ), Z, X ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.15/1.52 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.15/1.52 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.15/1.52 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.15/1.52 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.15/1.52 , T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.15/1.52 , T, X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.15/1.52 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 1.15/1.52 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 1.15/1.52 W, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 1.15/1.52 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 1.15/1.52 , X ), T, X ), W, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 1.15/1.52 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 1.15/1.52 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 1.15/1.52 W, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 1.15/1.52 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.15/1.52 , X ), W, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.15/1.52 X ), Y ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.15/1.52 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.15/1.52 X ), Y ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.52 , X ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.52 , X ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 1.15/1.52 , X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.15/1.52 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 1.15/1.52 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 1.15/1.52 Z, X ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.15/1.52 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.15/1.52 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 'tc_nat' ), 'tc_nat' ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.15/1.52 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.15/1.52 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.15/1.52 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.52 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.15/1.52 ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.15/1.52 ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Power_Opower__class_Opower'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.15/1.52 T, X ), 'c_Divides_Odiv__class_Odiv'( 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.52 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.15/1.52 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.15/1.52 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.15/1.52 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.15/1.52 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), Y,
% 1.15/1.52 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.15/1.52 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 1.15/1.52 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 1.15/1.52 , T ), =( X, Z ) ],
% 1.15/1.52 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.15/1.52 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 1.15/1.52 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 1.15/1.52 , T ), =( X, Z ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.15/1.52 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.15/1.52 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.15/1.52 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.15/1.52 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 1.15/1.52 , X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.15/1.52 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.15/1.52 Y, X ), Z, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.15/1.52 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.15/1.52 Y, X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.15/1.52 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.15/1.52 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.15/1.52 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.15/1.52 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.15/1.52 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.15/1.52 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( =( X, 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.15/1.52 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.15/1.52 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 1.15/1.52 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 1.15/1.52 X ), Z, X ) ) ],
% 1.15/1.52 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 'tc_nat' ), 'tc_nat' ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.52 , X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.15/1.52 , Z, X ), Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Int_Onat'(
% 1.15/1.52 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 'tc_nat' ), 'tc_Int_Oint' ) ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.52 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.15/1.52 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.15/1.52 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.52 ) ],
% 1.15/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 1.15/1.52 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.15/1.52 'tc_nat' ), X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.15/1.52 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.15/1.52 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.15/1.52 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'(
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ),
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 1.15/1.52 ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X
% 1.15/1.52 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X
% 1.15/1.52 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.52 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) )
% 1.15/1.52 ],
% 1.15/1.52 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.15/1.52 X ) ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 1.15/1.52 , X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.15/1.52 ), X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Int_Oiszero'( Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.52 [ 'c_HOL_Oeq__class_Oeq'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.15/1.52 'tc_Int_Oint' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ),
% 1.15/1.52 'tc_Int_Oint' ), ~( 'c_HOL_Oeq__class_Oeq'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ 'c_HOL_Oeq__class_Oeq'( X, Y, 'tc_Int_Oint' ), ~(
% 1.15/1.52 'c_HOL_Oeq__class_Oeq'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.15/1.52 'tc_Int_Oint' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ),
% 1.15/1.52 'tc_Int_Oint' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ),
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) )
% 1.15/1.52 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.15/1.52 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 Y, X, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.15/1.52 , Y, 'tc_nat' ) ) ],
% 1.15/1.52 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'( Y,
% 1.15/1.52 X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.52 X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.15/1.52 Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.15/1.52 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.15/1.52 ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.15/1.52 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.15/1.52 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.15/1.52 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.15/1.52 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.15/1.52 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.15/1.52 'tc_nat' ), Z, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z
% 1.15/1.52 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.15/1.52 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 X ), T, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.15/1.52 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.15/1.52 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.15/1.52 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.15/1.52 'tc_nat' ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.15/1.52 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.15/1.52 'tc_nat' ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.15/1.52 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.15/1.52 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.15/1.52 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.15/1.52 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.15/1.52 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.15/1.52 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.15/1.52 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.15/1.52 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.15/1.52 'tc_nat' ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.15/1.52 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.15/1.52 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.15/1.52 'tc_nat' ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Nat_Osemiring__1__class_Oof__nat'( X
% 1.15/1.52 , 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint'
% 1.15/1.52 ), 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_Int_Oint' ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Nat_Osemiring__1__class_Oof__nat'( X
% 1.15/1.52 , 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint'
% 1.15/1.52 ), 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_Int_Oint' ) ) ],
% 1.15/1.52 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X,
% 1.15/1.52 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' ), 'tc_Int_Oint' )
% 1.15/1.52 , 'tc_Int_Oint' ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.15/1.52 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 1.15/1.52 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.15/1.52 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), Y,
% 1.15/1.52 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.52 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.15/1.52 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.15/1.52 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.15/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.15/1.52 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.15/1.52 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.15/1.52 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), =( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 1.15/1.52 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.15/1.52 ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.15/1.52 , X ), X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.15/1.52 , X ), X ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.15/1.52 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.15/1.52 ],
% 1.15/1.52 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.52 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.15/1.52 ), 'tc_nat' ), X ) ],
% 1.15/1.52 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.15/1.52 , X, 'tc_nat' ), X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~( 'c_lessequals'( Y,
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.15/1.52 ), Y ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.15/1.52 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.15/1.52 ), ~( =( 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.15/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.15/1.52 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 1.15/1.52 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.15/1.52 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.15/1.52 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 1.15/1.52 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.15/1.52 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.15/1.52 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.15/1.52 , Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.52 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.15/1.52 ), Y ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.15/1.52 ) ) ],
% 1.15/1.52 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.15/1.52 ), Y ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.15/1.52 ), Y ) ],
% 1.15/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.52 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.15/1.52 ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.15/1.52 X ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.15/1.52 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.52 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.52 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.15/1.52 'tc_Int_Oint' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_Int_Oint' ),
% 1.15/1.52 'tc_Int_Oint' ), ~( 'c_lessequals'( Y, T, 'tc_Int_Oint' ) ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( X, Z, 'tc_Int_Oint' ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 1.15/1.52 ,
% 1.15/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.15/1.52 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.15/1.52 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.15/1.52 , X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.15/1.52 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.15/1.52 , X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.15/1.52 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.15/1.52 , X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.15/1.52 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.15/1.52 , X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.15/1.52 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.15/1.52 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.15/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.52 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.15/1.52 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.15/1.52 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 1.15/1.52 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.15/1.52 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.15/1.52 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.15/1.52 'c_HOL_Oone__class_Oone'( X ), X ), 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.52 'c_Int_OPls' ) ), 'tc_nat' ), Y, 'tc_nat' ) ), X ),
% 1.15/1.52 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.15/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.15/1.53 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.15/1.53 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'(
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' )
% 1.15/1.53 ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.53 'c_Suc'( 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' )
% 1.15/1.53 ), X ), X ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.15/1.53 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.15/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.15/1.53 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ),
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.53 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.15/1.53 , X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ),
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.15/1.53 ), X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.15/1.53 , X ), 'c_Int_Onumber__class_Onumber__of'( 'c_HOL_Oplus__class_Oplus'( Y
% 1.15/1.53 , 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint' ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.53 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.15/1.53 , X ), 'c_Int_Onumber__class_Onumber__of'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.53 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.15/1.53 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.53 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.53 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.15/1.53 , X ), ~( 'c_lessequals'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint'
% 1.15/1.53 ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ), 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.15/1.53 , X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.15/1.53 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y,
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.15/1.53 , X ), ~( 'c_lessequals'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint'
% 1.15/1.53 ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.15/1.53 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.15/1.53 , X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.53 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), X ), X ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.15/1.53 , X ) ) ],
% 1.15/1.53 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.15/1.53 , Y, X ) ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.15/1.53 , Y, X ) ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.15/1.53 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.53 ), X ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.15/1.53 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.53 X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.15/1.53 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.15/1.53 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.15/1.53 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.15/1.53 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.15/1.53 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.15/1.53 X ), Z, X ) ) ],
% 1.15/1.53 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.15/1.53 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.53 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.53 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.53 , X ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.15/1.53 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.15/1.53 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.15/1.53 , Y, 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( Z, Y, X ), X ), Z ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), Z ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.53 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.15/1.53 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.53 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.15/1.53 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.15/1.53 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.15/1.53 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.15/1.53 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.15/1.53 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.15/1.53 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.53 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.15/1.53 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.15/1.53 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.15/1.53 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.53 [ ~( 'class_HOL_Oeq'( X ) ), =( Y, Z ), ~( 'c_HOL_Oeq__class_Oeq'( Y, Z
% 1.15/1.53 , X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), X ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.15/1.53 , X ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.53 , X ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( X,
% 1.15/1.53 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' )
% 1.15/1.53 , 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( X,
% 1.15/1.53 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' )
% 1.15/1.53 , 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( X,
% 1.15/1.53 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' )
% 1.15/1.53 , 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( X,
% 1.15/1.53 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' )
% 1.15/1.53 , 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.15/1.53 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.15/1.53 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.15/1.53 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.53 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z,
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.53 ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.15/1.53 [ =( 'c_Int_Onat'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint'
% 1.15/1.53 ) ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ],
% 1.15/1.53 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.15/1.53 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.53 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.15/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 1.15/1.53 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.15/1.53 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.15/1.53 , Z, 'tc_nat' ) ) ],
% 1.15/1.53 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 1.15/1.53 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.15/1.53 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.15/1.53 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.15/1.53 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.53 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.15/1.53 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.53 , 'tc_nat' ), X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.15/1.53 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 1.15/1.53 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.15/1.53 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.15/1.53 ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( T ), X ),
% 1.15/1.53 'c_Power_Opower__class_Opower'( Z, 'c_Suc'( T ), X ), X ) ) ],
% 1.15/1.53 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.53 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( T,
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( Y, U, 'tc_nat' ), 'tc_nat' ) ) ), =(
% 1.15/1.53 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.15/1.53 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.15/1.53 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.53 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.15/1.53 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.15/1.53 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.53 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.15/1.53 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.53 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.15/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.15/1.53 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.15/1.53 Y, T, X ) ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X
% 1.15/1.53 ), Y, X ) ), =( Z, T ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.15/1.53 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.15/1.53 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.15/1.53 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.15/1.53 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_Divides_Osemiring__div'( X )
% 1.15/1.53 ), =( 'c_Divides_Odiv__class_Omod'( 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 Y, X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.15/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_Divides_Osemiring__div'( X )
% 1.15/1.53 ), ~( =( 'c_Divides_Odiv__class_Omod'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.15/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.53 , 'tc_nat' ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.15/1.53 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.53 , 'tc_nat' ), 'tc_nat' ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.15/1.53 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.15/1.53 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.15/1.53 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.15/1.53 ), X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.15/1.53 Y, X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.15/1.53 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.15/1.53 X ), X ) ) ],
% 1.15/1.53 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.15/1.53 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y
% 1.15/1.53 , Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X
% 1.15/1.53 ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z
% 1.15/1.53 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_Power_Opower__class_Opower'( Y
% 1.15/1.53 , Z, X ), X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.15/1.53 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y,
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( T, X )
% 1.15/1.53 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.15/1.53 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ),
% 1.15/1.53 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ),
% 1.15/1.53 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.15/1.53 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.15/1.53 ) ), X, 'tc_nat' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 1.15/1.53 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.15/1.53 ) ), X, 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.15/1.53 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 1.15/1.53 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 Y, 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.15/1.53 Z, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'(
% 1.15/1.53 Z, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), 'c_Int_Oiszero'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.15/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.53 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 1.15/1.53 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 1.15/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.15/1.53 ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.15/1.53 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.15/1.53 ) ],
% 1.15/1.53 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), 'c_Suc'( 'c_Suc'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.15/1.53 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 1.15/1.53 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.15/1.53 ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.15/1.53 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.15/1.53 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.15/1.53 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.15/1.53 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.15/1.53 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.15/1.53 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.15/1.53 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.15/1.53 X ), T, X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.15/1.53 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.15/1.53 X ), T, X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.15/1.53 [ 'c_HOL_Oeq__class_Oeq'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.15/1.53 'tc_Int_Oint' ), ~( 'c_HOL_Oeq__class_Oeq'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'c_HOL_Oeq__class_Oeq'( X, Y, 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_HOL_Oeq__class_Oeq'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.15/1.53 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.15/1.53 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.15/1.53 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.15/1.53 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.15/1.53 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.15/1.53 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit1'( X ),
% 1.15/1.53 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit1'( X ),
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OPls', 'tc_Int_Oint' ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OPls',
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oeq__class_Oeq'( 'c_Int_OPls', 'c_Int_OPls', 'tc_Int_Oint' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.15/1.53 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Int_OPls', 'tc_Int_Oint' ), X )
% 1.15/1.53 ],
% 1.15/1.53 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_OPls', X, 'tc_Int_Oint' ), X ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Int_OPls', 'tc_Int_Oint' ), X ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.15/1.53 ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.15/1.53 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.15/1.53 ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.15/1.53 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ),
% 1.15/1.53 'tc_Int_Oint' ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ),
% 1.15/1.53 'tc_Int_Oint' ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y )
% 1.15/1.53 , 'tc_Int_Oint' ), 'c_Int_OBit0'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.15/1.53 'c_Int_Osucc'( Y ), 'tc_Int_Oint' ) ) ) ],
% 1.15/1.53 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y
% 1.15/1.53 ), 'tc_Int_Oint' ), 'c_Int_OBit1'( 'c_HOL_Ominus__class_Ominus'(
% 1.15/1.53 'c_Int_Opred'( X ), Y, 'tc_Int_Oint' ) ) ) ],
% 1.15/1.53 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.15/1.53 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.15/1.53 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.15/1.53 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.15/1.53 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.15/1.53 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.15/1.53 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y )
% 1.15/1.53 , 'tc_Int_Oint' ), 'c_Int_OBit0'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.15/1.53 'tc_Int_Oint' ) ) ) ],
% 1.15/1.53 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y
% 1.15/1.53 ), 'tc_Int_Oint' ), 'c_Int_OBit0'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.15/1.53 'tc_Int_Oint' ) ) ) ],
% 1.15/1.53 [ =( 'c_Int_OBit0'( X ), 'c_HOL_Oplus__class_Oplus'( X, X, 'tc_Int_Oint'
% 1.15/1.53 ) ) ],
% 1.15/1.53 [ 'c_HOL_Oeq__class_Oeq'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.15/1.53 'tc_Int_Oint' ), ~( 'c_HOL_Oeq__class_Oeq'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'c_HOL_Oeq__class_Oeq'( X, Y, 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_HOL_Oeq__class_Oeq'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.15/1.53 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ) ), X ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.15/1.53 Y, Z, X ), X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Z,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 X ) ) ],
% 1.15/1.53 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.15/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.15/1.53 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.53 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ) ), X ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.15/1.53 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.15/1.53 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.15/1.53 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.15/1.53 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.15/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X
% 1.15/1.53 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.15/1.53 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.15/1.53 'c_HOL_Oone__class_Oone'( X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), Y, 'tc_nat' ), X ),
% 1.15/1.53 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' )
% 1.15/1.53 , X ), X ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.15/1.53 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 X ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ), X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.15/1.53 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), X ), =( Z,
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), X ), =( Y,
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.15/1.53 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), X )
% 1.15/1.53 ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.15/1.53 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.53 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.15/1.53 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.53 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.15/1.53 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.53 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.15/1.53 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.53 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.15/1.53 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.15/1.53 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.15/1.53 , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.53 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.15/1.53 , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.15/1.53 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.15/1.53 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.15/1.53 , 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.15/1.53 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.15/1.53 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.15/1.53 , 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X,
% 1.15/1.53 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.15/1.53 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.15/1.53 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ), 'c_lessequals'( X
% 1.15/1.53 , 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.15/1.53 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.15/1.53 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.15/1.53 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.15/1.53 , ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.15/1.53 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' )
% 1.15/1.53 ) ],
% 1.15/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.15/1.53 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), Y, X ), Z, X ), X )
% 1.15/1.53 ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), X ), X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.15/1.53 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.15/1.53 ],
% 1.15/1.53 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.15/1.53 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'(
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' )
% 1.15/1.53 ), 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.15/1.53 ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ) ) ],
% 1.15/1.53 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.15/1.53 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.15/1.53 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.15/1.53 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.15/1.53 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.15/1.53 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.15/1.53 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.15/1.53 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.15/1.53 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.15/1.53 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.15/1.53 ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.15/1.53 ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.15/1.53 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' )
% 1.15/1.53 , X ), 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ), X ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.15/1.53 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ), =( Y
% 1.15/1.53 , Z ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.15/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), =(
% 1.15/1.53 Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.53 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.15/1.53 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.15/1.53 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'( 'c_Suc'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.15/1.53 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Int_Onat'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_Int_Oint' ) ) ) ],
% 1.15/1.53 [ =( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.15/1.53 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit1'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y
% 1.15/1.53 , X ) ) ],
% 1.15/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.15/1.53 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), X ), Y, X ), Z, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.15/1.53 ) ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit1'( Y ), X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.53 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 1.15/1.53 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.53 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.53 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.15/1.53 ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.53 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.15/1.53 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.15/1.53 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.15/1.53 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.15/1.53 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.15/1.53 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.15/1.53 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.15/1.53 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.15/1.53 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.15/1.53 X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.15/1.53 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.15/1.53 Z, T, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.53 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.15/1.53 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'(
% 1.15/1.53 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.15/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.15/1.53 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.15/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 1.15/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.15/1.53 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.53 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.15/1.53 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.15/1.53 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.15/1.53 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.53 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.15/1.53 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.15/1.53 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.53 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.15/1.53 , X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.15/1.53 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.15/1.53 ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.15/1.53 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.15/1.53 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 1.15/1.53 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.15/1.53 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.15/1.53 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.15/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Power_Opower__class_Opower'(
% 1.15/1.53 Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.15/1.53 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.15/1.53 'tc_Int_Oint' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_Int_Oint' ),
% 1.15/1.53 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_Int_Oint' ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.15/1.53 ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.15/1.53 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.15/1.53 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.15/1.53 X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.15/1.53 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 Z, T, X ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 Z, T, X ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.15/1.53 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.15/1.53 X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.15/1.53 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 Y, T, X ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 Y, T, X ) ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.15/1.53 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( Z, Y,
% 1.15/1.53 'tc_Int_Oint' ) ), ~( 'c_lessequals'( X, Z, 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( X, X, 'tc_Int_Oint' ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.15/1.53 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.15/1.53 , X ) ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.15/1.53 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.15/1.53 , X ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.53 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 1.15/1.53 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.15/1.53 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.15/1.53 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.15/1.53 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.15/1.53 ) ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.15/1.53 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.15/1.53 ) ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.15/1.53 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.53 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.15/1.53 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.15/1.53 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.15/1.53 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( Y, X,
% 1.15/1.53 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.53 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.15/1.53 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.15/1.53 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.53 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.15/1.53 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.15/1.53 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.15/1.53 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.53 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 1.15/1.53 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.53 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 1.15/1.53 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.53 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.15/1.53 , X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 1.15/1.53 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.15/1.53 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.15/1.53 ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~( 'c_lessequals'(
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.15/1.53 ), X ), Z, X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.15/1.53 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.15/1.53 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.15/1.53 , Y, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.53 ) ],
% 1.15/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 1.15/1.53 , X ), X ), Y ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.53 ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.15/1.53 , Y, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.15/1.53 , T, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.15/1.53 , T, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.15/1.53 , Y, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.15/1.53 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.15/1.53 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.53 , 'tc_nat' ), X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.15/1.53 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.53 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~( 'c_Int_Oiszero'(
% 1.15/1.53 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.15/1.53 'tc_nat' ), X ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.53 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Z, Y, X
% 1.15/1.53 ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.15/1.53 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.15/1.53 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.15/1.53 ), X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.15/1.53 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.15/1.53 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.15/1.53 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.15/1.53 ), X ) ) ],
% 1.15/1.53 [ =( X, 'c_Int_Onat'( 'c_Nat_Osemiring__1__class_Oof__nat'( X,
% 1.15/1.53 'tc_Int_Oint' ) ) ) ],
% 1.15/1.53 [ =( 'c_Int_Onat'( 'c_Nat_Osemiring__1__class_Oof__nat'( X,
% 1.15/1.53 'tc_Int_Oint' ) ), X ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.15/1.53 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.15/1.53 , 'tc_nat' ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.15/1.53 ), =( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.15/1.53 , U, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( U,
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.15/1.53 , U, X ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 1.15/1.53 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, Z, X ), T, X ) ) ],
% 1.15/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.53 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 1.15/1.53 , X ) ) ],
% 1.15/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.15/1.53 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 1.15/1.53 , X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.15/1.53 ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.15/1.53 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.15/1.53 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.15/1.53 ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.15/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.15/1.53 Y, X ), X ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.53 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.15/1.53 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y, X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.53 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( Y,
% 1.15/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.15/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.15/1.53 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ),
% 1.15/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.15/1.53 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 1.15/1.53 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.15/1.53 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.15/1.53 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 1.15/1.53 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.15/1.53 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.15/1.53 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.15/1.53 'c_lessequals'( Z, Y, X ) ],
% 1.15/1.53 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.15/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 1.15/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 1.15/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.15/1.53 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 1.15/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 1.15/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 1.15/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), 'c_lessequals'( Y, X,
% 1.15/1.53 'tc_Int_Oint' ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.15/1.53 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.15/1.53 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.15/1.53 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.15/1.53 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.15/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.53 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.15/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.15/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), 'c_Int_Oiszero'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ) ],
% 1.15/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), Y, X ), Y ) ],
% 1.15/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'( Y
% 1.15/1.53 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ), Y ) ],
% 1.15/1.53 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.15/1.53 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.15/1.53 ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y
% 1.15/1.53 ), X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.15/1.53 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.15/1.53 Y ), X ), X ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.15/1.53 , X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.15/1.53 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), X ), Y, X ), 'c_HOL_Oplus__class_Oplus'( Y, Y, X ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 Y, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), X ), X ), 'c_HOL_Oplus__class_Oplus'( Y, Y, X ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ ~( 'c_HOL_Oeq__class_Oeq'( 'c_Int_OPls', 'c_Int_OBit1'( X ),
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ =( 'c_Int_Osucc'( 'c_Int_OPls' ), 'c_Int_OBit1'( 'c_Int_OPls' ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ ~( 'c_HOL_Oeq__class_Oeq'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.15/1.53 'c_Int_OPls', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.15/1.53 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ =( 'c_Int_Osucc'( 'c_Int_OBit1'( X ) ), 'c_Int_OBit0'( 'c_Int_Osucc'(
% 1.15/1.53 X ) ) ) ],
% 1.15/1.53 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y )
% 1.15/1.53 , 'tc_Int_Oint' ), 'c_Int_OBit1'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.15/1.53 'tc_Int_Oint' ) ) ) ],
% 1.15/1.53 [ =( 'c_Int_Osucc'( 'c_Int_OBit0'( X ) ), 'c_Int_OBit1'( X ) ) ],
% 1.15/1.53 [ ~( 'c_HOL_Oeq__class_Oeq'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.15/1.53 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.15/1.53 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.15/1.53 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.15/1.53 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ =( 'c_Int_Opred'( 'c_Int_OBit1'( X ) ), 'c_Int_OBit0'( X ) ) ],
% 1.15/1.53 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y
% 1.15/1.53 ), 'tc_Int_Oint' ), 'c_Int_OBit1'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.15/1.53 'tc_Int_Oint' ) ) ) ],
% 1.15/1.53 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y )
% 1.15/1.53 , 'tc_Int_Oint' ), 'c_Int_OBit1'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.15/1.53 'tc_Int_Oint' ) ) ) ],
% 1.15/1.53 [ ~( 'c_HOL_Oeq__class_Oeq'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ),
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ =( 'c_Int_Opred'( 'c_Int_OBit0'( X ) ), 'c_Int_OBit1'( 'c_Int_Opred'(
% 1.15/1.53 X ) ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.15/1.53 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.15/1.53 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y
% 1.15/1.53 ), 'tc_Int_Oint' ), 'c_Int_OBit0'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.15/1.53 'tc_Int_Oint' ) ) ) ],
% 1.15/1.53 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.15/1.53 'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.15/1.53 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X,
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oeq__class_Oeq'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.15/1.53 'tc_Int_Oint' ), ~( 'c_HOL_Oeq__class_Oeq'( 'c_Int_OPls', X,
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oeq__class_Oeq'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_HOL_Oeq__class_Oeq'( 'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' )
% 1.15/1.53 ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.15/1.53 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.15/1.53 'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.15/1.53 'tc_Int_Oint' ), 'c_Int_OBit0'( 'c_HOL_Ominus__class_Ominus'(
% 1.15/1.53 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ) ],
% 1.15/1.53 [ 'c_HOL_Oeq__class_Oeq'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.15/1.53 'tc_Int_Oint' ), ~( 'c_HOL_Oeq__class_Oeq'( X, 'c_Int_OPls',
% 1.15/1.53 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oeq__class_Oeq'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.15/1.53 'c_HOL_Oeq__class_Oeq'( 'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' )
% 1.15/1.53 ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.15/1.53 Y, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ],
% 1.15/1.53 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.15/1.53 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.15/1.53 ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.15/1.53 ) ) ],
% 1.15/1.53 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Int_Onat'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_Int_Oint' ) ) ) ],
% 1.15/1.53 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X, X,
% 1.15/1.53 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.15/1.53 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ],
% 1.15/1.53 [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ), ~(
% 1.15/1.53 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.15/1.53 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.15/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' )
% 1.15/1.53 ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ), X ),
% 1.15/1.53 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.15/1.53 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ],
% 1.15/1.53 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.15/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.15/1.53 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' )
% 1.15/1.53 , 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.15/1.53 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.15/1.53 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes'( Y, Y, X ) ) ],
% 1.15/1.53 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_Int_Oint' ) ) ],
% 1.15/1.53 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.15/1.53 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ), 'tc_nat' ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.15/1.53 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.15/1.53 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.15/1.53 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ],
% 1.15/1.53 [ =( 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.15/1.53 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.15/1.53 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.15/1.53 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.15/1.53 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 1.15/1.53 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.15/1.53 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.15/1.53 'c_HOL_Oplus__class_Oplus'( X, X, 'tc_nat' ) ) ],
% 1.15/1.53 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' )
% 1.15/1.53 , 'c_HOL_Oplus__class_Oplus'( X, X, 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.15/1.53 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_Power_Opower__class_Opower'( Y
% 1.15/1.53 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ],
% 1.15/1.53 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.15/1.53 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.15/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.15/1.53 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.15/1.53 X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.15/1.53 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.15/1.53 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X
% 1.15/1.53 ) ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.15/1.53 ), Y ) ],
% 1.15/1.53 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.15/1.53 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.15/1.53 ), Y ) ],
% 1.15/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.15/1.53 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.15/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.15/1.53 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.15/1.53 ) ],
% 1.15/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.15/1.53 ) ) ],
% 1.15/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), Y
% 1.15/1.53 , X ), Y ) ],
% 1.15/1.53 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.15/1.53 Y, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.15/1.53 , X ), Y ) ],
% 1.15/1.53 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.15/1.53 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.15/1.53 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.15/1.53 'tc_nat' ) ) ],
% 1.15/1.53 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.15/1.53 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.15/1.53 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.15/1.53 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.15/1.53 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.15/1.53 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.15/1.53 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.15/1.53 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.15/1.53 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.15/1.53 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.15/1.53 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.15/1.53 [ ~( =( 'c_FFT__Mirabelle_Oroot'( 'c_Int_Onumber__class_Onumber__of'(
% 1.15/1.53 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.15/1.53 ) ), 'c_Complex_Oii' ) ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.15/1.53 ],
% 1.15/1.53 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.15/1.53 ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.15/1.53 ],
% 1.15/1.53 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_HOL_Oeq'( 'tc_nat' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.15/1.53 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.15/1.53 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.15/1.53 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.15/1.53 ],
% 1.15/1.53 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.15/1.53 ],
% 1.15/1.53 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Nat_Osemiring__char__0'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Odvd'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_HOL_Oeq'( 'tc_Int_Oint' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.15/1.53 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.15/1.53 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.15/1.53 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.15/1.53 ],
% 1.15/1.53 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.15/1.53 ],
% 1.15/1.53 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.15/1.53 ],
% 1.15/1.53 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_Complex_Ocomplex' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.15/1.53 ,
% 1.15/1.53 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_RealVector_Oreal__field'( 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_Nat_Osemiring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_Ring__and__Field_Odvd'( 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ],
% 1.15/1.53 [ 'class_HOL_Oeq'( 'tc_Complex_Ocomplex' ) ]
% 1.15/1.53 ] .
% 1.15/1.53
% 1.15/1.53
% 1.15/1.53 percentage equality = 0.214834, percentage horn = 0.841135
% 1.15/1.53 This is a problem with some equality
% 1.15/1.53
% 1.15/1.53
% 1.15/1.53
% 1.15/1.53 Options Used:
% 1.15/1.53
% 1.15/1.53 useres = 1
% 1.15/1.53 useparamod = 1
% 1.15/1.53 useeqrefl = 1
% 1.15/1.53 useeqfact = 1
% 1.15/1.53 usefactor = 1
% 1.15/1.53 usesimpsplitting = 0
% 1.15/1.53 usesimpdemod = 5
% 1.15/1.53 usesimpres = 3
% 1.15/1.53
% 1.15/1.53 resimpinuse = 1000
% 1.15/1.53 resimpclauses = 20000
% 1.15/1.53 substype = eqrewr
% 1.15/1.53 backwardsubs = 1
% 1.15/1.53 selectoldest = 5
% 1.15/1.53
% 1.15/1.53 litorderings [0] = split
% 1.15/1.53 litorderings [1] = extend the termordering, first sorting on arguments
% 1.15/1.53
% 1.15/1.53 termordering = kbo
% 1.15/1.53
% 1.15/1.53 litapriori = 0
% 1.15/1.53 termapriori = 1
% 1.15/1.53 litaposteriori = 0
% 1.15/1.53 termaposteriori = 0
% 1.15/1.53 demodaposteriori = 0
% 1.15/1.53 ordereqreflfact = 0
% 1.15/1.53
% 1.15/1.53 litselect = negord
% 1.15/1.53
% 1.15/1.53 maxweight = 15
% 1.15/1.53 maxdepth = 30000
% 1.15/1.53 maxlength = 115
% 1.15/1.53 maxnrvars = 195
% 1.15/1.53 excuselevel = 1
% 1.15/1.53 increasemaxweight = 1
% 1.15/1.53
% 1.15/1.53 maxselected = 10000000
% 1.15/1.53 maxnrclauses = 10000000
% 1.15/1.53
% 1.15/1.53 showgenerated = 0
% 1.15/1.53 showkept = 0
% 1.15/1.53 showselected = 0
% 1.15/1.53 showdeleted = 0
% 1.15/1.53 showresimp = 1
% 1.15/1.53 showstatus = 2000
% 1.15/1.53
% 1.15/1.53 prologoutput = 1
% 1.15/1.53 nrgoals = 5000000
% 1.15/1.53 totalproof = 1
% 1.15/1.53
% 1.15/1.53 Symbols occurring in the translation:
% 1.15/1.53
% 1.15/1.53 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.15/1.53 . [1, 2] (w:1, o:143, a:1, s:1, b:0),
% 1.15/1.53 ! [4, 1] (w:0, o:60, a:1, s:1, b:0),
% 1.15/1.53 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.15/1.53 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.15/1.53 'class_Ring__and__Field_Odivision__ring' [40, 1] (w:1, o:69, a:1, s:1
% 1.15/1.53 , b:0),
% 1.15/1.53 'c_HOL_Otimes__class_Otimes' [43, 3] (w:1, o:175, a:1, s:1, b:0),
% 1.15/1.53 'c_HOL_Oone__class_Oone' [44, 1] (w:1, o:70, a:1, s:1, b:0),
% 1.15/1.53 'c_HOL_Oinverse__class_Oinverse' [45, 2] (w:1, o:168, a:1, s:1, b:0)
% 1.49/1.84 ,
% 1.49/1.84 'c_Suc' [47, 1] (w:1, o:71, a:1, s:1, b:0),
% 1.49/1.84 'class_Ring__and__Field_Oordered__ring__strict' [48, 1] (w:1, o:75
% 1.49/1.84 , a:1, s:1, b:0),
% 1.49/1.84 'c_HOL_Oplus__class_Oplus' [51, 3] (w:1, o:177, a:1, s:1, b:0),
% 1.49/1.84 'c_HOL_Ozero__class_Ozero' [52, 1] (w:1, o:76, a:1, s:1, b:0),
% 1.49/1.84 'class_Ring__and__Field_Oidom' [53, 1] (w:1, o:77, a:1, s:1, b:0),
% 1.49/1.84 'class_Int_Onumber__ring' [54, 1] (w:1, o:79, a:1, s:1, b:0),
% 1.49/1.84 'tc_nat' [58, 0] (w:1, o:36, a:1, s:1, b:0),
% 1.49/1.84 'class_Ring__and__Field_Opordered__ring' [59, 1] (w:1, o:86, a:1, s:1
% 1.49/1.84 , b:0),
% 1.49/1.84 'c_lessequals' [60, 3] (w:1, o:178, a:1, s:1, b:0),
% 1.49/1.84 'class_Ring__and__Field_Omult__mono' [61, 1] (w:1, o:87, a:1, s:1, b:
% 1.49/1.84 0),
% 1.49/1.84 'class_Ring__and__Field_Omult__mono1' [62, 1] (w:1, o:88, a:1, s:1
% 1.49/1.84 , b:0),
% 1.49/1.84 'c_Divides_Odiv__class_Omod' [64, 3] (w:1, o:179, a:1, s:1, b:0),
% 1.49/1.84 'c_HOL_Oord__class_Oless' [65, 3] (w:1, o:176, a:1, s:1, b:0),
% 1.49/1.84 'class_Ring__and__Field_Ofield' [66, 1] (w:1, o:89, a:1, s:1, b:0),
% 1.49/1.84 'class_Ring__and__Field_Odivision__by__zero' [67, 1] (w:1, o:90, a:1
% 1.49/1.84 , s:1, b:0),
% 1.49/1.84 'c_HOL_Oinverse__class_Odivide' [68, 3] (w:1, o:180, a:1, s:1, b:0),
% 1.49/1.84
% 1.49/1.84 'class_Ring__and__Field_Oordered__semidom' [69, 1] (w:1, o:80, a:1
% 1.49/1.84 , s:1, b:0),
% 1.49/1.84 'c_Power_Opower__class_Opower' [70, 3] (w:1, o:181, a:1, s:1, b:0),
% 1.49/1.84 'class_Ring__and__Field_Oordered__field' [71, 1] (w:1, o:81, a:1, s:1
% 1.49/1.84 , b:0),
% 1.49/1.84 'class_RealVector_Oreal__normed__field' [72, 1] (w:1, o:91, a:1, s:1
% 1.49/1.84 , b:0),
% 1.49/1.84 'c_HOL_Ominus__class_Ominus' [73, 3] (w:1, o:182, a:1, s:1, b:0),
% 1.49/1.84 'c_HOL_Ouminus__class_Ouminus' [75, 2] (w:1, o:169, a:1, s:1, b:0),
% 1.49/1.84 'c_Divides_Odiv__class_Odiv' [77, 3] (w:1, o:183, a:1, s:1, b:0),
% 1.49/1.84 'class_Ring__and__Field_Ocomm__semiring__1' [78, 1] (w:1, o:67, a:1
% 1.49/1.84 , s:1, b:0),
% 1.49/1.84 'c_Ring__and__Field_Odvd__class_Odvd' [79, 3] (w:1, o:184, a:1, s:1
% 1.49/1.84 , b:0),
% 1.49/1.84 'class_OrderedGroup_Ogroup__add' [80, 1] (w:1, o:93, a:1, s:1, b:0),
% 1.49/1.84
% 1.49/1.84 'class_OrderedGroup_Opordered__ab__group__add__abs' [81, 1] (w:1, o:
% 1.49/1.84 95, a:1, s:1, b:0),
% 1.49/1.84 'c_HOL_Oabs__class_Oabs' [82, 2] (w:1, o:170, a:1, s:1, b:0),
% 1.49/1.84 'class_Ring__and__Field_Oordered__semiring__strict' [83, 1] (w:1, o:
% 1.49/1.84 82, a:1, s:1, b:0),
% 1.49/1.84 'class_Divides_Osemiring__div' [84, 1] (w:1, o:97, a:1, s:1, b:0),
% 1.49/1.84 'class_Ring__and__Field_Oordered__idom' [85, 1] (w:1, o:83, a:1, s:1
% 1.49/1.84 , b:0),
% 1.49/1.84 'c_Int_Onumber__class_Onumber__of' [86, 2] (w:1, o:171, a:1, s:1, b:0
% 1.49/1.84 ),
% 1.49/1.84 'c_Int_OPls' [87, 0] (w:1, o:38, a:1, s:1, b:0),
% 1.49/1.84 'tc_Int_Oint' [88, 0] (w:1, o:39, a:1, s:1, b:0),
% 1.49/1.84 'c_Parity_Oeven__odd__class_Oeven' [89, 2] (w:1, o:172, a:1, s:1, b:0
% 1.49/1.84 ),
% 1.49/1.84 'class_Ring__and__Field_Osemiring__0' [90, 1] (w:1, o:102, a:1, s:1
% 1.49/1.84 , b:0),
% 1.49/1.84 'class_Power_Opower' [91, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.49/1.84 'class_Ring__and__Field_Ozero__neq__one' [92, 1] (w:1, o:124, a:1, s:
% 1.49/1.84 1, b:0),
% 1.49/1.84 'class_Ring__and__Field_Ono__zero__divisors' [93, 1] (w:1, o:74, a:1
% 1.49/1.84 , s:1, b:0),
% 1.49/1.84 'class_Ring__and__Field_Omult__zero' [94, 1] (w:1, o:73, a:1, s:1, b:
% 1.49/1.84 0),
% 1.49/1.84 'class_Int_Onumber' [95, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.49/1.84 'class_OrderedGroup_Opordered__ab__group__add' [98, 1] (w:1, o:103
% 1.49/1.84 , a:1, s:1, b:0),
% 1.49/1.84 'class_Ring__and__Field_Oring__1__no__zero__divisors' [100, 1] (w:1
% 1.49/1.84 , o:98, a:1, s:1, b:0),
% 1.49/1.84 'class_OrderedGroup_Oab__semigroup__idem__mult' [101, 1] (w:1, o:104
% 1.49/1.84 , a:1, s:1, b:0),
% 1.49/1.84 'class_OrderedGroup_Olordered__ab__group__add' [104, 1] (w:1, o:105
% 1.49/1.84 , a:1, s:1, b:0),
% 1.49/1.84 'class_Ring__and__Field_Oring' [105, 1] (w:1, o:99, a:1, s:1, b:0),
% 1.49/1.84 'class_Ring__and__Field_Opordered__ring__abs' [106, 1] (w:1, o:126
% 1.49/1.84 , a:1, s:1, b:0),
% 1.49/1.84 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [107, 1]
% 1.49/1.84 (w:1, o:106, a:1, s:1, b:0),
% 1.49/1.84 'class_OrderedGroup_Opordered__ab__semigroup__add' [108, 1] (w:1, o:
% 1.49/1.84 107, a:1, s:1, b:0),
% 1.49/1.84 'c_Nat_Osemiring__1__class_Oof__nat' [111, 2] (w:1, o:173, a:1, s:1
% 1.49/1.84 , b:0),
% 1.49/1.84 'c_Int_Onat' [112, 1] (w:1, o:127, a:1, s:1, b:0),
% 12.76/13.13 'class_Ring__and__Field_Osemiring__1' [113, 1] (w:1, o:128, a:1, s:1
% 12.76/13.13 , b:0),
% 12.76/13.13 'class_OrderedGroup_Ocomm__monoid__mult' [116, 1] (w:1, o:108, a:1
% 12.76/13.13 , s:1, b:0),
% 12.76/13.13 'class_Ring__and__Field_Odvd' [117, 1] (w:1, o:129, a:1, s:1, b:0),
% 12.76/13.13 'class_Ring__and__Field_Ocomm__ring' [118, 1] (w:1, o:65, a:1, s:1
% 12.76/13.13 , b:0),
% 12.76/13.13 'class_Orderings_Oorder' [121, 1] (w:1, o:109, a:1, s:1, b:0),
% 12.76/13.13 'class_Orderings_Olinorder' [122, 1] (w:1, o:110, a:1, s:1, b:0),
% 12.76/13.13 'class_Ring__and__Field_Opordered__cancel__semiring' [123, 1] (w:1
% 12.76/13.13 , o:130, a:1, s:1, b:0),
% 12.76/13.13 'class_Divides_Oring__div' [124, 1] (w:1, o:96, a:1, s:1, b:0),
% 12.76/13.13 'class_OrderedGroup_Oab__semigroup__mult' [125, 1] (w:1, o:111, a:1
% 12.76/13.13 , s:1, b:0),
% 12.76/13.13 'class_RealVector_Oreal__normed__algebra' [130, 1] (w:1, o:131, a:1
% 12.76/13.13 , s:1, b:0),
% 12.76/13.13 'class_Lattices_Oboolean__algebra' [135, 1] (w:1, o:132, a:1, s:1, b:
% 12.76/13.13 0),
% 12.76/13.13 'class_OrderedGroup_Olordered__ab__group__add__abs' [136, 1] (w:1, o:
% 12.76/13.13 112, a:1, s:1, b:0),
% 12.76/13.13 'class_OrderedGroup_Opordered__comm__monoid__add' [138, 1] (w:1, o:
% 12.76/13.13 113, a:1, s:1, b:0),
% 12.76/13.13 'c_Int_Opred' [139, 1] (w:1, o:133, a:1, s:1, b:0),
% 12.76/13.13 'class_Ring__and__Field_Oring__no__zero__divisors' [140, 1] (w:1, o:
% 12.76/13.13 100, a:1, s:1, b:0),
% 12.76/13.13 'c_Int_Osucc' [141, 1] (w:1, o:134, a:1, s:1, b:0),
% 12.76/13.13 'class_Ring__and__Field_Ocomm__ring__1' [143, 1] (w:1, o:66, a:1, s:1
% 12.76/13.13 , b:0),
% 12.76/13.13 'class_OrderedGroup_Oab__group__add' [144, 1] (w:1, o:114, a:1, s:1
% 12.76/13.13 , b:0),
% 12.76/13.13 'class_Ring__and__Field_Ocomm__semiring' [145, 1] (w:1, o:68, a:1, s:
% 12.76/13.13 1, b:0),
% 12.76/13.13 'class_OrderedGroup_Oordered__ab__group__add' [146, 1] (w:1, o:94, a:
% 12.76/13.13 1, s:1, b:0),
% 12.76/13.13 'class_HOL_Oeq' [147, 1] (w:1, o:78, a:1, s:1, b:0),
% 12.76/13.13 'c_HOL_Oeq__class_Oeq' [148, 3] (w:1, o:185, a:1, s:1, b:0),
% 12.76/13.13 'class_Ring__and__Field_Opordered__semiring' [149, 1] (w:1, o:135, a:
% 12.76/13.13 1, s:1, b:0),
% 12.76/13.13 'class_Ring__and__Field_Oabs__if' [150, 1] (w:1, o:136, a:1, s:1, b:0
% 12.76/13.13 ),
% 12.76/13.13 'class_Ring__and__Field_Oordered__semiring' [151, 1] (w:1, o:84, a:1
% 12.76/13.13 , s:1, b:0),
% 12.76/13.13 'class_Nat_Osemiring__char__0' [152, 1] (w:1, o:92, a:1, s:1, b:0),
% 12.76/13.13 'class_OrderedGroup_Ocomm__monoid__add' [154, 1] (w:1, o:115, a:1, s:
% 12.76/13.13 1, b:0),
% 12.76/13.13 'class_Ring__and__Field_Olordered__ring' [156, 1] (w:1, o:72, a:1, s:
% 12.76/13.13 1, b:0),
% 12.76/13.13 'c_Int_OBit0' [157, 1] (w:1, o:137, a:1, s:1, b:0),
% 12.76/13.13 'class_OrderedGroup_Omonoid__mult' [158, 1] (w:1, o:116, a:1, s:1, b:
% 12.76/13.13 0),
% 12.76/13.13 'class_OrderedGroup_Ocancel__ab__semigroup__add' [159, 1] (w:1, o:117
% 12.76/13.13 , a:1, s:1, b:0),
% 12.76/13.13 'class_OrderedGroup_Ocancel__semigroup__add' [160, 1] (w:1, o:118, a:
% 12.76/13.13 1, s:1, b:0),
% 12.76/13.13 'class_Orderings_Opreorder' [162, 1] (w:1, o:119, a:1, s:1, b:0),
% 12.76/13.13 'class_OrderedGroup_Oab__semigroup__add' [166, 1] (w:1, o:120, a:1
% 12.76/13.13 , s:1, b:0),
% 12.76/13.13 'class_Ring__and__Field_Osemiring' [167, 1] (w:1, o:138, a:1, s:1, b:
% 12.76/13.13 0),
% 12.76/13.13 'class_RealVector_Oreal__field' [168, 1] (w:1, o:139, a:1, s:1, b:0)
% 12.76/13.13 ,
% 12.76/13.13 'c_Int_OBit1' [170, 1] (w:1, o:140, a:1, s:1, b:0),
% 12.76/13.13 'class_Ring__and__Field_Oring__1' [171, 1] (w:1, o:101, a:1, s:1, b:0
% 12.76/13.13 ),
% 12.76/13.13 'c_Int_Oiszero' [173, 2] (w:1, o:174, a:1, s:1, b:0),
% 12.76/13.13 'class_Ring__and__Field_Oordered__comm__semiring__strict' [174, 1]
% 12.76/13.13 (w:1, o:85, a:1, s:1, b:0),
% 12.76/13.13 'class_OrderedGroup_Omonoid__add' [175, 1] (w:1, o:121, a:1, s:1, b:0
% 12.76/13.13 ),
% 12.76/13.13 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [176, 1]
% 12.76/13.13 (w:1, o:122, a:1, s:1, b:0),
% 12.76/13.13 'class_Int_Oring__char__0' [182, 1] (w:1, o:141, a:1, s:1, b:0),
% 12.76/13.13 'c_FFT__Mirabelle_Oroot' [183, 1] (w:1, o:142, a:1, s:1, b:0),
% 12.76/13.13 'c_Complex_Oii' [184, 0] (w:1, o:58, a:1, s:1, b:0),
% 12.76/13.13 'tc_Complex_Ocomplex' [185, 0] (w:1, o:59, a:1, s:1, b:0).
% 12.76/13.13
% 12.76/13.13
% 12.76/13.13 Starting Search:
% 12.76/13.13
% 12.76/13.13 Resimplifying inuse:
% 12.76/13.13 Done
% 12.76/13.13
% 12.76/13.13
% 12.76/13.13 Intermediate Status:
% 12.76/13.13 Generated: 5005
% 12.76/13.13 Kept: 2003
% 12.76/13.13 Inuse: 42
% 12.76/13.13 Deleted: 0
% 12.76/13.13 Deletedinuse: 0
% 12.76/13.13
% 12.76/13.13 Resimplifying inuse:
% 12.76/13.13 Done
% 12.76/13.13
% 12.76/13.13 Resimplifying inuse:
% 12.76/13.13 Done
% 12.76/13.13
% 12.76/13.13
% 12.76/13.13 Intermediate Status:
% 12.76/13.13 Generated: 12305
% 12.76/13.13 Kept: 4012
% 12.76/13.13 Inuse: 163
% 12.76/13.13 Deleted: 2
% 12.76/13.13 Deletedinuse: 0
% 12.76/13.13
% 12.76/13.13 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 20228
% 47.72/48.07 Kept: 6196
% 47.72/48.07 Inuse: 269
% 47.72/48.07 Deleted: 12
% 47.72/48.07 Deletedinuse: 0
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 28059
% 47.72/48.07 Kept: 8226
% 47.72/48.07 Inuse: 382
% 47.72/48.07 Deleted: 16
% 47.72/48.07 Deletedinuse: 0
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 37152
% 47.72/48.07 Kept: 10748
% 47.72/48.07 Inuse: 487
% 47.72/48.07 Deleted: 27
% 47.72/48.07 Deletedinuse: 1
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 46737
% 47.72/48.07 Kept: 13060
% 47.72/48.07 Inuse: 539
% 47.72/48.07 Deleted: 30
% 47.72/48.07 Deletedinuse: 3
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 54866
% 47.72/48.07 Kept: 15068
% 47.72/48.07 Inuse: 569
% 47.72/48.07 Deleted: 30
% 47.72/48.07 Deletedinuse: 3
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 80953
% 47.72/48.07 Kept: 17069
% 47.72/48.07 Inuse: 609
% 47.72/48.07 Deleted: 35
% 47.72/48.07 Deletedinuse: 3
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 94616
% 47.72/48.07 Kept: 20148
% 47.72/48.07 Inuse: 676
% 47.72/48.07 Deleted: 38
% 47.72/48.07 Deletedinuse: 3
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying clauses:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 100613
% 47.72/48.07 Kept: 23043
% 47.72/48.07 Inuse: 681
% 47.72/48.07 Deleted: 504
% 47.72/48.07 Deletedinuse: 3
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 108371
% 47.72/48.07 Kept: 25073
% 47.72/48.07 Inuse: 701
% 47.72/48.07 Deleted: 504
% 47.72/48.07 Deletedinuse: 3
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 126005
% 47.72/48.07 Kept: 28144
% 47.72/48.07 Inuse: 740
% 47.72/48.07 Deleted: 505
% 47.72/48.07 Deletedinuse: 3
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 138595
% 47.72/48.07 Kept: 30217
% 47.72/48.07 Inuse: 795
% 47.72/48.07 Deleted: 507
% 47.72/48.07 Deletedinuse: 5
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 152685
% 47.72/48.07 Kept: 32300
% 47.72/48.07 Inuse: 835
% 47.72/48.07 Deleted: 507
% 47.72/48.07 Deletedinuse: 5
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 173802
% 47.72/48.07 Kept: 35927
% 47.72/48.07 Inuse: 850
% 47.72/48.07 Deleted: 507
% 47.72/48.07 Deletedinuse: 5
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 194220
% 47.72/48.07 Kept: 39743
% 47.72/48.07 Inuse: 860
% 47.72/48.07 Deleted: 508
% 47.72/48.07 Deletedinuse: 6
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying clauses:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 203098
% 47.72/48.07 Kept: 41762
% 47.72/48.07 Inuse: 867
% 47.72/48.07 Deleted: 742
% 47.72/48.07 Deletedinuse: 8
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 213381
% 47.72/48.07 Kept: 44021
% 47.72/48.07 Inuse: 880
% 47.72/48.07 Deleted: 742
% 47.72/48.07 Deletedinuse: 8
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 226550
% 47.72/48.07 Kept: 46768
% 47.72/48.07 Inuse: 890
% 47.72/48.07 Deleted: 742
% 47.72/48.07 Deletedinuse: 8
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 240047
% 47.72/48.07 Kept: 49570
% 47.72/48.07 Inuse: 925
% 47.72/48.07 Deleted: 742
% 47.72/48.07 Deletedinuse: 8
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 249898
% 47.72/48.07 Kept: 51579
% 47.72/48.07 Inuse: 945
% 47.72/48.07 Deleted: 742
% 47.72/48.07 Deletedinuse: 8
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 262716
% 47.72/48.07 Kept: 53595
% 47.72/48.07 Inuse: 961
% 47.72/48.07 Deleted: 742
% 47.72/48.07 Deletedinuse: 8
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 274685
% 47.72/48.07 Kept: 55630
% 47.72/48.07 Inuse: 995
% 47.72/48.07 Deleted: 742
% 47.72/48.07 Deletedinuse: 8
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 285121
% 47.72/48.07 Kept: 57778
% 47.72/48.07 Inuse: 1025
% 47.72/48.07 Deleted: 742
% 47.72/48.07 Deletedinuse: 8
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 300552
% 47.72/48.07 Kept: 59912
% 47.72/48.07 Inuse: 1060
% 47.72/48.07 Deleted: 742
% 47.72/48.07 Deletedinuse: 8
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 318798
% 47.72/48.07 Kept: 62222
% 47.72/48.07 Inuse: 1075
% 47.72/48.07 Deleted: 742
% 47.72/48.07 Deletedinuse: 8
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying clauses:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07
% 47.72/48.07 Intermediate Status:
% 47.72/48.07 Generated: 348039
% 47.72/48.07 Kept: 65715
% 47.72/48.07 Inuse: 1085
% 47.72/48.07 Deleted: 871
% 47.72/48.07 Deletedinuse: 8
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 47.72/48.07 Done
% 47.72/48.07
% 47.72/48.07 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 364995
% 104.27/104.67 Kept: 67799
% 104.27/104.67 Inuse: 1115
% 104.27/104.67 Deleted: 871
% 104.27/104.67 Deletedinuse: 8
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 379896
% 104.27/104.67 Kept: 71465
% 104.27/104.67 Inuse: 1125
% 104.27/104.67 Deleted: 879
% 104.27/104.67 Deletedinuse: 16
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 385832
% 104.27/104.67 Kept: 74163
% 104.27/104.67 Inuse: 1130
% 104.27/104.67 Deleted: 879
% 104.27/104.67 Deletedinuse: 16
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 395944
% 104.27/104.67 Kept: 76167
% 104.27/104.67 Inuse: 1154
% 104.27/104.67 Deleted: 879
% 104.27/104.67 Deletedinuse: 16
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 407559
% 104.27/104.67 Kept: 78170
% 104.27/104.67 Inuse: 1193
% 104.27/104.67 Deleted: 879
% 104.27/104.67 Deletedinuse: 16
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 420065
% 104.27/104.67 Kept: 81835
% 104.27/104.67 Inuse: 1219
% 104.27/104.67 Deleted: 883
% 104.27/104.67 Deletedinuse: 19
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying clauses:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 437417
% 104.27/104.67 Kept: 84240
% 104.27/104.67 Inuse: 1228
% 104.27/104.67 Deleted: 1570
% 104.27/104.67 Deletedinuse: 19
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 457215
% 104.27/104.67 Kept: 86855
% 104.27/104.67 Inuse: 1237
% 104.27/104.67 Deleted: 1574
% 104.27/104.67 Deletedinuse: 22
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 487672
% 104.27/104.67 Kept: 90222
% 104.27/104.67 Inuse: 1257
% 104.27/104.67 Deleted: 1574
% 104.27/104.67 Deletedinuse: 22
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 503993
% 104.27/104.67 Kept: 92814
% 104.27/104.67 Inuse: 1286
% 104.27/104.67 Deleted: 1575
% 104.27/104.67 Deletedinuse: 22
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 518141
% 104.27/104.67 Kept: 95216
% 104.27/104.67 Inuse: 1296
% 104.27/104.67 Deleted: 1575
% 104.27/104.67 Deletedinuse: 22
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 535061
% 104.27/104.67 Kept: 97531
% 104.27/104.67 Inuse: 1311
% 104.27/104.67 Deleted: 1575
% 104.27/104.67 Deletedinuse: 22
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 556624
% 104.27/104.67 Kept: 99937
% 104.27/104.67 Inuse: 1321
% 104.27/104.67 Deleted: 1575
% 104.27/104.67 Deletedinuse: 22
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 567061
% 104.27/104.67 Kept: 101940
% 104.27/104.67 Inuse: 1342
% 104.27/104.67 Deleted: 1575
% 104.27/104.67 Deletedinuse: 22
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying clauses:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 582359
% 104.27/104.67 Kept: 104231
% 104.27/104.67 Inuse: 1366
% 104.27/104.67 Deleted: 1826
% 104.27/104.67 Deletedinuse: 22
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 596467
% 104.27/104.67 Kept: 106237
% 104.27/104.67 Inuse: 1399
% 104.27/104.67 Deleted: 1828
% 104.27/104.67 Deletedinuse: 24
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 607636
% 104.27/104.67 Kept: 108495
% 104.27/104.67 Inuse: 1421
% 104.27/104.67 Deleted: 1832
% 104.27/104.67 Deletedinuse: 28
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 646082
% 104.27/104.67 Kept: 112807
% 104.27/104.67 Inuse: 1451
% 104.27/104.67 Deleted: 1835
% 104.27/104.67 Deletedinuse: 31
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 660949
% 104.27/104.67 Kept: 115413
% 104.27/104.67 Inuse: 1471
% 104.27/104.67 Deleted: 1835
% 104.27/104.67 Deletedinuse: 31
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 695997
% 104.27/104.67 Kept: 117925
% 104.27/104.67 Inuse: 1481
% 104.27/104.67 Deleted: 1835
% 104.27/104.67 Deletedinuse: 31
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 705220
% 104.27/104.67 Kept: 120996
% 104.27/104.67 Inuse: 1483
% 104.27/104.67 Deleted: 1835
% 104.27/104.67 Deletedinuse: 31
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying clauses:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 716597
% 104.27/104.67 Kept: 122998
% 104.27/104.67 Inuse: 1515
% 104.27/104.67 Deleted: 2380
% 104.27/104.67 Deletedinuse: 32
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 746917
% 104.27/104.67 Kept: 126499
% 104.27/104.67 Inuse: 1526
% 104.27/104.67 Deleted: 2387
% 104.27/104.67 Deletedinuse: 39
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 104.27/104.67 Done
% 104.27/104.67
% 104.27/104.67
% 104.27/104.67 Intermediate Status:
% 104.27/104.67 Generated: 756516
% 104.27/104.67 Kept: 128911
% 104.27/104.67 Inuse: 1546
% 104.27/104.67 Deleted: 2387
% 104.27/104.67 Deletedinuse: 39
% 104.27/104.67
% 104.27/104.67 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 765650
% 202.38/202.80 Kept: 131296
% 202.38/202.80 Inuse: 1566
% 202.38/202.80 Deleted: 2387
% 202.38/202.80 Deletedinuse: 39
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 783602
% 202.38/202.80 Kept: 136932
% 202.38/202.80 Inuse: 1576
% 202.38/202.80 Deleted: 2387
% 202.38/202.80 Deletedinuse: 39
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 799093
% 202.38/202.80 Kept: 139693
% 202.38/202.80 Inuse: 1581
% 202.38/202.80 Deleted: 2387
% 202.38/202.80 Deletedinuse: 39
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 818279
% 202.38/202.80 Kept: 144660
% 202.38/202.80 Inuse: 1586
% 202.38/202.80 Deleted: 2387
% 202.38/202.80 Deletedinuse: 39
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying clauses:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 825611
% 202.38/202.80 Kept: 147343
% 202.38/202.80 Inuse: 1589
% 202.38/202.80 Deleted: 2626
% 202.38/202.80 Deletedinuse: 39
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 832627
% 202.38/202.80 Kept: 149349
% 202.38/202.80 Inuse: 1605
% 202.38/202.80 Deleted: 2626
% 202.38/202.80 Deletedinuse: 39
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 840595
% 202.38/202.80 Kept: 151634
% 202.38/202.80 Inuse: 1621
% 202.38/202.80 Deleted: 2626
% 202.38/202.80 Deletedinuse: 39
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 848286
% 202.38/202.80 Kept: 153667
% 202.38/202.80 Inuse: 1639
% 202.38/202.80 Deleted: 2626
% 202.38/202.80 Deletedinuse: 39
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 853861
% 202.38/202.80 Kept: 155680
% 202.38/202.80 Inuse: 1649
% 202.38/202.80 Deleted: 2626
% 202.38/202.80 Deletedinuse: 39
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 861362
% 202.38/202.80 Kept: 157712
% 202.38/202.80 Inuse: 1662
% 202.38/202.80 Deleted: 2626
% 202.38/202.80 Deletedinuse: 39
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 870367
% 202.38/202.80 Kept: 159915
% 202.38/202.80 Inuse: 1681
% 202.38/202.80 Deleted: 2626
% 202.38/202.80 Deletedinuse: 39
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 879016
% 202.38/202.80 Kept: 162154
% 202.38/202.80 Inuse: 1701
% 202.38/202.80 Deleted: 2632
% 202.38/202.80 Deletedinuse: 45
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 887683
% 202.38/202.80 Kept: 164210
% 202.38/202.80 Inuse: 1720
% 202.38/202.80 Deleted: 2632
% 202.38/202.80 Deletedinuse: 45
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying clauses:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 894777
% 202.38/202.80 Kept: 166349
% 202.38/202.80 Inuse: 1736
% 202.38/202.80 Deleted: 3395
% 202.38/202.80 Deletedinuse: 45
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 905075
% 202.38/202.80 Kept: 168452
% 202.38/202.80 Inuse: 1756
% 202.38/202.80 Deleted: 3395
% 202.38/202.80 Deletedinuse: 45
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 914747
% 202.38/202.80 Kept: 170458
% 202.38/202.80 Inuse: 1773
% 202.38/202.80 Deleted: 3395
% 202.38/202.80 Deletedinuse: 45
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 926620
% 202.38/202.80 Kept: 172480
% 202.38/202.80 Inuse: 1802
% 202.38/202.80 Deleted: 3395
% 202.38/202.80 Deletedinuse: 45
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 938858
% 202.38/202.80 Kept: 174565
% 202.38/202.80 Inuse: 1826
% 202.38/202.80 Deleted: 3395
% 202.38/202.80 Deletedinuse: 45
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 950128
% 202.38/202.80 Kept: 176584
% 202.38/202.80 Inuse: 1852
% 202.38/202.80 Deleted: 3395
% 202.38/202.80 Deletedinuse: 45
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 960166
% 202.38/202.80 Kept: 178609
% 202.38/202.80 Inuse: 1873
% 202.38/202.80 Deleted: 3395
% 202.38/202.80 Deletedinuse: 45
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 971929
% 202.38/202.80 Kept: 180932
% 202.38/202.80 Inuse: 1891
% 202.38/202.80 Deleted: 3395
% 202.38/202.80 Deletedinuse: 45
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 997227
% 202.38/202.80 Kept: 185761
% 202.38/202.80 Inuse: 1911
% 202.38/202.80 Deleted: 3395
% 202.38/202.80 Deletedinuse: 45
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying clauses:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 1016397
% 202.38/202.80 Kept: 189485
% 202.38/202.80 Inuse: 1916
% 202.38/202.80 Deleted: 3640
% 202.38/202.80 Deletedinuse: 45
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80 Resimplifying inuse:
% 202.38/202.80 Done
% 202.38/202.80
% 202.38/202.80
% 202.38/202.80 Intermediate Status:
% 202.38/202.80 Generated: 1048569
% 202.38/202.80 Kept: 192481
% 202.38/202.80 Inuse: 1926
% 202.38/202.80 Deleted: 3640
% 202.38/202.80 Deletedinuse: 45
% 202.38/202.80
% 202.38/202.80 ResimplifyiCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------