TSTP Solution File: SWV632-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV632-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n032.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 300.02s 300.44s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWV632-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12 % Command : bliksem %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % DateTime : Wed Jun 15 07:43:43 EDT 2022
% 0.11/0.31 % CPUTime :
% 1.11/1.47 *** allocated 10000 integers for termspace/termends
% 1.11/1.47 *** allocated 10000 integers for clauses
% 1.11/1.47 *** allocated 10000 integers for justifications
% 1.11/1.47 *** allocated 15000 integers for termspace/termends
% 1.11/1.47 *** allocated 22500 integers for termspace/termends
% 1.11/1.47 *** allocated 33750 integers for termspace/termends
% 1.11/1.47 Bliksem 1.12
% 1.11/1.47
% 1.11/1.47
% 1.11/1.47 Automatic Strategy Selection
% 1.11/1.47
% 1.11/1.47 Clauses:
% 1.11/1.47 [
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.47 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.11/1.47 'c_HOL_Oabs__class_Oabs'( T, X ), X ) ), ~(
% 1.11/1.47 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.11/1.47 'tc_nat' ), 'tc_nat' ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.11/1.47 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.11/1.47 ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.11/1.47 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.11/1.47 ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.47 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.11/1.47 X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.47 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.11/1.47 ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.47 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.11/1.47 X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.47 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.11/1.47 ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.11/1.47 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.11/1.47 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.11/1.47 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.11/1.47 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.11/1.47 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.11/1.47 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.11/1.47 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.11/1.47 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.47 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.47 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Odiv'( Y, Z,
% 1.11/1.47 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 1.11/1.47 'tc_nat' ), 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.47 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.47 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.47 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.11/1.47 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.47 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.47 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.47 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.47 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.11/1.47 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.47 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.47 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.47 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.47 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.11/1.47 ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.47 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.47 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.11/1.47 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.11/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.11/1.47 'c_Divides_Odiv__class_Odiv'( T, U, X ), X ),
% 1.11/1.47 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( U, T, X ) ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.47 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.47 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'(
% 1.11/1.47 'tc_nat' ), X, 'tc_nat' ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.11/1.47 X ) ],
% 1.11/1.47 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.11/1.47 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.47 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.47 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.47 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.47 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.47 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.47 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.47 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.11/1.47 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.11/1.47 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.47 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.47 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.11/1.47 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.47 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.11/1.47 ), X ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.47 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.47 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.11/1.47 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.11/1.47 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.47 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.11/1.47 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.11/1.47 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.47 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.47 ), X ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.11/1.47 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.11/1.47 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.11/1.47 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.11/1.47 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.11/1.47 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.47 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.11/1.47 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.11/1.47 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.11/1.47 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.11/1.47 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.11/1.47 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.47 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.11/1.47 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 1.11/1.47 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.11/1.47 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.47 , X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.47 , X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.47 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.47 , X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.11/1.47 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.47 , X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.47 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) )
% 1.11/1.47 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.11/1.47 , 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.11/1.47 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.11/1.47 ), =( Z, Y ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.47 ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.11/1.47 ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.47 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.11/1.47 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.11/1.47 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.11/1.47 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.47 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.11/1.47 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 1.11/1.47 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.47 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.11/1.48 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.11/1.48 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 1.11/1.48 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 1.11/1.48 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y, X ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.11/1.48 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.48 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.11/1.48 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.11/1.48 , X ) ) ), =( Y, Z ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.11/1.48 , X ) ) ), =( Y, Z ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ), Z ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( T, X ), X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.48 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.48 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.48 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.48 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.11/1.48 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.11/1.48 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 1.11/1.48 , X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 1.11/1.48 , X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.11/1.48 , X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.11/1.48 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.11/1.48 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.48 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~(
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.11/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.48 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.11/1.48 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.48 Z, T, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.11/1.48 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat'
% 1.11/1.48 ), 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.11/1.48 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.48 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.11/1.48 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.48 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.11/1.48 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint' ), X ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.11/1.48 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.11/1.48 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.11/1.48 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.48 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.48 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.48 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 1.11/1.48 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.48 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.11/1.48 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.48 , T, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.48 , Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.48 , T, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.48 , Z, X ), X ) ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.11/1.48 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.11/1.48 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.11/1.48 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.48 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ), Z ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.11/1.48 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.11/1.48 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' )
% 1.11/1.48 , 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), T, X ),
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.11/1.48 , T, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), X ) ), =( Z
% 1.11/1.48 , 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 1.11/1.48 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.11/1.48 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z
% 1.11/1.48 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' )
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.11/1.48 , Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.11/1.48 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.11/1.48 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.11/1.48 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.11/1.48 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.48 , Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.11/1.48 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.11/1.48 , T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.11/1.48 ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.48 , Z, X ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.11/1.48 ), ~( 'c_lessequals'( T, Y, X ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.48 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T )
% 1.11/1.48 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.48 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.11/1.48 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.11/1.48 ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.11/1.48 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.48 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =(
% 1.11/1.48 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 1.11/1.48 X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.11/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.11/1.48 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.11/1.48 Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.11/1.48 Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.11/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.11/1.48 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.11/1.48 X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.11/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.11/1.48 Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.11/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.11/1.48 X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ), T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.11/1.48 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), Y, X ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y
% 1.11/1.48 , 'tc_nat' ) ) ],
% 1.11/1.48 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 1.11/1.48 , 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.11/1.48 , 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.11/1.48 Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z
% 1.11/1.48 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.11/1.48 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oone__class_Oone'(
% 1.11/1.48 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.48 T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X ) ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.11/1.48 , Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), T, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 , X ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.11/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.11/1.48 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.11/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Z,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ), X ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.11/1.48 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.11/1.48 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.11/1.48 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.11/1.48 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 1.11/1.48 , X ), W, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Z, W, X ), X ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.11/1.48 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Z,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( U, W, X ), X ), T, X ), X ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y,
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z, X ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z, X ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Y ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( Z, Y, X ), X ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Z, Y, X ), X ), Z ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.48 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.48 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.48 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.11/1.48 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.48 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.48 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.11/1.48 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.11/1.48 Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.48 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.48 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.48 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.48 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.11/1.48 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 Y, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.48 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.48 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.11/1.48 , X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X ) ],
% 1.11/1.48 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Odiv'(
% 1.11/1.48 Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.11/1.48 X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Odiv'(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.11/1.48 X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), X ) ), ~(
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.48 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.11/1.48 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.48 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.11/1.48 ), X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.11/1.48 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.11/1.48 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.48 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.48 ), X ), Z, X ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.11/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.11/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.11/1.48 [ ~( =( 'c_Nat_Osemiring__1__class_Oof__nat'( X, 'tc_Int_Oint' ),
% 1.11/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' ) ) ), =( X, Y ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( =( 'c_Nat_Osemiring__1__class_Oof__nat'( X, 'tc_Int_Oint' ),
% 1.11/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' ) ) ), =( X, Y ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.48 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.48 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ), X ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.48 , 'tc_nat' ), 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.48 , 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ), 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ), X ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.48 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.11/1.48 , T, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.11/1.48 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.11/1.48 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.11/1.48 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.11/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.11/1.48 W, X ), X ), ~( 'c_lessequals'( T, 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.11/1.48 , X ), W, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.11/1.48 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U, X ), W, X ), X ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 T, U, X ), Y, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.11/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.11/1.48 W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 1.11/1.48 , X ), T, X ), W, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.11/1.48 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.48 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 1.11/1.48 ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.11/1.48 ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 1.11/1.48 Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 1.11/1.48 ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.48 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 1.11/1.48 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.48 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.11/1.48 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oabs__class_Oabs'(
% 1.11/1.48 Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.11/1.48 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.48 X, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.11/1.48 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.11/1.48 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Odiv'(
% 1.11/1.48 X, 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.11/1.48 ), 'tc_nat' ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Z, Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.11/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Y, T, X ),
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.11/1.48 , X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.11/1.48 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.11/1.48 , X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.11/1.48 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.11/1.48 , Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.11/1.48 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.48 ), X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.48 ), X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.48 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.11/1.48 ), X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.11/1.48 ), X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.48 ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.11/1.48 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.11/1.48 ],
% 1.11/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 1.11/1.48 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), Y, X ), Z, X ) ) ],
% 1.11/1.48 [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'(
% 1.11/1.48 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.11/1.48 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.11/1.48 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.11/1.48 ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.48 X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.11/1.48 'tc_nat' ), X, 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.48 X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 1.11/1.48 'tc_nat' ), X, 'tc_nat' ) ],
% 1.11/1.48 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.48 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.11/1.48 X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X
% 1.11/1.48 ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 1.11/1.48 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.11/1.48 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.48 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.48 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 1.11/1.48 ), Y ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.11/1.48 ), X ), Y ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.11/1.48 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.48 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.48 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.48 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.11/1.48 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.11/1.48 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.11/1.48 , T, X ), X ), T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), T, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.48 , 'tc_nat' ), 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.11/1.48 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.11/1.48 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.11/1.48 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.48 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.11/1.48 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.11/1.48 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.11/1.48 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.11/1.48 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.11/1.48 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.11/1.48 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.11/1.48 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.48 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X ), X ) )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.11/1.48 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.11/1.48 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 Y, X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.11/1.48 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ), T, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 1.11/1.48 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.48 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 1.11/1.48 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.11/1.48 , X ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 1.11/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Z, Y, X ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.11/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.48 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.48 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( 'c_Divides_Odiv__class_Odiv'( Y
% 1.11/1.48 , X, 'tc_nat' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.11/1.48 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.48 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 1.11/1.48 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 1.11/1.48 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.11/1.48 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.48 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.11/1.48 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.11/1.48 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.48 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.11/1.48 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.11/1.48 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.48 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.48 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.11/1.48 'c_Power_Opower__class_Opower'( T, 'c_Suc'( Z ), X ) ) ), =( Y, T ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.48 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( X, Z, 'tc_nat'
% 1.11/1.48 ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ), 'tc_nat' ), Z, 'tc_nat' )
% 1.11/1.48 , 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.11/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.11/1.48 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.11/1.48 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.11/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.11/1.48 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.11/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.11/1.48 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.11/1.48 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.11/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.11/1.48 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.11/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.48 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 Y, T, X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.11/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.48 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 Y, T, X ), Z, X ) ) ],
% 1.11/1.48 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' )
% 1.11/1.48 , 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.11/1.48 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.11/1.48 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.11/1.48 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' )
% 1.11/1.48 , 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.11/1.48 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.11/1.48 Y, 'tc_nat' ), 'tc_nat' ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.11/1.48 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.11/1.48 Y, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.11/1.48 'tc_nat' ) ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.11/1.48 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), 'c_Suc'( 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.11/1.48 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.11/1.48 Y, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.48 Z, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), Z
% 1.11/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), X
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.11/1.48 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), Z, X ) ), =( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.11/1.48 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Z,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), T, X ) ), =( T,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 1.11/1.48 X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), X ) ), =( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.48 Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, T
% 1.11/1.48 , X ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, Z
% 1.11/1.48 , X ), 'c_Divides_Odiv__class_Odiv'( T, Z, X ), X ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 Z, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.11/1.48 , X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.11/1.48 , X ), Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 1.11/1.48 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.11/1.48 , T, X ), X ), T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.11/1.48 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.11/1.48 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.11/1.48 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.11/1.48 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.48 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X
% 1.11/1.48 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.11/1.48 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.11/1.48 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.11/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.48 Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X )
% 1.11/1.48 , 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.11/1.48 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat' ) ), 'tc_nat' ) )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.11/1.48 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.48 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.11/1.48 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.11/1.48 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.11/1.48 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.48 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.11/1.48 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.11/1.48 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.48 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.48 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.11/1.48 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.11/1.48 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.11/1.48 ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.11/1.48 ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.11/1.48 ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.11/1.48 ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.48 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.11/1.48 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.48 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.11/1.48 ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.11/1.48 , T, X ) ) ), =( Z, T ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.11/1.48 , T, X ) ) ), =( Y, Z ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.48 'tc_nat' ) ), =( Y, Z ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.48 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.48 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.48 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.11/1.48 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.48 X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.11/1.48 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.48 , T, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.48 , Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 1.11/1.48 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.48 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ), T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 1.11/1.48 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.48 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.11/1.48 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.11/1.48 Z, X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.48 Y, Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.11/1.48 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.48 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.48 ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.48 ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.11/1.48 'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.48 ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.48 'c_Suc'( X ), 'tc_nat' ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.48 'c_Suc'( X ), 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.48 'c_Int_OMin', X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.11/1.48 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.48 , Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.11/1.48 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.11/1.48 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.11/1.48 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.11/1.48 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.48 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 1.11/1.48 ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.48 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.48 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.11/1.48 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 ) ), =( Y, Z ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 ) ), =( Y, Z ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.48 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.11/1.48 , U, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.11/1.48 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.11/1.48 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.11/1.48 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.11/1.48 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.48 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.48 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.11/1.48 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), T
% 1.11/1.48 , X ), 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.11/1.48 X ), Z, X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 1.11/1.48 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 1.11/1.48 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 1.11/1.48 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 1.11/1.48 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 1.11/1.48 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.11/1.48 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.11/1.48 , 'c_Power_Opower__class_Opower'( Y, Z, X ) ), ~(
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.48 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.48 , 'tc_nat' ), 'tc_nat' ), 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ), X ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Z,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'(
% 1.11/1.48 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.11/1.48 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.11/1.48 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 1.11/1.48 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.11/1.48 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.11/1.48 ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.48 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.11/1.48 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 T, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.48 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( T, Y, X ), X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.11/1.48 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.11/1.48 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y, X ), ~( 'c_lessequals'( Z,
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.11/1.48 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.11/1.48 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.48 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.11/1.48 , 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.48 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.11/1.48 X ) ) ), =( Z, T ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.11/1.48 X ) ) ), =( Z, T ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.11/1.48 X ) ) ), =( Y, T ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.11/1.48 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.48 ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.48 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Z
% 1.11/1.48 , X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ), =( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.11/1.48 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.11/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.11/1.48 Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.11/1.48 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.48 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.11/1.48 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.48 ), X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 1.11/1.48 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.11/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.11/1.48 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.11/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.11/1.48 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.48 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.48 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.11/1.48 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.11/1.48 ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.48 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.48 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.48 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.11/1.48 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.11/1.48 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.11/1.48 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 1.11/1.48 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.48 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.11/1.48 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ), X ), ~(
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.48 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.11/1.48 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 1.11/1.48 [ =( 'c_Suc'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Odiv'(
% 1.11/1.48 X, 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.11/1.48 ), 'tc_nat' ) ), X ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.11/1.48 ), 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.11/1.48 ), 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z
% 1.11/1.48 ), X ), 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), X ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.11/1.48 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.11/1.48 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ) ), Y, 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat'
% 1.11/1.48 ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ) ), Y, 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.11/1.48 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.48 X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_RealVector_Oreal__field'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.48 , U, X ), X ), W, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Z, U, X ), W, X ), X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, T, X ), W, X ), U, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.11/1.48 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.11/1.48 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, U,
% 1.11/1.48 X ), X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, T, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ), X ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.48 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.11/1.48 , ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.48 'tc_nat' ), Y, 'tc_nat' ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.48 'tc_nat' ), X, 'tc_nat' ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.48 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.48 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.11/1.48 , Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.48 T, Z, X ) ) ), =( Y, T ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.11/1.48 , Z ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.48 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.48 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.11/1.48 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.11/1.48 'c_Power_Opower__class_Opower'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.48 'c_Int_OMin', X ), Y, X ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.11/1.48 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.48 ), X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 Y, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), T, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.48 , X ), X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.48 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.11/1.48 ), X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.48 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.11/1.48 , X ), X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y, X )
% 1.11/1.48 , X ), Z ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 1.11/1.48 , X ), Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.11/1.48 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.48 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ), T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.48 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.48 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.48 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.48 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.11/1.48 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.11/1.48 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.48 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.48 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.11/1.48 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.48 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.48 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.48 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.48 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.48 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.48 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.48 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.48 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.11/1.48 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.11/1.48 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), Y,
% 1.11/1.48 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.48 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.48 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.11/1.48 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.11/1.48 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.11/1.48 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.11/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), =( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 1.11/1.48 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.11/1.48 , X ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.11/1.48 , X ), X ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.48 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.11/1.48 ],
% 1.11/1.48 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.11/1.48 ), 'tc_nat' ), X ) ],
% 1.11/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.11/1.48 , X, 'tc_nat' ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.11/1.48 ), Y ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.11/1.48 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 1.11/1.48 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.11/1.48 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 1.11/1.48 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.11/1.48 , Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.11/1.48 ), Y ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.11/1.48 ), Y ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.11/1.48 ), Y ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.11/1.48 X ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.11/1.48 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.11/1.48 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.11/1.48 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.11/1.48 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.11/1.48 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.11/1.48 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.11/1.48 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.48 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.48 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.11/1.48 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.11/1.48 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.48 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.48 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.11/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.11/1.48 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z
% 1.11/1.48 , X ), 'c_Power_Opower__class_Opower'( Y, Z, X ) ), ~(
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.11/1.48 , X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.11/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.11/1.48 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.11/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.11/1.48 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.11/1.48 , X ), W, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 1.11/1.48 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), T, X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y, X )
% 1.11/1.48 , X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ), X ), T, X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Z, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 Y, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), T, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.11/1.48 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.48 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.48 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'( Z,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.11/1.48 , X ), X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.11/1.48 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ),
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.48 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.11/1.48 ), X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.11/1.48 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.48 ), X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 X, Y, 'tc_nat' ) ), X, 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) )
% 1.11/1.48 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 1.11/1.48 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.11/1.48 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.11/1.48 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.11/1.48 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.11/1.48 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.11/1.48 [ ~( =( 'c_Complex_Oii', 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex'
% 1.11/1.48 ) ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.11/1.48 X ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 X, T, 'tc_nat' ) ],
% 1.11/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.11/1.48 X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.11/1.48 X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.11/1.48 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_lessequals'( Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.11/1.48 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.48 'c_lessequals'( Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.11/1.48 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.11/1.48 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 1.11/1.48 X ) ) ],
% 1.11/1.48 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_Int_Oint'
% 1.11/1.48 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', 'tc_Int_Oint' ) ) )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Z, 'c_Divides_Odiv__class_Odiv'( Y, T, X ), X
% 1.11/1.48 ) ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( T, 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), X
% 1.11/1.48 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.11/1.48 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.11/1.48 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.11/1.48 , Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.11/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.11/1.48 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 , Z, X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.11/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.11/1.48 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.11/1.48 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 , Z, X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.11/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.11/1.48 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.11/1.48 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X
% 1.11/1.48 ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.11/1.48 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ),
% 1.11/1.48 ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X
% 1.11/1.48 ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.11/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.48 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 , T, X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.11/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.48 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 , T, X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.11/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.11/1.48 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.11/1.48 Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.48 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.11/1.48 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.11/1.48 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.11/1.48 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.11/1.48 , T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), T, X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.11/1.48 , T, X ), Z, X ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.11/1.48 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.11/1.48 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.11/1.48 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.11/1.48 , T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.11/1.48 , T, X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.11/1.48 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 1.11/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 1.11/1.48 W, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 1.11/1.48 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 1.11/1.48 , X ), T, X ), W, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 1.11/1.48 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 1.11/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 1.11/1.48 W, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 1.11/1.48 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.11/1.48 , X ), W, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.11/1.48 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 1.11/1.49 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 1.11/1.49 Z, X ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.49 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.11/1.49 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 'tc_nat' ), 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.11/1.49 ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.11/1.49 ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.11/1.49 T, X ), 'c_Divides_Odiv__class_Odiv'( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ), ~(
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), Y,
% 1.11/1.49 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.11/1.49 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.49 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.11/1.49 Y, X ), Z, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.11/1.49 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.11/1.49 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.11/1.49 Y, X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.11/1.49 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.11/1.49 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.11/1.49 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.11/1.49 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.11/1.49 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.11/1.49 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( =( X, 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.11/1.49 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.11/1.49 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.11/1.49 X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.11/1.49 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 1.11/1.49 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 1.11/1.49 X ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.11/1.49 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 1.11/1.49 , X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.49 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.11/1.49 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.49 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.11/1.49 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.11/1.49 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.11/1.49 , T, X ), X ), T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.11/1.49 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.11/1.49 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.49 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.49 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.11/1.49 , X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.11/1.49 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.11/1.49 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.11/1.49 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 1.11/1.49 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 Y, Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 Y, Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.11/1.49 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.11/1.49 X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.11/1.49 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.11/1.49 X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.11/1.49 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.11/1.49 X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.11/1.49 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.11/1.49 X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.11/1.49 ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.11/1.49 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.11/1.49 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.11/1.49 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.11/1.49 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.11/1.49 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.11/1.49 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.11/1.49 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.11/1.49 , X ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.11/1.49 , X ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.49 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.49 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.49 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.11/1.49 X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.49 X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.11/1.49 , Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.11/1.49 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 1.11/1.49 , 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.11/1.49 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.11/1.49 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.49 , Z, X ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 1.11/1.49 , X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.49 , Y, X ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.11/1.49 , Z, X ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.11/1.49 , Z, X ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.49 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.11/1.49 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.49 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.11/1.49 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.11/1.49 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.11/1.49 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.11/1.49 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.11/1.49 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.11/1.49 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.11/1.49 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.11/1.49 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.11/1.49 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.11/1.49 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.11/1.49 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.11/1.49 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.11/1.49 , T, X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 Y, T, X ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.11/1.49 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y,
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( T, X )
% 1.11/1.49 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.11/1.49 , Z, X ), Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , X ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , X ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.11/1.49 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ) ), =( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.49 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.49 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.49 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.11/1.49 , T, X ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.11/1.49 ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.11/1.49 ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.11/1.49 ), X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), Y, X ),
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 Y, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ),
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.11/1.49 , X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.11/1.49 ), X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z
% 1.11/1.49 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ), Z, X
% 1.11/1.49 ), 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.49 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.49 , Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.49 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.49 , Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), Y, X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), X ), X ) ],
% 1.11/1.49 [ =( 'c_Int_OBit1'( 'c_Int_OMin' ), 'c_Int_OMin' ) ],
% 1.11/1.49 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OMin' ) ), =( X, 'c_Int_OMin' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( =( 'c_Int_OMin', 'c_Int_OBit1'( X ) ) ), =( 'c_Int_OMin', X ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ =( 'c_Int_OMin', 'c_Int_OBit1'( 'c_Int_OMin' ) ) ],
% 1.11/1.49 [ ~( =( 'c_Int_OPls', 'c_Int_OMin' ) ) ],
% 1.11/1.49 [ ~( =( 'c_Int_OMin', 'c_Int_OPls' ) ) ],
% 1.11/1.49 [ ~( =( 'c_Int_OMin', 'c_Int_OBit0'( X ) ) ) ],
% 1.11/1.49 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OMin' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 'tc_nat' ), 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 , X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.11/1.49 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.49 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 ) ],
% 1.11/1.49 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 1.11/1.49 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.49 'tc_nat' ), X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.11/1.49 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.11/1.49 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.11/1.49 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ),
% 1.11/1.49 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 1.11/1.49 ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X
% 1.11/1.49 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X
% 1.11/1.49 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Int_Oiszero'( Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ),
% 1.11/1.49 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) )
% 1.11/1.49 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.11/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 Y, X, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.11/1.49 , Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.49 X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.49 X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.11/1.49 Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.11/1.49 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.11/1.49 ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.11/1.49 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.11/1.49 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.11/1.49 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.11/1.49 , X ) ) ],
% 1.11/1.49 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.11/1.49 , Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.11/1.49 , Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.49 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ), X ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.11/1.49 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ),
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.11/1.49 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.11/1.49 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.11/1.49 X ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 , X ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.11/1.49 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( Z, Y, X ), X ), Z ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), Z ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.49 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.11/1.49 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.11/1.49 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.11/1.49 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.11/1.49 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.49 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.49 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.11/1.49 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.11/1.49 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.49 , X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 , X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.11/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.11/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.11/1.49 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.11/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.11/1.49 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 1.11/1.49 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.11/1.49 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.11/1.49 , Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.49 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.11/1.49 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.11/1.49 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , 'tc_nat' ), X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.11/1.49 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.49 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.11/1.49 ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( T ), X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( Z, 'c_Suc'( T ), X ), X ) ) ],
% 1.11/1.49 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.49 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( T,
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, U, 'tc_nat' ), 'tc_nat' ) ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.11/1.49 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.11/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.11/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.11/1.49 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.49 Y, T, X ) ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X
% 1.11/1.49 ), Y, X ) ), =( Z, T ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.11/1.49 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.11/1.49 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.11/1.49 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_Divides_Osemiring__div'( X )
% 1.11/1.49 ), =( 'c_Divides_Odiv__class_Omod'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 Y, X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_Divides_Osemiring__div'( X )
% 1.11/1.49 ), ~( =( 'c_Divides_Odiv__class_Omod'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , 'tc_nat' ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , 'tc_nat' ), 'tc_nat' ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.49 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.49 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.49 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.11/1.49 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y
% 1.11/1.49 , Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X
% 1.11/1.49 ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z
% 1.11/1.49 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_Power_Opower__class_Opower'( Y
% 1.11/1.49 , Z, X ), X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ),
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.49 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.11/1.49 ) ), X, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 1.11/1.49 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.11/1.49 ) ), X, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 Y, 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.11/1.49 Z, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'(
% 1.11/1.49 Z, X ), X ) ) ],
% 1.11/1.49 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.49 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.11/1.49 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.11/1.49 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X
% 1.11/1.49 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.11/1.49 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.11/1.49 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.11/1.49 , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.11/1.49 , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.11/1.49 X ), Y ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.11/1.49 X ), Y ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.49 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.49 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.11/1.49 Y, X ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.11/1.49 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.11/1.49 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.11/1.49 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.49 Z, T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.11/1.49 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 1.11/1.49 , 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X
% 1.11/1.49 ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.11/1.49 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , 'tc_nat' ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.11/1.49 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.11/1.49 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.49 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.11/1.49 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.49 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( Y,
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( Y, X,
% 1.11/1.49 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.11/1.49 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'(
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.11/1.49 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.49 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 1.11/1.49 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 1.11/1.49 , T ), =( X, Z ) ],
% 1.11/1.49 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.49 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 1.11/1.49 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 1.11/1.49 , T ), =( X, Z ) ],
% 1.11/1.49 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.11/1.49 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 1.11/1.49 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X,
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 1.11/1.49 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.49 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.11/1.49 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.49 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.11/1.49 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 1.11/1.49 ],
% 1.11/1.49 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.11/1.49 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.11/1.49 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 1.11/1.49 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.11/1.49 ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.11/1.49 , X, 'tc_nat' ), X ) ],
% 1.11/1.49 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.11/1.49 ), 'tc_nat' ), X ) ],
% 1.11/1.49 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.49 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.11/1.49 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.49 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.11/1.49 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.49 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z,
% 1.11/1.49 Y, 'tc_nat' ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.11/1.49 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.11/1.49 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.11/1.49 'tc_nat' ), Z, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z
% 1.11/1.49 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), X ), X ), X ) ) ],
% 1.11/1.49 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.11/1.49 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.11/1.49 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.11/1.49 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.49 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.11/1.49 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.11/1.49 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ), X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.49 , X ), X ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) )
% 1.11/1.49 ],
% 1.11/1.49 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.11/1.49 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.49 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'( 'c_Suc'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.11/1.49 [ =( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_Int_Oint' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Z,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), X ), =( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), X ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), X )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ =( 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_Complex_Ocomplex' ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'( Y ), Z,
% 1.11/1.49 'tc_Complex_Ocomplex' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.11/1.49 X ) ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 1.11/1.49 , X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.49 ), X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.11/1.49 ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.11/1.49 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.49 ), X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.11/1.49 ), =( 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 Y, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ),
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.11/1.49 , T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.11/1.49 X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Z
% 1.11/1.49 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.11/1.49 , T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.11/1.49 ) ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit1'( Y ), X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), 'c_Int_Oiszero'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), Y, X ), Y ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'( Y
% 1.11/1.49 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ), Y ) ],
% 1.11/1.49 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.11/1.49 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.11/1.49 ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y
% 1.11/1.49 ), X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.11/1.49 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.49 Y ), X ), X ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.49 , X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.49 Y, X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.49 ), X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, T, X ), X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.11/1.49 'tc_nat' ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.49 ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.49 Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 'c_Suc'( Z ), X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.49 ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.11/1.49 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.49 Y, T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.11/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.11/1.49 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.11/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.11/1.49 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.11/1.49 ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), 'c_Int_Oiszero'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 1.11/1.49 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.11/1.49 ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.11/1.49 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.11/1.49 ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), 'c_Suc'( 'c_Suc'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.11/1.49 ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.11/1.49 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.11/1.49 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.11/1.49 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.49 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.11/1.49 X ), T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.49 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.11/1.49 X ), T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 1.11/1.49 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.11/1.49 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.11/1.49 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.11/1.49 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.49 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.49 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.11/1.49 X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.11/1.49 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.49 Z, T, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.11/1.49 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.11/1.49 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.11/1.49 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.11/1.49 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.11/1.49 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.11/1.49 , X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.11/1.49 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.11/1.49 ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 1.11/1.49 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.11/1.49 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.11/1.49 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Power_Opower__class_Opower'(
% 1.11/1.49 Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.11/1.49 ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.11/1.49 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.49 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.11/1.49 X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.49 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 Z, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 Z, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.49 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.11/1.49 X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.49 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 Y, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 Y, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.49 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.11/1.49 , X ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.49 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.11/1.49 , X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 1.11/1.49 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.11/1.49 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.11/1.49 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.49 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.11/1.49 ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.49 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.11/1.49 ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.11/1.49 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.11/1.49 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.49 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.49 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.49 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 1.11/1.49 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 1.11/1.49 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.11/1.49 , X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 1.11/1.49 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.11/1.49 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.11/1.49 ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.49 ), X ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.11/1.49 , Y, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 1.11/1.49 , X ), X ), Y ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), Y, X ),
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.49 , Y, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.11/1.49 , T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.11/1.49 , T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.49 , Y, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , 'tc_nat' ), X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~( 'c_Int_Oiszero'(
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.49 'tc_nat' ), X ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Z, Y, X
% 1.11/1.49 ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.49 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.49 ), X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.49 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.49 ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 ), =( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.49 , U, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( U,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.11/1.49 , U, X ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.11/1.49 ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.11/1.49 Y, X ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.11/1.49 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 1.11/1.49 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 1.11/1.49 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.11/1.49 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.11/1.49 'c_lessequals'( Z, Y, X ) ],
% 1.11/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.11/1.49 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.11/1.49 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.49 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X, X,
% 1.11/1.49 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.49 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.11/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' )
% 1.11/1.49 ) ],
% 1.11/1.49 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' )
% 1.11/1.49 , 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.11/1.49 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.11/1.49 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_Int_Oint' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.11/1.49 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.11/1.49 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.11/1.49 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 1.11/1.49 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ), X ), 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), Y, 'tc_nat' ) ), X ),
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' )
% 1.11/1.49 ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 'c_Suc'( 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' )
% 1.11/1.49 ), X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.11/1.49 ), ~( =( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.49 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.11/1.49 ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.11/1.49 ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.11/1.49 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ), =( Y
% 1.11/1.49 , Z ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), =(
% 1.11/1.49 Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' )
% 1.11/1.49 ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( X, 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ),
% 1.11/1.49 'c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1'( X ), 'tc_nat' ) ),
% 1.11/1.49 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'( X ), X,
% 1.11/1.49 'tc_Complex_Ocomplex' ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex'
% 1.11/1.49 ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.11/1.49 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X
% 1.11/1.49 ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.11/1.49 ), Y ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.11/1.49 ), Y ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.49 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.11/1.49 ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.11/1.49 ) ) ],
% 1.11/1.49 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.11/1.49 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), Y, 'tc_nat' ), X ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' )
% 1.11/1.49 , X ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ), X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Z,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), Y, X ), Z, X ), X )
% 1.11/1.49 ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), 'c_Suc'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), Y, 'tc_nat' )
% 1.11/1.49 ), X ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), Y, 'tc_nat' )
% 1.11/1.49 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), X ), Y, X ), 'c_HOL_Oplus__class_Oplus'( Y, Y, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 Y, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), X ), X ), 'c_HOL_Oplus__class_Oplus'( Y, Y, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.11/1.49 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ), 'c_Power_Opower__class_Opower'( Y
% 1.11/1.49 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ), 'tc_nat' ) ],
% 1.11/1.49 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X, X, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' )
% 1.11/1.49 , 'c_HOL_Oplus__class_Oplus'( X, X, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.11/1.49 ) ), 'c_Complex_Oii' ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' )
% 1.11/1.49 , X ), 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), X ), Y, X ), Z, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ) ), X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.49 Y, Z, X ), X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ) ), X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 1.11/1.49 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, Z, X ), T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.49 Y, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ],
% 1.11/1.49 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.49 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 1.11/1.49 Y, Z, X ), X ) ) ],
% 1.11/1.49 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.11/1.49 X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.11/1.49 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.11/1.49 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ), X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.11/1.49 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), X ) ) ],
% 1.11/1.49 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.11/1.49 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.11/1.49 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.11/1.49 X ), T, X ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.49 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.11/1.49 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.49 T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.11/1.49 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.11/1.49 X ), T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.11/1.49 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.11/1.49 T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.11/1.49 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.11/1.49 X ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.11/1.49 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.11/1.49 T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.49 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.49 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.49 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.49 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), Y
% 1.11/1.49 , X ), Y ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 Y, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.11/1.49 , X ), Y ) ],
% 1.11/1.49 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.11/1.49 , T, X ), 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 Z, T, 'tc_nat' ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.49 , Y, X ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.49 , Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit1'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y
% 1.11/1.49 , X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.11/1.49 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), Z, 'tc_nat' ), X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 1.11/1.49 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.11/1.49 [ ~( =( 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'v_m',
% 1.11/1.49 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( 'v_i',
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'v_j',
% 1.11/1.49 'tc_nat' ), 'tc_nat' ), 'tc_Complex_Ocomplex' ),
% 1.11/1.49 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'( 'v_m' ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'v_i', 'v_j', 'tc_nat' ),
% 1.11/1.49 'tc_Complex_Ocomplex' ) ) ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.11/1.49 ],
% 1.11/1.49 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.11/1.49 ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.11/1.49 ],
% 1.11/1.49 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.11/1.49 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.11/1.49 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.11/1.49 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.11/1.49 ],
% 1.11/1.49 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.11/1.49 ],
% 1.11/1.49 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Nat_Osemiring__char__0'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Odvd'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.11/1.49 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.11/1.49 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.11/1.49 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.11/1.49 ],
% 1.11/1.49 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.11/1.49 ],
% 1.11/1.49 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.11/1.49 ],
% 1.11/1.49 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_RealVector_Oreal__field'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_Nat_Osemiring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_Ring__and__Field_Odvd'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.49 [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.49 ] .
% 1.11/1.49
% 1.11/1.49
% 1.11/1.49 percentage equality = 0.220358, percentage horn = 0.832420
% 1.11/1.49 This is a problem with some equality
% 1.11/1.49
% 1.11/1.49
% 1.11/1.49
% 1.11/1.49 Options Used:
% 1.11/1.49
% 1.11/1.49 useres = 1
% 1.11/1.49 useparamod = 1
% 1.11/1.49 useeqrefl = 1
% 1.11/1.49 useeqfact = 1
% 1.11/1.49 usefactor = 1
% 1.11/1.49 usesimpsplitting = 0
% 1.11/1.49 usesimpdemod = 5
% 1.11/1.49 usesimpres = 3
% 1.11/1.49
% 1.11/1.49 resimpinuse = 1000
% 1.11/1.49 resimpclauses = 20000
% 1.11/1.49 substype = eqrewr
% 1.11/1.49 backwardsubs = 1
% 1.11/1.49 selectoldest = 5
% 1.11/1.49
% 1.11/1.49 litorderings [0] = split
% 1.11/1.49 litorderings [1] = extend the termordering, first sorting on arguments
% 1.11/1.49
% 1.11/1.49 termordering = kbo
% 1.11/1.49
% 1.11/1.49 litapriori = 0
% 1.11/1.49 termapriori = 1
% 1.11/1.49 litaposteriori = 0
% 1.11/1.49 termaposteriori = 0
% 1.11/1.49 demodaposteriori = 0
% 1.11/1.49 ordereqreflfact = 0
% 1.11/1.49
% 1.11/1.49 litselect = negord
% 1.11/1.49
% 1.11/1.49 maxweight = 15
% 1.11/1.49 maxdepth = 30000
% 1.11/1.49 maxlength = 115
% 1.11/1.49 maxnrvars = 195
% 1.11/1.49 excuselevel = 1
% 1.11/1.49 increasemaxweight = 1
% 1.11/1.49
% 1.11/1.49 maxselected = 10000000
% 1.11/1.49 maxnrclauses = 10000000
% 1.11/1.49
% 1.11/1.49 showgenerated = 0
% 1.11/1.49 showkept = 0
% 1.11/1.49 showselected = 0
% 1.11/1.49 showdeleted = 0
% 1.11/1.49 showresimp = 1
% 1.11/1.49 showstatus = 2000
% 1.11/1.49
% 1.11/1.49 prologoutput = 1
% 1.11/1.49 nrgoals = 5000000
% 1.11/1.49 totalproof = 1
% 1.11/1.49
% 1.11/1.49 Symbols occurring in the translation:
% 1.11/1.49
% 1.11/1.49 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.11/1.49 . [1, 2] (w:1, o:136, a:1, s:1, b:0),
% 1.11/1.49 ! [4, 1] (w:0, o:56, a:1, s:1, b:0),
% 1.11/1.49 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.11/1.49 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.11/1.49 'class_Ring__and__Field_Ocomm__semiring__1' [40, 1] (w:1, o:63, a:1
% 1.11/1.49 , s:1, b:0),
% 1.11/1.49 'c_Ring__and__Field_Odvd__class_Odvd' [43, 3] (w:1, o:168, a:1, s:1
% 1.11/1.49 , b:0),
% 1.11/1.49 'class_Ring__and__Field_Oordered__idom' [45, 1] (w:1, o:69, a:1, s:1
% 1.11/1.49 , b:0),
% 1.11/1.49 'c_Power_Opower__class_Opower' [48, 3] (w:1, o:169, a:1, s:1, b:0),
% 1.11/1.49 'c_lessequals' [50, 3] (w:1, o:170, a:1, s:1, b:0),
% 1.11/1.49 'c_HOL_Oabs__class_Oabs' [51, 2] (w:1, o:161, a:1, s:1, b:0),
% 1.11/1.49 'tc_nat' [52, 0] (w:1, o:27, a:1, s:1, b:0),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven' [53, 2] (w:1, o:162, a:1, s:1, b:0
% 1.11/1.49 ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero' [54, 1] (w:1, o:70, a:1, s:1, b:0),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes' [56, 3] (w:1, o:171, a:1, s:1, b:0),
% 1.11/1.49 'class_Ring__and__Field_Oidom' [57, 1] (w:1, o:71, a:1, s:1, b:0),
% 1.11/1.49 'c_Suc' [59, 1] (w:1, o:72, a:1, s:1, b:0),
% 1.11/1.49 'c_HOL_Oord__class_Oless' [61, 3] (w:1, o:172, a:1, s:1, b:0),
% 1.11/1.49 'class_OrderedGroup_Opordered__ab__semigroup__add' [63, 1] (w:1, o:75
% 1.11/1.49 , a:1, s:1, b:0),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus' [64, 3] (w:1, o:173, a:1, s:1, b:0),
% 1.11/1.49 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [65, 1]
% 1.11/1.49 (w:1, o:76, a:1, s:1, b:0),
% 1.11/1.49 'class_Ring__and__Field_Opordered__ring__abs' [66, 1] (w:1, o:83, a:1
% 1.11/1.49 , s:1, b:0),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv' [67, 3] (w:1, o:174, a:1, s:1, b:0),
% 1.11/1.49 'c_Divides_Odiv__class_Omod' [68, 3] (w:1, o:175, a:1, s:1, b:0),
% 1.11/1.49 'class_OrderedGroup_Olordered__ab__group__add' [69, 1] (w:1, o:84, a:
% 1.11/1.49 1, s:1, b:0),
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus' [70, 2] (w:1, o:163, a:1, s:1, b:0),
% 1.11/1.49 'class_Ring__and__Field_Oordered__semidom' [71, 1] (w:1, o:78, a:1
% 1.11/1.49 , s:1, b:0),
% 1.11/1.49 'c_HOL_Oone__class_Oone' [72, 1] (w:1, o:85, a:1, s:1, b:0),
% 1.11/1.49 'class_Ring__and__Field_Oordered__field' [73, 1] (w:1, o:79, a:1, s:1
% 1.11/1.49 , b:0),
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero' [74, 1] (w:1, o:87, a:1
% 1.11/1.49 , s:1, b:0),
% 1.11/1.49 'class_Int_Onumber' [75, 1] (w:1, o:88, a:1, s:1, b:0),
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide' [76, 3] (w:1, o:176, a:1, s:1, b:0),
% 1.11/1.49
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of' [78, 2] (w:1, o:165, a:1, s:1, b:0
% 3.76/4.13 ),
% 3.76/4.13 'c_HOL_Oinverse__class_Oinverse' [79, 2] (w:1, o:164, a:1, s:1, b:0)
% 3.76/4.13 ,
% 3.76/4.13 'class_Divides_Osemiring__div' [80, 1] (w:1, o:90, a:1, s:1, b:0),
% 3.76/4.13 'class_OrderedGroup_Opordered__ab__group__add' [82, 1] (w:1, o:91, a:
% 3.76/4.13 1, s:1, b:0),
% 3.76/4.13 'class_Power_Opower' [83, 1] (w:1, o:110, a:1, s:1, b:0),
% 3.76/4.13 'class_Ring__and__Field_Ozero__neq__one' [84, 1] (w:1, o:111, a:1, s:
% 3.76/4.13 1, b:0),
% 3.76/4.13 'class_Ring__and__Field_Ono__zero__divisors' [85, 1] (w:1, o:68, a:1
% 3.76/4.13 , s:1, b:0),
% 3.76/4.13 'class_Ring__and__Field_Omult__zero' [86, 1] (w:1, o:65, a:1, s:1, b:
% 3.76/4.13 0),
% 3.76/4.13 'class_Ring__and__Field_Osemiring__0' [87, 1] (w:1, o:116, a:1, s:1
% 3.76/4.13 , b:0),
% 3.76/4.13 'class_Ring__and__Field_Oordered__ring__strict' [88, 1] (w:1, o:77
% 3.76/4.13 , a:1, s:1, b:0),
% 3.76/4.13 'class_OrderedGroup_Opordered__ab__group__add__abs' [89, 1] (w:1, o:
% 3.76/4.13 92, a:1, s:1, b:0),
% 3.76/4.13 'class_Orderings_Olinorder' [90, 1] (w:1, o:93, a:1, s:1, b:0),
% 3.76/4.13 'class_Orderings_Oorder' [91, 1] (w:1, o:94, a:1, s:1, b:0),
% 3.76/4.13 'class_Lattices_Oboolean__algebra' [92, 1] (w:1, o:117, a:1, s:1, b:0
% 3.76/4.13 ),
% 3.76/4.13 'class_OrderedGroup_Ogroup__add' [93, 1] (w:1, o:95, a:1, s:1, b:0),
% 3.76/4.13
% 3.76/4.13 'class_Ring__and__Field_Ofield' [94, 1] (w:1, o:118, a:1, s:1, b:0),
% 3.76/4.13
% 3.76/4.13 'class_OrderedGroup_Olordered__ab__group__add__abs' [95, 1] (w:1, o:
% 3.76/4.13 96, a:1, s:1, b:0),
% 3.76/4.13 'class_OrderedGroup_Opordered__comm__monoid__add' [96, 1] (w:1, o:97
% 3.76/4.13 , a:1, s:1, b:0),
% 3.76/4.13 'class_Ring__and__Field_Oordered__semiring__strict' [97, 1] (w:1, o:
% 3.76/4.13 80, a:1, s:1, b:0),
% 3.76/4.13 'c_HOL_Ominus__class_Ominus' [99, 3] (w:1, o:177, a:1, s:1, b:0),
% 3.76/4.13 'class_RealVector_Oreal__normed__field' [100, 1] (w:1, o:119, a:1, s:
% 3.76/4.13 1, b:0),
% 3.76/4.13 'tc_Int_Oint' [102, 0] (w:1, o:35, a:1, s:1, b:0),
% 3.76/4.13 'class_Ring__and__Field_Ocomm__ring__1' [103, 1] (w:1, o:61, a:1, s:1
% 3.76/4.13 , b:0),
% 3.76/4.13 'class_OrderedGroup_Oab__group__add' [104, 1] (w:1, o:98, a:1, s:1
% 3.76/4.13 , b:0),
% 3.76/4.13 'class_Int_Onumber__ring' [105, 1] (w:1, o:120, a:1, s:1, b:0),
% 3.76/4.13 'class_Ring__and__Field_Oabs__if' [106, 1] (w:1, o:121, a:1, s:1, b:0
% 3.76/4.13 ),
% 3.76/4.13 'class_Ring__and__Field_Oordered__semiring' [107, 1] (w:1, o:81, a:1
% 3.76/4.13 , s:1, b:0),
% 3.76/4.13 'class_Ring__and__Field_Omult__mono1' [111, 1] (w:1, o:66, a:1, s:1
% 3.76/4.13 , b:0),
% 3.76/4.13 'class_Ring__and__Field_Omult__mono' [112, 1] (w:1, o:67, a:1, s:1
% 3.76/4.13 , b:0),
% 3.76/4.13 'class_Ring__and__Field_Opordered__ring' [113, 1] (w:1, o:122, a:1
% 3.76/4.13 , s:1, b:0),
% 3.76/4.13 'class_Ring__and__Field_Odivision__ring' [115, 1] (w:1, o:123, a:1
% 3.76/4.13 , s:1, b:0),
% 3.76/4.13 'c_Int_OMin' [116, 0] (w:1, o:40, a:1, s:1, b:0),
% 3.76/4.13 'class_Ring__and__Field_Osemiring__1' [117, 1] (w:1, o:124, a:1, s:1
% 3.76/4.13 , b:0),
% 3.76/4.13 'c_Nat_Osemiring__1__class_Oof__nat' [118, 2] (w:1, o:166, a:1, s:1
% 3.76/4.13 , b:0),
% 3.76/4.13 'class_Ring__and__Field_Odvd' [121, 1] (w:1, o:125, a:1, s:1, b:0),
% 3.76/4.13 'class_Ring__and__Field_Ocomm__ring' [122, 1] (w:1, o:62, a:1, s:1
% 3.76/4.13 , b:0),
% 3.76/4.13 'class_Ring__and__Field_Opordered__cancel__semiring' [125, 1] (w:1
% 3.76/4.13 , o:126, a:1, s:1, b:0),
% 3.76/4.13 'class_Divides_Oring__div' [126, 1] (w:1, o:89, a:1, s:1, b:0),
% 3.76/4.13 'class_Nat_Osemiring__char__0' [127, 1] (w:1, o:73, a:1, s:1, b:0),
% 3.76/4.13 'class_OrderedGroup_Ocomm__monoid__add' [129, 1] (w:1, o:99, a:1, s:1
% 3.76/4.13 , b:0),
% 3.76/4.13 'class_Ring__and__Field_Oring' [130, 1] (w:1, o:112, a:1, s:1, b:0),
% 3.76/4.13
% 3.76/4.13 'class_Ring__and__Field_Olordered__ring' [132, 1] (w:1, o:64, a:1, s:
% 3.76/4.13 1, b:0),
% 3.76/4.13 'class_Orderings_Opreorder' [133, 1] (w:1, o:100, a:1, s:1, b:0),
% 3.76/4.13 'class_OrderedGroup_Oab__semigroup__add' [134, 1] (w:1, o:101, a:1
% 3.76/4.13 , s:1, b:0),
% 3.76/4.13 'class_OrderedGroup_Oordered__ab__group__add' [135, 1] (w:1, o:74, a:
% 3.76/4.13 1, s:1, b:0),
% 3.76/4.13 'class_Ring__and__Field_Opordered__semiring' [136, 1] (w:1, o:127, a:
% 3.76/4.13 1, s:1, b:0),
% 3.76/4.13 'c_FFT__Mirabelle_Oroot' [137, 1] (w:1, o:128, a:1, s:1, b:0),
% 3.76/4.13 'tc_Complex_Ocomplex' [138, 0] (w:1, o:45, a:1, s:1, b:0),
% 3.76/4.13 'class_RealVector_Oreal__normed__algebra' [139, 1] (w:1, o:129, a:1
% 3.76/4.13 , s:1, b:0),
% 3.76/4.13 'class_OrderedGroup_Omonoid__mult' [140, 1] (w:1, o:102, a:1, s:1, b:
% 3.76/4.13 0),
% 3.76/4.13 'c_Int_Oiszero' [141, 2] (w:1, o:167, a:1, s:1, b:0),
% 20.15/20.52 'class_OrderedGroup_Ocancel__ab__semigroup__add' [142, 1] (w:1, o:103
% 20.15/20.52 , a:1, s:1, b:0),
% 20.15/20.52 'class_OrderedGroup_Ocancel__semigroup__add' [143, 1] (w:1, o:104, a:
% 20.15/20.52 1, s:1, b:0),
% 20.15/20.52 'class_RealVector_Oreal__field' [145, 1] (w:1, o:130, a:1, s:1, b:0)
% 20.15/20.52 ,
% 20.15/20.52 'class_Ring__and__Field_Oordered__comm__semiring__strict' [146, 1]
% 20.15/20.52 (w:1, o:82, a:1, s:1, b:0),
% 20.15/20.52 'class_OrderedGroup_Omonoid__add' [147, 1] (w:1, o:105, a:1, s:1, b:0
% 20.15/20.52 ),
% 20.15/20.52 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [148, 1]
% 20.15/20.52 (w:1, o:106, a:1, s:1, b:0),
% 20.15/20.52 'c_Int_OPls' [149, 0] (w:1, o:47, a:1, s:1, b:0),
% 20.15/20.52 'c_Int_OBit1' [150, 1] (w:1, o:132, a:1, s:1, b:0),
% 20.15/20.52 'c_Int_OBit0' [151, 1] (w:1, o:131, a:1, s:1, b:0),
% 20.15/20.52 'c_Complex_Oii' [153, 0] (w:1, o:49, a:1, s:1, b:0),
% 20.15/20.52 'class_Ring__and__Field_Oring__no__zero__divisors' [158, 1] (w:1, o:
% 20.15/20.52 113, a:1, s:1, b:0),
% 20.15/20.52 'class_Ring__and__Field_Ocomm__semiring' [159, 1] (w:1, o:86, a:1, s:
% 20.15/20.52 1, b:0),
% 20.15/20.52 'class_OrderedGroup_Ocomm__monoid__mult' [160, 1] (w:1, o:107, a:1
% 20.15/20.52 , s:1, b:0),
% 20.15/20.52 'class_Ring__and__Field_Osemiring' [161, 1] (w:1, o:133, a:1, s:1, b:
% 20.15/20.52 0),
% 20.15/20.52 'class_Ring__and__Field_Oring__1' [162, 1] (w:1, o:114, a:1, s:1, b:0
% 20.15/20.52 ),
% 20.15/20.52 'class_Ring__and__Field_Oring__1__no__zero__divisors' [165, 1] (w:1
% 20.15/20.52 , o:115, a:1, s:1, b:0),
% 20.15/20.52 'class_Int_Oring__char__0' [166, 1] (w:1, o:134, a:1, s:1, b:0),
% 20.15/20.52 'c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1' [168, 1] (w:1, o:
% 20.15/20.52 135, a:1, s:1, b:0),
% 20.15/20.52 'class_OrderedGroup_Oab__semigroup__mult' [173, 1] (w:1, o:108, a:1
% 20.15/20.52 , s:1, b:0),
% 20.15/20.52 'class_OrderedGroup_Oab__semigroup__idem__mult' [174, 1] (w:1, o:109
% 20.15/20.52 , a:1, s:1, b:0),
% 20.15/20.52 'v_m' [175, 0] (w:1, o:53, a:1, s:1, b:0),
% 20.15/20.52 'v_i' [176, 0] (w:1, o:54, a:1, s:1, b:0),
% 20.15/20.52 'v_j' [177, 0] (w:1, o:55, a:1, s:1, b:0).
% 20.15/20.52
% 20.15/20.52
% 20.15/20.52 Starting Search:
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52
% 20.15/20.52 Intermediate Status:
% 20.15/20.52 Generated: 3494
% 20.15/20.52 Kept: 2128
% 20.15/20.52 Inuse: 187
% 20.15/20.52 Deleted: 9
% 20.15/20.52 Deletedinuse: 0
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52
% 20.15/20.52 Intermediate Status:
% 20.15/20.52 Generated: 12656
% 20.15/20.52 Kept: 4419
% 20.15/20.52 Inuse: 288
% 20.15/20.52 Deleted: 13
% 20.15/20.52 Deletedinuse: 0
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52
% 20.15/20.52 Intermediate Status:
% 20.15/20.52 Generated: 19367
% 20.15/20.52 Kept: 6460
% 20.15/20.52 Inuse: 336
% 20.15/20.52 Deleted: 15
% 20.15/20.52 Deletedinuse: 0
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52
% 20.15/20.52 Intermediate Status:
% 20.15/20.52 Generated: 24955
% 20.15/20.52 Kept: 8493
% 20.15/20.52 Inuse: 379
% 20.15/20.52 Deleted: 17
% 20.15/20.52 Deletedinuse: 0
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52
% 20.15/20.52 Intermediate Status:
% 20.15/20.52 Generated: 32049
% 20.15/20.52 Kept: 10507
% 20.15/20.52 Inuse: 441
% 20.15/20.52 Deleted: 17
% 20.15/20.52 Deletedinuse: 0
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52
% 20.15/20.52 Intermediate Status:
% 20.15/20.52 Generated: 40335
% 20.15/20.52 Kept: 12629
% 20.15/20.52 Inuse: 498
% 20.15/20.52 Deleted: 18
% 20.15/20.52 Deletedinuse: 0
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52
% 20.15/20.52 Intermediate Status:
% 20.15/20.52 Generated: 46728
% 20.15/20.52 Kept: 15183
% 20.15/20.52 Inuse: 513
% 20.15/20.52 Deleted: 18
% 20.15/20.52 Deletedinuse: 0
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52
% 20.15/20.52 Intermediate Status:
% 20.15/20.52 Generated: 53185
% 20.15/20.52 Kept: 17184
% 20.15/20.52 Inuse: 558
% 20.15/20.52 Deleted: 18
% 20.15/20.52 Deletedinuse: 0
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52
% 20.15/20.52 Intermediate Status:
% 20.15/20.52 Generated: 59281
% 20.15/20.52 Kept: 19214
% 20.15/20.52 Inuse: 602
% 20.15/20.52 Deleted: 19
% 20.15/20.52 Deletedinuse: 0
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52 Resimplifying clauses:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52
% 20.15/20.52 Intermediate Status:
% 20.15/20.52 Generated: 65845
% 20.15/20.52 Kept: 22086
% 20.15/20.52 Inuse: 616
% 20.15/20.52 Deleted: 333
% 20.15/20.52 Deletedinuse: 0
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52
% 20.15/20.52 Intermediate Status:
% 20.15/20.52 Generated: 78813
% 20.15/20.52 Kept: 24828
% 20.15/20.52 Inuse: 650
% 20.15/20.52 Deleted: 335
% 20.15/20.52 Deletedinuse: 1
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52
% 20.15/20.52 Intermediate Status:
% 20.15/20.52 Generated: 86441
% 20.15/20.52 Kept: 26955
% 20.15/20.52 Inuse: 680
% 20.15/20.52 Deleted: 335
% 20.15/20.52 Deletedinuse: 1
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 20.15/20.52 Done
% 20.15/20.52
% 20.15/20.52
% 20.15/20.52 Intermediate Status:
% 20.15/20.52 Generated: 110259
% 20.15/20.52 Kept: 30033
% 20.15/20.52 Inuse: 700
% 20.15/20.52 Deleted: 335
% 20.15/20.52 Deletedinuse: 1
% 20.15/20.52
% 20.15/20.52 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 119658
% 68.67/69.06 Kept: 32418
% 68.67/69.06 Inuse: 715
% 68.67/69.06 Deleted: 335
% 68.67/69.06 Deletedinuse: 1
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 126856
% 68.67/69.06 Kept: 34573
% 68.67/69.06 Inuse: 750
% 68.67/69.06 Deleted: 335
% 68.67/69.06 Deletedinuse: 1
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 137050
% 68.67/69.06 Kept: 37130
% 68.67/69.06 Inuse: 785
% 68.67/69.06 Deleted: 335
% 68.67/69.06 Deletedinuse: 1
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 145826
% 68.67/69.06 Kept: 39141
% 68.67/69.06 Inuse: 798
% 68.67/69.06 Deleted: 337
% 68.67/69.06 Deletedinuse: 1
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying clauses:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 149882
% 68.67/69.06 Kept: 41181
% 68.67/69.06 Inuse: 807
% 68.67/69.06 Deleted: 515
% 68.67/69.06 Deletedinuse: 1
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 185233
% 68.67/69.06 Kept: 44025
% 68.67/69.06 Inuse: 828
% 68.67/69.06 Deleted: 515
% 68.67/69.06 Deletedinuse: 1
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 195821
% 68.67/69.06 Kept: 46143
% 68.67/69.06 Inuse: 868
% 68.67/69.06 Deleted: 515
% 68.67/69.06 Deletedinuse: 1
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 207344
% 68.67/69.06 Kept: 48821
% 68.67/69.06 Inuse: 888
% 68.67/69.06 Deleted: 515
% 68.67/69.06 Deletedinuse: 1
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 215965
% 68.67/69.06 Kept: 50910
% 68.67/69.06 Inuse: 898
% 68.67/69.06 Deleted: 515
% 68.67/69.06 Deletedinuse: 1
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 227282
% 68.67/69.06 Kept: 52940
% 68.67/69.06 Inuse: 933
% 68.67/69.06 Deleted: 515
% 68.67/69.06 Deletedinuse: 1
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 243582
% 68.67/69.06 Kept: 55369
% 68.67/69.06 Inuse: 943
% 68.67/69.06 Deleted: 515
% 68.67/69.06 Deletedinuse: 1
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 257117
% 68.67/69.06 Kept: 58580
% 68.67/69.06 Inuse: 963
% 68.67/69.06 Deleted: 515
% 68.67/69.06 Deletedinuse: 1
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 267610
% 68.67/69.06 Kept: 61457
% 68.67/69.06 Inuse: 968
% 68.67/69.06 Deleted: 515
% 68.67/69.06 Deletedinuse: 1
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying clauses:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 277378
% 68.67/69.06 Kept: 63478
% 68.67/69.06 Inuse: 1000
% 68.67/69.06 Deleted: 675
% 68.67/69.06 Deletedinuse: 1
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 284636
% 68.67/69.06 Kept: 65688
% 68.67/69.06 Inuse: 1018
% 68.67/69.06 Deleted: 675
% 68.67/69.06 Deletedinuse: 1
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 295541
% 68.67/69.06 Kept: 67703
% 68.67/69.06 Inuse: 1049
% 68.67/69.06 Deleted: 680
% 68.67/69.06 Deletedinuse: 6
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 305408
% 68.67/69.06 Kept: 69721
% 68.67/69.06 Inuse: 1080
% 68.67/69.06 Deleted: 680
% 68.67/69.06 Deletedinuse: 6
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 315231
% 68.67/69.06 Kept: 71735
% 68.67/69.06 Inuse: 1112
% 68.67/69.06 Deleted: 680
% 68.67/69.06 Deletedinuse: 6
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 325933
% 68.67/69.06 Kept: 73799
% 68.67/69.06 Inuse: 1133
% 68.67/69.06 Deleted: 680
% 68.67/69.06 Deletedinuse: 6
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 338146
% 68.67/69.06 Kept: 75810
% 68.67/69.06 Inuse: 1159
% 68.67/69.06 Deleted: 680
% 68.67/69.06 Deletedinuse: 6
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 348195
% 68.67/69.06 Kept: 77816
% 68.67/69.06 Inuse: 1192
% 68.67/69.06 Deleted: 680
% 68.67/69.06 Deletedinuse: 6
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 361532
% 68.67/69.06 Kept: 79843
% 68.67/69.06 Inuse: 1231
% 68.67/69.06 Deleted: 680
% 68.67/69.06 Deletedinuse: 6
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying clauses:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 375908
% 68.67/69.06 Kept: 82020
% 68.67/69.06 Inuse: 1268
% 68.67/69.06 Deleted: 1251
% 68.67/69.06 Deletedinuse: 6
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06 Resimplifying inuse:
% 68.67/69.06 Done
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 387650
% 68.67/69.06 Kept: 84035
% 68.67/69.06 Inuse: 1305
% 68.67/69.06 Deleted: 1254
% 68.67/69.06 Deletedinuse: 9
% 68.67/69.06
% 68.67/69.06
% 68.67/69.06 Intermediate Status:
% 68.67/69.06 Generated: 395657
% 68.67/69.06 Kept: 87123
% 68.67/69.06 Inuse: 1317
% 146.31/146.75 Deleted: 1255
% 146.31/146.75 Deletedinuse: 9
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 413726
% 146.31/146.75 Kept: 90213
% 146.31/146.75 Inuse: 1332
% 146.31/146.75 Deleted: 1256
% 146.31/146.75 Deletedinuse: 10
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 438175
% 146.31/146.75 Kept: 93391
% 146.31/146.75 Inuse: 1352
% 146.31/146.75 Deleted: 1257
% 146.31/146.75 Deletedinuse: 11
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 452845
% 146.31/146.75 Kept: 96228
% 146.31/146.75 Inuse: 1367
% 146.31/146.75 Deleted: 1257
% 146.31/146.75 Deletedinuse: 11
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 468113
% 146.31/146.75 Kept: 98548
% 146.31/146.75 Inuse: 1382
% 146.31/146.75 Deleted: 1257
% 146.31/146.75 Deletedinuse: 11
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 482915
% 146.31/146.75 Kept: 101058
% 146.31/146.75 Inuse: 1392
% 146.31/146.75 Deleted: 1257
% 146.31/146.75 Deletedinuse: 11
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying clauses:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 501594
% 146.31/146.75 Kept: 103292
% 146.31/146.75 Inuse: 1407
% 146.31/146.75 Deleted: 1522
% 146.31/146.75 Deletedinuse: 11
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 512772
% 146.31/146.75 Kept: 105422
% 146.31/146.75 Inuse: 1432
% 146.31/146.75 Deleted: 1522
% 146.31/146.75 Deletedinuse: 11
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 524491
% 146.31/146.75 Kept: 107451
% 146.31/146.75 Inuse: 1464
% 146.31/146.75 Deleted: 1522
% 146.31/146.75 Deletedinuse: 11
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 537907
% 146.31/146.75 Kept: 109683
% 146.31/146.75 Inuse: 1497
% 146.31/146.75 Deleted: 1522
% 146.31/146.75 Deletedinuse: 11
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 555678
% 146.31/146.75 Kept: 114059
% 146.31/146.75 Inuse: 1506
% 146.31/146.75 Deleted: 1522
% 146.31/146.75 Deletedinuse: 11
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 581980
% 146.31/146.75 Kept: 117198
% 146.31/146.75 Inuse: 1517
% 146.31/146.75 Deleted: 1522
% 146.31/146.75 Deletedinuse: 11
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 596051
% 146.31/146.75 Kept: 120030
% 146.31/146.75 Inuse: 1537
% 146.31/146.75 Deleted: 1522
% 146.31/146.75 Deletedinuse: 11
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 631602
% 146.31/146.75 Kept: 122994
% 146.31/146.75 Inuse: 1552
% 146.31/146.75 Deleted: 1522
% 146.31/146.75 Deletedinuse: 11
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying clauses:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 649813
% 146.31/146.75 Kept: 125026
% 146.31/146.75 Inuse: 1589
% 146.31/146.75 Deleted: 1694
% 146.31/146.75 Deletedinuse: 12
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 659856
% 146.31/146.75 Kept: 127031
% 146.31/146.75 Inuse: 1616
% 146.31/146.75 Deleted: 1694
% 146.31/146.75 Deletedinuse: 12
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 669773
% 146.31/146.75 Kept: 129039
% 146.31/146.75 Inuse: 1642
% 146.31/146.75 Deleted: 1695
% 146.31/146.75 Deletedinuse: 13
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 680403
% 146.31/146.75 Kept: 131063
% 146.31/146.75 Inuse: 1652
% 146.31/146.75 Deleted: 1695
% 146.31/146.75 Deletedinuse: 13
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 690639
% 146.31/146.75 Kept: 133085
% 146.31/146.75 Inuse: 1674
% 146.31/146.75 Deleted: 1697
% 146.31/146.75 Deletedinuse: 14
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 706951
% 146.31/146.75 Kept: 138346
% 146.31/146.75 Inuse: 1686
% 146.31/146.75 Deleted: 1697
% 146.31/146.75 Deletedinuse: 14
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 726311
% 146.31/146.75 Kept: 140562
% 146.31/146.75 Inuse: 1701
% 146.31/146.75 Deleted: 1698
% 146.31/146.75 Deletedinuse: 15
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 737881
% 146.31/146.75 Kept: 142610
% 146.31/146.75 Inuse: 1711
% 146.31/146.75 Deleted: 1698
% 146.31/146.75 Deletedinuse: 15
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying clauses:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 750142
% 146.31/146.75 Kept: 144611
% 146.31/146.75 Inuse: 1721
% 146.31/146.75 Deleted: 2645
% 146.31/146.75 Deletedinuse: 15
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 759520
% 146.31/146.75 Kept: 146826
% 146.31/146.75 Inuse: 1741
% 146.31/146.75 Deleted: 2645
% 146.31/146.75 Deletedinuse: 15
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 146.31/146.75 Done
% 146.31/146.75
% 146.31/146.75
% 146.31/146.75 Intermediate Status:
% 146.31/146.75 Generated: 774577
% 146.31/146.75 Kept: 149101
% 146.31/146.75 Inuse: 1771
% 146.31/146.75 Deleted: 2645
% 146.31/146.75 Deletedinuse: 15
% 146.31/146.75
% 146.31/146.75 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 783945
% 269.81/270.30 Kept: 151271
% 269.81/270.30 Inuse: 1796
% 269.81/270.30 Deleted: 2657
% 269.81/270.30 Deletedinuse: 22
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 810299
% 269.81/270.30 Kept: 157686
% 269.81/270.30 Inuse: 1811
% 269.81/270.30 Deleted: 2666
% 269.81/270.30 Deletedinuse: 28
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 824858
% 269.81/270.30 Kept: 163733
% 269.81/270.30 Inuse: 1813
% 269.81/270.30 Deleted: 2666
% 269.81/270.30 Deletedinuse: 28
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30 Resimplifying clauses:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 839971
% 269.81/270.30 Kept: 166413
% 269.81/270.30 Inuse: 1818
% 269.81/270.30 Deleted: 3427
% 269.81/270.30 Deletedinuse: 28
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 858642
% 269.81/270.30 Kept: 169841
% 269.81/270.30 Inuse: 1826
% 269.81/270.30 Deleted: 3436
% 269.81/270.30 Deletedinuse: 35
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 872030
% 269.81/270.30 Kept: 172084
% 269.81/270.30 Inuse: 1856
% 269.81/270.30 Deleted: 3437
% 269.81/270.30 Deletedinuse: 36
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 885951
% 269.81/270.30 Kept: 174659
% 269.81/270.30 Inuse: 1871
% 269.81/270.30 Deleted: 3437
% 269.81/270.30 Deletedinuse: 36
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 897939
% 269.81/270.30 Kept: 176683
% 269.81/270.30 Inuse: 1885
% 269.81/270.30 Deleted: 3437
% 269.81/270.30 Deletedinuse: 36
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 907575
% 269.81/270.30 Kept: 178858
% 269.81/270.30 Inuse: 1906
% 269.81/270.30 Deleted: 3437
% 269.81/270.30 Deletedinuse: 36
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 917692
% 269.81/270.30 Kept: 180893
% 269.81/270.30 Inuse: 1929
% 269.81/270.30 Deleted: 3437
% 269.81/270.30 Deletedinuse: 36
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 929000
% 269.81/270.30 Kept: 182918
% 269.81/270.30 Inuse: 1949
% 269.81/270.30 Deleted: 3437
% 269.81/270.30 Deletedinuse: 36
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 948177
% 269.81/270.30 Kept: 186658
% 269.81/270.30 Inuse: 1956
% 269.81/270.30 Deleted: 3438
% 269.81/270.30 Deletedinuse: 37
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30 Resimplifying clauses:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 967500
% 269.81/270.30 Kept: 190478
% 269.81/270.30 Inuse: 1961
% 269.81/270.30 Deleted: 4419
% 269.81/270.30 Deletedinuse: 40
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 999280
% 269.81/270.30 Kept: 193451
% 269.81/270.30 Inuse: 1971
% 269.81/270.30 Deleted: 4419
% 269.81/270.30 Deletedinuse: 40
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 1031591
% 269.81/270.30 Kept: 196759
% 269.81/270.30 Inuse: 1981
% 269.81/270.30 Deleted: 4419
% 269.81/270.30 Deletedinuse: 40
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 1042949
% 269.81/270.30 Kept: 198852
% 269.81/270.30 Inuse: 2001
% 269.81/270.30 Deleted: 4419
% 269.81/270.30 Deletedinuse: 40
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 1076228
% 269.81/270.30 Kept: 202494
% 269.81/270.30 Inuse: 2011
% 269.81/270.30 Deleted: 4419
% 269.81/270.30 Deletedinuse: 40
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 1089565
% 269.81/270.30 Kept: 204513
% 269.81/270.30 Inuse: 2040
% 269.81/270.30 Deleted: 4419
% 269.81/270.30 Deletedinuse: 40
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 1098287
% 269.81/270.30 Kept: 209385
% 269.81/270.30 Inuse: 2041
% 269.81/270.30 Deleted: 4419
% 269.81/270.30 Deletedinuse: 40
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30 Resimplifying clauses:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 1111024
% 269.81/270.30 Kept: 211514
% 269.81/270.30 Inuse: 2046
% 269.81/270.30 Deleted: 4882
% 269.81/270.30 Deletedinuse: 41
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 1124499
% 269.81/270.30 Kept: 213705
% 269.81/270.30 Inuse: 2056
% 269.81/270.30 Deleted: 4883
% 269.81/270.30 Deletedinuse: 42
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 1134788
% 269.81/270.30 Kept: 215992
% 269.81/270.30 Inuse: 2071
% 269.81/270.30 Deleted: 4883
% 269.81/270.30 Deletedinuse: 42
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 1164328
% 269.81/270.30 Kept: 223595
% 269.81/270.30 Inuse: 2080
% 269.81/270.30 Deleted: 4883
% 269.81/270.30 Deletedinuse: 42
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 1171900
% 269.81/270.30 Kept: 225622
% 269.81/270.30 Inuse: 2096
% 269.81/270.30 Deleted: 4884
% 269.81/270.30 Deletedinuse: 43
% 269.81/270.30
% 269.81/270.30 Resimplifying inuse:
% 269.81/270.30 Done
% 269.81/270.30
% 269.81/270.30
% 269.81/270.30 Intermediate Status:
% 269.81/270.30 Generated: 1186254
% 269.81/270.30 Kept: 227781
% 269.81/270.30 Inuse: 2106
% 269.81/270.30 Deleted: 4884
% 269.81/270.30 DeleCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------