TSTP Solution File: SWV676-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV676-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.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 16:27:42 EDT 2022
% Result : Timeout 300.04s 300.52s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWV676-1 : TPTP v8.1.0. Released v4.1.0.
% 0.14/0.14 % Command : bliksem %s
% 0.14/0.36 % Computer : n025.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % DateTime : Wed Jun 15 00:27:25 EDT 2022
% 0.14/0.36 % 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_Divides_Osemiring__div'( X ) ),
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.11/1.47 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.11/1.47 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 1.11/1.47 ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.11/1.47 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.11/1.47 ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 1.11/1.47 Y, 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.11/1.47 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 1.11/1.47 ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.11/1.47 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.11/1.47 ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.47 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 1.11/1.47 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.47 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.11/1.47 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.11/1.47 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.47 , Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.11/1.47 , Z, 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oone__class_Oone'( '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, 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.47 , Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.11/1.47 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.47 X, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.11/1.47 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.11/1.47 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 1.11/1.47 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.11/1.47 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat'
% 1.11/1.47 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.11/1.47 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 1.11/1.47 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.11/1.47 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), T, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 1.11/1.47 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 1.11/1.47 , X ) ) ],
% 1.11/1.47 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.11/1.47 ), X, 'tc_nat' ) ],
% 1.11/1.47 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.11/1.47 ), Y, '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 ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.11/1.47 ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.11/1.47 ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.11/1.47 ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.11/1.47 ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.11/1.47 ],
% 1.11/1.47 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.11/1.47 , X, 'tc_nat' ), X ) ],
% 1.11/1.47 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.11/1.47 ), 'tc_nat' ), X ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.11/1.47 ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 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, 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.47 , Y, X ), 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, 'c_HOL_Otimes__class_Otimes'( Y
% 1.11/1.47 , Z, X ), X ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.11/1.47 , Z, X ), X ) ],
% 1.11/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.47 [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'(
% 1.11/1.47 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.11/1.47 [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.11/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 1.11/1.47 , 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 1.11/1.47 =( 'c_GCD_Ogcd__class_Ogcd'( X, Z, 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.47 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.47 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.11/1.47 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.47 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.11/1.47 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.11/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( '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_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.11/1.47 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( '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_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.11/1.47 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.47 X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.11/1.47 'tc_nat' ), X, 'tc_nat' ) ],
% 1.11/1.47 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.47 X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 1.11/1.47 'tc_nat' ), X, 'tc_nat' ) ],
% 1.11/1.47 [ ~( 'class_Divides_Osemiring__div'( 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'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.11/1.47 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.11/1.47 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Divides_Osemiring__div'( 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'( Y, T, X ) ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.11/1.47 , T, X ), X ) ) ],
% 1.11/1.47 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.11/1.47 ), 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ],
% 1.11/1.47 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.47 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y,
% 1.11/1.47 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Z, 'c_HOL_Oone__class_Oone'(
% 1.11/1.47 'tc_nat' ) ), ~( '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_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Z, 'c_HOL_Oone__class_Oone'(
% 1.11/1.47 'tc_nat' ) ), ~( '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 [ ~( '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 ),
% 1.11/1.47 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.11/1.47 ) ],
% 1.11/1.47 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_GCD_Ogcd__class_Ogcd'( Y, 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat'
% 1.11/1.47 ), 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.11/1.47 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.11/1.47 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.11/1.47 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.47 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.11/1.47 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, 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 ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.47 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, 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 ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.47 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), 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 ) ), 'c_lessequals'( Y,
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.11/1.47 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.11/1.47 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ), ~(
% 1.11/1.47 '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 ) ), 'c_lessequals'( Y
% 1.11/1.47 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.47 , Z, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.47 , T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.47 , Z, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.47 , T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.47 'c_Power_Opower__class_Opower'( Y, T, X ), X ),
% 1.11/1.47 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.11/1.47 'tc_nat' ), X ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.11/1.47 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.47 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.11/1.47 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.11/1.47 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.47 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.47 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.47 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.47 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), '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' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, 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'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( 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_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( 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_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.11/1.47 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.47 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.47 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.11/1.47 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.47 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), '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 ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.47 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~(
% 1.11/1.47 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, 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 ) ), 'c_lessequals'( Y,
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.47 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~(
% 1.11/1.47 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( 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 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 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_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( '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 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, 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_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.47 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.47 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.47 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.47 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ), Z ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.47 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.47 , Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.47 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 Y, X, 'tc_nat' ), =( Y, X ) ],
% 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, X, 'tc_nat' ) ), =( Y, X ) ]
% 1.11/1.47 ,
% 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'( X, Y, 'tc_nat' )
% 1.11/1.47 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 Y, X, 'tc_nat' ), =( 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 [ ~( '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' )
% 1.11/1.47 ), ~( '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 [ ~( '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_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 ) ), =( 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_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 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Z, Y
% 1.11/1.47 , 'tc_nat' ), '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, 'c_GCD_Ogcd__class_Ogcd'( Y, Z
% 1.11/1.47 , 'tc_nat' ), '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, 'c_GCD_Ogcd__class_Ogcd'( Y, Z
% 1.11/1.47 , 'tc_nat' ), '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, 'c_GCD_Ogcd__class_Ogcd'( Z, Y
% 1.11/1.47 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.11/1.47 , 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.11/1.47 , Z, 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.11/1.47 , 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y
% 1.11/1.47 , 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'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z
% 1.11/1.47 , 'tc_nat' ), '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, 'c_GCD_Ogcd__class_Ogcd'( Z, Y
% 1.11/1.47 , 'tc_nat' ), '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 [ '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_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, 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'( Y, Y, 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, 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 [ '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'( X, Y, 'tc_nat' ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 1.11/1.47 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.11/1.47 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 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 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), '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 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), '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 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.11/1.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.47 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.47 , Y, X ) ) ],
% 1.11/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 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 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.47 , 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 ), T, X
% 1.11/1.47 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.11/1.47 , T, X ), X ), T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.47 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.47 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.11/1.47 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.11/1.47 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.11/1.47 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.11/1.47 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.47 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.11/1.47 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.11/1.47 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.11/1.47 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.11/1.47 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.11/1.47 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.11/1.47 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.47 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X
% 1.11/1.47 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.47 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.11/1.47 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.47 Y, T, X ), 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'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.11/1.47 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.47 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.47 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 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 ), T, X
% 1.11/1.47 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, 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 ), T, X
% 1.11/1.47 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.11/1.47 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.11/1.47 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.11/1.47 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.47 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.11/1.47 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.11/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.47 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( X, 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' ) ), =( Y, Z ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.47 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.47 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.47 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.11/1.47 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.47 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.47 , T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.47 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.47 , Z, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 1.11/1.47 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.47 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 X ), T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 1.11/1.47 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.47 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.47 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.47 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.11/1.47 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.11/1.47 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.11/1.47 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.11/1.47 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.47 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.11/1.47 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.47 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 1.11/1.47 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.47 'c_Suc'( X ), 'tc_nat' ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.47 'c_Suc'( X ), '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 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.47 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.47 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.11/1.47 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.47 , Y, X ) ) ],
% 1.11/1.47 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.47 'tc_nat' ), Y, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.47 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.11/1.47 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 1.11/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.47 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z,
% 1.11/1.47 Y, 'tc_nat' ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.11/1.47 ), Y, 'tc_nat' ), T, '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_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 1.11/1.47 ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.47 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 1.11/1.47 ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 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'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.47 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.11/1.47 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.11/1.47 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 X ), X ) ) ],
% 1.11/1.47 [ ~( =( X, 'c_HOL_Otimes__class_Otimes'( Y, 'c_GCD_Ogcd__class_Ogcd'( Z
% 1.11/1.47 , X, 'tc_nat' ), 'tc_nat' ) ) ), ~( =( Z, 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.47 , 'c_GCD_Ogcd__class_Ogcd'( Z, X, 'tc_nat' ), 'tc_nat' ) ) ), =(
% 1.11/1.47 'c_GCD_Ogcd__class_Ogcd'( Z, X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 'tc_nat' ) ), =( 'c_GCD_Ogcd__class_Ogcd'( T, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 1.11/1.47 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 1.11/1.47 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 1.11/1.47 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 1.11/1.47 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'(
% 1.11/1.47 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), '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 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.11/1.47 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.47 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.11/1.47 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 1.11/1.47 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, 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 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, 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 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 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_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.11/1.47 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.11/1.47 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.11/1.47 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 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'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 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'( Y, 'c_HOL_Ozero__class_Ozero'( 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_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 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_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 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'( Y, 'c_HOL_Ozero__class_Ozero'( X ), 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_Oinverse__class_Odivide'( 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_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.47 T, Z, X ) ) ), =( Y, T ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.11/1.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.11/1.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.47 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.47 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.47 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.11/1.47 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.11/1.47 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.11/1.47 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.11/1.47 'tc_nat' ), Z, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 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' ), 'c_Divides_Odiv__class_Omod'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 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'( Z, T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( T, Z, 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'( T, Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.47 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 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 [ '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 [ ~( '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 [ ~( '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 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oone__class_Oone'( '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'( X, Z, 'tc_nat' ) ),
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 1.11/1.47 , 'tc_nat' ), Z, 'tc_nat' ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 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 ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 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 ), Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 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 ), Z, 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, 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.47 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 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, 'c_HOL_Otimes__class_Otimes'( Z
% 1.11/1.47 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 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'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.11/1.47 , X ), Z, 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, Z, X ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.11/1.47 , X ), Z, 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'( Z, T, X ), X )
% 1.11/1.47 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.11/1.47 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.11/1.47 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 1.11/1.47 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.47 , X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.47 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.47 , Y, X ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 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' ), T, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z
% 1.11/1.47 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' )
% 1.11/1.47 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.11/1.47 , Z, 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.11/1.47 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.11/1.47 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.11/1.47 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.11/1.47 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.47 , Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.11/1.47 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.11/1.47 , T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.11/1.47 ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.47 , Z, X ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.11/1.47 ), ~( 'c_lessequals'( T, Y, X ) ) ],
% 1.11/1.47 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.11/1.47 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 1.11/1.47 ],
% 1.11/1.47 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.47 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T )
% 1.11/1.47 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.47 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.11/1.47 ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 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'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.11/1.47 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.11/1.47 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 1.11/1.47 X ), Z, 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_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.11/1.47 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.11/1.47 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.11/1.47 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 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.11/1.47 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.11/1.47 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.11/1.47 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 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.11/1.47 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.11/1.47 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.11/1.47 X ), Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.11/1.47 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.11/1.47 Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 X ), Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.11/1.47 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.11/1.47 X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 X ), T, X ) ) ],
% 1.11/1.47 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Z, 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( '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 [ ~( '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'( Y, 'c_HOL_Ozero__class_Ozero'( X ), 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_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Y, 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 'c_HOL_Oord__class_Oless'( Y, '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_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Z, 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'( Y, '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_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Y, 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 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), 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_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.11/1.47 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 1.11/1.47 , 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.47 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.11/1.47 , 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( T, U, 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 ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.11/1.47 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oone__class_Oone'(
% 1.11/1.47 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.47 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.47 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.11/1.47 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.11/1.47 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 1.11/1.47 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.11/1.47 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.11/1.47 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.11/1.47 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.11/1.47 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.11/1.47 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), 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,
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.11/1.47 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 1.11/1.47 , X ), W, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Z, W, X ), X ) ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.11/1.47 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.11/1.47 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Z,
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( U, W, X ), X ), T, X ), X ) ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ],
% 1.11/1.47 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.47 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.47 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.47 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.47 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.47 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), 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 ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 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 ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, 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_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, 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 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.11/1.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, 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_Ofield'( X ) ), ~( =(
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.47 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.11/1.47 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ],
% 1.11/1.47 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.11/1.47 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.11/1.47 T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.11/1.47 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.11/1.47 X ), Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.11/1.47 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.11/1.47 T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.11/1.47 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.11/1.47 X ), T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.11/1.47 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.47 T, X ), X ) ) ],
% 1.11/1.47 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.47 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.11/1.47 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.11/1.47 X ), T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.11/1.47 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.11/1.47 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.11/1.47 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.11/1.47 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.11/1.47 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.11/1.47 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.11/1.47 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( 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, Z, 'tc_nat' ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.11/1.47 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.11/1.47 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), '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_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), '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_OrderedGroup_Olordered__ab__group__add'( 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_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 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 ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.11/1.47 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.47 ,
% 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_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 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 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.11/1.47 , X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 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'( Z, T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.47 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 X ), T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.47 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( '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_HOL_Oord__class_Oless'( 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 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.11/1.47 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.11/1.47 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.47 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), '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' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( '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_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.47 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_HOL_Oord__class_Oless'( '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_HOL_Oord__class_Oless'( 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 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.47 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.47 ~( 'c_HOL_Oord__class_Oless'( X, Z, '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 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( 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,
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 1.11/1.47 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.11/1.47 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), Y,
% 1.11/1.47 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.11/1.47 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.11/1.47 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), =( Z,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.11/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 1.11/1.47 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.11/1.47 ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.11/1.47 , X ), X ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.11/1.47 , X ), X ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.11/1.47 ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.11/1.47 ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.11/1.47 ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.47 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, '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_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.11/1.47 ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.11/1.47 ],
% 1.11/1.47 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.47 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.11/1.47 ), 'tc_nat' ), X ) ],
% 1.11/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.11/1.47 , X, 'tc_nat' ), X ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.11/1.47 ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.11/1.47 ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 1.11/1.47 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.11/1.47 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.11/1.47 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 1.11/1.47 Y, Z, 'tc_nat' ), 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.11/1.47 , Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat'
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 1.11/1.47 Y, Z, 'tc_nat' ), 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.11/1.47 , Y, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat'
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 1.11/1.47 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.11/1.47 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.11/1.47 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 1.11/1.47 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.11/1.47 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.11/1.47 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.11/1.47 , 'tc_nat' ), Y, 'tc_nat' ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.11/1.47 , 'tc_nat' ), X, 'tc_nat' ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.11/1.47 , 'tc_nat' ), X, 'tc_nat' ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.11/1.47 , 'tc_nat' ), Y, 'tc_nat' ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.11/1.47 , 'tc_nat' ), X, 'tc_nat' ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.11/1.47 , 'tc_nat' ), Y, 'tc_nat' ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 1.11/1.47 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.11/1.47 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.11/1.47 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 1.11/1.47 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.11/1.47 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.11/1.47 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 1.11/1.47 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.11/1.47 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.11/1.47 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.11/1.47 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 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, Z, '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'( Y, 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, X, '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'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.47 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.47 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.47 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 1.11/1.47 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.47 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.11/1.47 , X ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.47 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.11/1.47 , X ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.47 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 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, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.11/1.47 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.47 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.47 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.11/1.47 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.47 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.47 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.47 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, 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_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'( 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'( 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'( 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'( 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_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.11/1.47 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.47 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.11/1.47 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.11/1.47 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.11/1.47 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.47 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.11/1.47 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.11/1.47 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.11/1.47 W, X ), X ), ~( 'c_lessequals'( T, 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.11/1.47 , X ), W, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.11/1.47 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U, X ), W, X ), X ), ~(
% 1.11/1.47 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 T, U, X ), Y, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.11/1.47 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.11/1.47 W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 1.11/1.47 , X ), T, X ), W, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 1.11/1.47 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.47 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.11/1.47 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.11/1.47 , X ), '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, Z, X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.47 Z, T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.11/1.47 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.11/1.47 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.11/1.47 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.47 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.11/1.47 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.11/1.47 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.11/1.47 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.11/1.47 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.47 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.11/1.47 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.47 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.47 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, 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 ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 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 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 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 ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.47 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( 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 ) ), 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.47 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.11/1.47 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, 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 ) ), 'c_lessequals'( Y,
% 1.11/1.47 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 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 ), Z, X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 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 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.11/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 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_Ozero__class_Ozero'( X ),
% 1.11/1.47 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.11/1.47 , X ), X ) ],
% 1.11/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.11/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.47 '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_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( '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_HOL_Oplus__class_Oplus'( Y, T, X ), Z, 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 [ ~( '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_lessequals'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y,
% 1.11/1.48 'tc_nat' ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X,
% 1.11/1.48 'tc_nat' ), =( X, '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_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, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 1.11/1.48 , 'c_HOL_Otimes__class_Otimes'( T, Y, 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_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.11/1.48 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 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_HOL_Otimes__class_Otimes'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'(
% 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' ), 'tc_nat' ) ) ],
% 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_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 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.11/1.48 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ) ) ],
% 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 [ ~( =( '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_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__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_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__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 [ ~( '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 [ '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 '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_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_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_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.11/1.48 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 '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_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 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.11/1.48 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_Suc'( X ), X, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 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 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.11/1.48 , 'tc_nat' ), X ) ],
% 1.11/1.48 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.11/1.48 , 'tc_nat' ), 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__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_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_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'( 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_Ominus__class_Ominus'( U, Y, X ), Z
% 1.11/1.48 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.11/1.48 X ), Z, 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_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'(
% 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_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_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( T, U, 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_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 [ ~( '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_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.11/1.48 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.11/1.48 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.11/1.48 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.11/1.48 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.11/1.48 , X ), 'c_HOL_Ominus__class_Ominus'( '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_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.11/1.48 , X ), 'c_HOL_Ominus__class_Ominus'( '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_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_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_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_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_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 1.11/1.48 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), T, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.11/1.48 X ), Y ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.11/1.48 X ), Y ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.48 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 1.11/1.48 Y, Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.48 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.11/1.48 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.48 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.11/1.48 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.48 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.11/1.48 =( 'c_Power_Opower__class_Opower'( Y, Z, 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_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, Z, X ),
% 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_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.11/1.48 , T, X ), 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 Z, T, 'tc_nat' ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.11/1.48 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 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_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 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 '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_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_Otimes__class_Otimes'( '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_Otimes__class_Otimes'( Y, T, X )
% 1.11/1.48 , 'c_HOL_Otimes__class_Otimes'( Z, 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_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.11/1.48 , T, X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 Y, T, X ), Z, X ) ) ],
% 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__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_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'( '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'( '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 ) ), ~(
% 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__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__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, 'c_Suc'( Z ), X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 1.11/1.48 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.48 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.48 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.11/1.48 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.11/1.48 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.11/1.48 [ =( X, Y ), ~( '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_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 [ =( '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'( '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 [ '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_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, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 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_Suc'( X ), Y, '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, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 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 [ =( '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 [ '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 [ '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 [ 'c_lessequals'( 'c_Suc'( '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_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y,
% 1.11/1.48 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 1.11/1.48 'tc_nat' ), ~( 'c_lessequals'( '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 ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 1.11/1.48 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( '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_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_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 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_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 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 1.11/1.48 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 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_lessequals'( '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_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.11/1.48 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.11/1.48 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.11/1.48 'tc_nat' ) ],
% 1.11/1.48 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 1.11/1.48 'tc_nat' ) ],
% 1.11/1.48 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.11/1.48 'tc_nat' ) ],
% 1.11/1.48 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.11/1.48 'tc_nat' ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.48 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 1.11/1.48 ],
% 1.11/1.48 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.48 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 1.11/1.48 ],
% 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_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_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 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_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 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, X, 'tc_nat' ), X ) ],
% 1.11/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( '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 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.11/1.48 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 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'( Y, T, X ) ) ],
% 1.11/1.48 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.11/1.48 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =(
% 1.11/1.48 'c_GCD_Ogcd__class_Ogcd'( X, Z, 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.48 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.11/1.48 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =(
% 1.11/1.48 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.48 '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_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 [ =( '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_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_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.11/1.48 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 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 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 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' ) ) ), =( X,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( 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' ) ) ), =( Y, Z ), =( X,
% 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 '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_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_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 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
% 1.11/1.48 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 1.11/1.48 Z, X ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( '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_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' ) ), =( 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' ) ) ), =( 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_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_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 ,
% 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_Ozero__class_Ozero'( X ), 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_Otimes__class_Otimes'( Y, Z
% 1.11/1.48 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 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 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( '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'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.48 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 1.11/1.48 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 1.11/1.48 , T ), =( X, Z ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.48 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 1.11/1.48 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 1.11/1.48 , T ), =( X, 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'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.11/1.48 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 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_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.11/1.48 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 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_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), 'tc_nat' ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.48 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), 'tc_nat' ), =( X,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( Y,
% 1.11/1.48 'c_GCD_Ogcd__class_Ogcd'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat'
% 1.11/1.48 ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 1.11/1.48 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat'
% 1.11/1.48 ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 1.11/1.48 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( =( X, 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.11/1.48 'tc_nat' ) ) ],
% 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_Otimes__class_Otimes'( U, Y, X ), Z
% 1.11/1.48 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 1.11/1.48 X ), Z, X ) ) ],
% 1.11/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ), 'tc_nat' ) ],
% 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_Ozero__class_Ozero'( X )
% 1.11/1.48 , X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( '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_Oplus__class_Oplus'(
% 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 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 1.11/1.48 ), 'c_Suc'( '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 ) ), =( Y,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( 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_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.11/1.48 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( 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_HOL_Oone__class_Oone'( X ), X ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( '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_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 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__algebra'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.11/1.48 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 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__algebra'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 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_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( '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_Omult__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( '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_Omult__zero'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 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_Oring__no__zero__divisors'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( '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_Oring__no__zero__divisors'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 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_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X
% 1.11/1.48 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), X ), Z, 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_Otimes__class_Otimes'( Z, Y, X ), X
% 1.11/1.48 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 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 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.11/1.48 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ), =( X
% 1.11/1.48 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 Y, X, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.11/1.48 , Y, '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, 'c_HOL_Oplus__class_Oplus'( Y,
% 1.11/1.48 X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.11/1.48 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.11/1.48 , Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.11/1.48 , 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_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_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 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_Oord__class_Oless'( 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_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_Oinverse__class_Oinverse'( 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_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_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_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, X, '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 [ =( X, 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.11/1.48 'c_HOL_Oone__class_Oone'( '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 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'(
% 1.11/1.48 'tc_nat' ), 'tc_nat' ) ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.11/1.48 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.48 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.11/1.48 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.48 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.48 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.48 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.48 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.48 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.48 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.11/1.48 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.11/1.48 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.11/1.48 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.11/1.48 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 1.11/1.48 ],
% 1.11/1.48 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X,
% 1.11/1.48 'tc_nat' ) ],
% 1.11/1.48 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ),
% 1.11/1.48 'tc_nat' ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.11/1.48 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Z,
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.11/1.48 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat'
% 1.11/1.48 ), X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 1.11/1.48 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.11/1.48 ), U, 'tc_nat' ), 'tc_nat' ), ~( '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'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 1.11/1.48 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.11/1.48 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 X, Z, 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 1.11/1.48 ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.11/1.48 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.11/1.48 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 1.11/1.48 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.48 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 1.11/1.48 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z, 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 1.11/1.48 'tc_nat' ), Y, 'tc_nat' ), U, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.48 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 1.11/1.48 'c_lessequals'( T, X, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 1.11/1.48 'tc_nat' ), Y, 'tc_nat' ), Z, 'tc_nat' ), U ) ],
% 1.11/1.48 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.11/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.11/1.48 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.11/1.48 ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.11/1.48 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.48 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.48 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.48 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.11/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.48 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.11/1.48 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.11/1.48 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.11/1.48 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X,
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.11/1.48 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.11/1.48 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.11/1.48 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 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' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.48 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.48 'tc_nat' ), Y, 'tc_nat' ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( 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_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 ), '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_Odivision__ring'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( 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_Oone__class_Oone'( X ), X ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( 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_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_Otimes__class_Otimes'( Y, Z, X )
% 1.11/1.48 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.11/1.48 , X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), 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__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__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_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_Ofield'( 't_a' ) ), ~( =( 'v_a',
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 't_a' ) ) ) ],
% 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 Y, T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.11/1.48 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.11/1.48 'c_lessequals'( T, Z, 'tc_nat' ) ) ],
% 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 Y, T, X ), X ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.48 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( T, Y
% 1.11/1.48 , X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.48 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( T, Y
% 1.11/1.48 , X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, 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_Ominus__class_Ominus'( Y, Z, 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_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.11/1.48 ,
% 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_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 [ ~( '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_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_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__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'( 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__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'( 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_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 ) ), ~(
% 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'(
% 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'(
% 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_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_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 ), '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 [ ~( '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_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 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 ), ~( 'c_lessequals'( Y,
% 1.11/1.48 Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.48 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.11/1.48 Y, X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.11/1.48 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.11/1.48 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 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 ) ), =( 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_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 [ ~( '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_Oone__class_Oone'( X ), 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 ) ) ],
% 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_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 [ ~( '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_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_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.48 Y, X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.48 ), X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), 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_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.48 ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.11/1.48 Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.11/1.48 'c_Suc'( Z ), X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.48 ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.11/1.48 , Z, X ), T, X ), ~( 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.11/1.48 , U, X ), T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.11/1.48 , Z, X ), 'c_Power_Opower__class_Opower'( T, U, X ), X ), ~(
% 1.11/1.48 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.11/1.48 , Z, X ), 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.11/1.48 'c_lessequals'( Z, T, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.11/1.48 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 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_HOL_Oord__class_Oless'( 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 ) ),
% 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 '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_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 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, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 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__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_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 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_Oone__class_Oone'( X ), X ) ],
% 1.11/1.48 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( 'c_GCD_Ogcd__class_Ogcd'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), Y, 'tc_nat' ),
% 1.11/1.48 'c_GCD_Ogcd__class_Ogcd'( Z, Y, 'tc_nat' ) ) ],
% 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'( 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 ) ), ~(
% 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, 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'( 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 ) ), ~(
% 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, T, X ) ) ],
% 1.11/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, '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' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.11/1.48 '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_Ring__and__Field_Odvd__class_Odvd'( X, Y, '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 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.11/1.48 , Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( '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 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 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_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.11/1.48 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( T,
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, U, 'tc_nat' ), 'tc_nat' ) ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 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'( 'tc_nat' ), Y,
% 1.11/1.48 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 , 'c_Nat_Osemiring__1__class_Oof__nat'( 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_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 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_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 ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 Z, U, X ) ), ~( 'c_lessequals'( Y, T, 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 ), ~(
% 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_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.11/1.48 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.11/1.48 ,
% 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 Y, T, X ) ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X
% 1.11/1.48 ), Y, X ) ), =( Z, T ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.48 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'c_HOL_Oord__class_Oless'( '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_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.48 'tc_nat' ), '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_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.11/1.48 ) ), X, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 1.11/1.48 'tc_nat' ), '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_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.11/1.48 ) ), X, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.48 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 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 ), T
% 1.11/1.48 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( T, 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_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'( '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 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), 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_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'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 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_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, 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__semidom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.48 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.11/1.48 X ), T, 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'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.48 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.11/1.48 X ), T, 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'( Z, T, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.48 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.11/1.48 'tc_nat' ), X, 'tc_nat' ) ) ],
% 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_Otimes__class_Otimes'( Y, Z
% 1.11/1.48 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.11/1.48 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), ~( =( 'c_GCD_Ogcd__class_Ogcd'(
% 1.11/1.48 X, Z, 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =(
% 1.11/1.48 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat'
% 1.11/1.48 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.11/1.48 ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), '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_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_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, 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 ) ), '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_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'( Y,
% 1.11/1.48 '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_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, 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_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_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.11/1.48 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X ), ~(
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ],
% 1.11/1.48 [ =( 'c_GCD_Ogcd__class_Ogcd'( '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_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_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__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_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__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 ),
% 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__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 ),
% 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_Ocomm__semiring__1'( X ) ),
% 1.11/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Power_Opower__class_Opower'(
% 1.11/1.48 Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.11/1.48 ), 'c_HOL_Oplus__class_Oplus'( 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'( X, Y, 'tc_nat' ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.11/1.48 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.48 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.11/1.48 X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 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'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 Z, 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'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 Z, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.48 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.11/1.48 X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 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, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 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, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 Y, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.11/1.48 'c_lessequals'( '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_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 ) ),
% 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_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 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' ), 'c_Suc'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.11/1.48 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.11/1.48 ,
% 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 ), Y
% 1.11/1.48 , X ), '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_Otimes__class_Otimes'( Y, Z, X ), Z
% 1.11/1.48 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ) ],
% 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'(
% 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 ) ) ],
% 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_Ozero__class_Ozero'( X ), T, 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 ) ) ],
% 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'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 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 ) ) ],
% 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_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.11/1.48 , 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'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.48 , Y, X ), X ) ) ],
% 1.11/1.48 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_GCD_Ogcd__class_Ogcd'( Y, 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat'
% 1.11/1.48 ), 'tc_nat' ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.11/1.48 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, '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_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ), Y ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' )
% 1.11/1.48 ],
% 1.11/1.48 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'( X, Y,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 ), =( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.11/1.48 , U, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( U,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.11/1.48 , U, X ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.11/1.48 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' )
% 1.11/1.48 , 'c_GCD_Ogcd__class_Ogcd'( X, Z, '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'( 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_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 [ 'c_lessequals'( X, 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 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( 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 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( 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_GCD_Ogcd__class_Ogcd'( 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_GCD_Ogcd__class_Ogcd'( 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 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.11/1.48 , 'tc_nat' ), Z, 'tc_nat' ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X
% 1.11/1.48 , 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' )
% 1.11/1.48 ) ],
% 1.11/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.11/1.48 , 'tc_nat' ), Z, 'tc_nat' ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y
% 1.11/1.48 , 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, '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_Otimes__class_Otimes'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( Y,
% 1.11/1.48 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.11/1.48 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.11/1.48 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, 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'( Z, 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'( X, 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'( Y, Z, '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'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.11/1.48 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.11/1.48 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.48 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.11/1.48 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.11/1.48 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 1.11/1.48 'c_Suc'( X ), 'tc_nat' ) ],
% 1.11/1.48 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.11/1.48 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.11/1.48 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1'( X ) ) ),
% 1.11/1.48 ~( 'c_lessequals'( 'c_Suc'( Y ), X, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_Suc'( 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'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.11/1.48 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_Suc'( 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'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.11/1.48 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 1.11/1.48 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ),
% 1.11/1.48 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.48 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.11/1.48 Y, X ), Z, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.48 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.11/1.48 Z, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'(
% 1.11/1.48 Z, X ), 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_Otimes__class_Otimes'(
% 1.11/1.48 Y, 'c_HOL_Oinverse__class_Oinverse'( Z, 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 ) ) ],
% 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 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.11/1.48 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.11/1.48 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 1.11/1.48 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.11/1.48 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.11/1.48 ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.11/1.48 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.48 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.11/1.48 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.11/1.48 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 1.11/1.48 ), X, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.11/1.48 'tc_nat' ), Y, 'tc_nat' ), X ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 1.11/1.48 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.11/1.48 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.11/1.48 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 1.11/1.48 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 1.11/1.48 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.11/1.48 'c_lessequals'( Z, 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'( X, 'c_HOL_Ominus__class_Ominus'( Y
% 1.11/1.48 , Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.11/1.48 'c_lessequals'( Y, Z, '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'( X, 'c_HOL_Ominus__class_Ominus'( Z
% 1.11/1.48 , Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 1.11/1.48 'tc_nat' ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 1.11/1.48 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.11/1.48 'tc_nat' ), Y, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ),
% 1.11/1.48 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.11/1.48 'tc_nat' ), X, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ),
% 1.11/1.48 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( '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_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.11/1.48 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( '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_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.11/1.48 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z,
% 1.11/1.48 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Z, Y,
% 1.11/1.48 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 1.11/1.48 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.11/1.48 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.11/1.48 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.48 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 1.11/1.48 , 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.48 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.48 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.11/1.48 ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( T ), X ),
% 1.11/1.48 'c_Power_Opower__class_Opower'( Z, 'c_Suc'( T ), X ), X ) ) ],
% 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 [ ~( '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 Y, T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.11/1.48 ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 1.11/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.11/1.48 , 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 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 ) ), ~( 'c_lessequals'( Z
% 1.11/1.48 , Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.11/1.48 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.48 X, Y, 'tc_nat' ) ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.11/1.48 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.11/1.48 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 1.11/1.48 'tc_nat' ), X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.11/1.48 Y, T, X ), X ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.11/1.48 Z ), T, 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 1.11/1.48 'tc_nat' ), X ), Y, X ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.11/1.48 'c_lessequals'( Z, Y, X ) ],
% 1.11/1.48 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ),
% 1.11/1.48 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.11/1.48 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.11/1.48 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.11/1.48 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.48 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.11/1.48 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 1.11/1.48 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ), Y,
% 1.11/1.48 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Y,
% 1.11/1.48 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 1.11/1.48 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 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 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.11/1.48 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.11/1.48 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.11/1.48 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.11/1.48 'c_lessequals'( X, 'c_Suc'( 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'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.11/1.48 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.11/1.48 Y, X ), 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'( U, T, X ), ~( 'c_lessequals'( Z, Y, 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'( Z, Y, X ), ~( 'c_lessequals'( U, T, 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'( Y, X ),
% 1.11/1.48 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 1.11/1.48 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.11/1.48 [ ~( =( X, 'c_Suc'( 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 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.11/1.48 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.11/1.48 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.11/1.48 , Y, 'tc_nat' ) ) ],
% 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_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.11/1.48 , X ) ), ~( 'c_lessequals'( 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_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.11/1.48 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 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_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_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.11/1.48 , X, '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'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.11/1.48 ), X ), Y ) ],
% 1.11/1.48 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.11/1.48 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.11/1.48 ],
% 1.11/1.48 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.48 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 1.11/1.48 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.48 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.48 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.11/1.48 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 1.11/1.48 ,
% 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_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 1.11/1.48 'tc_nat' ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.11/1.48 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.11/1.48 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.11/1.48 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 1.11/1.48 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( Y )
% 1.11/1.48 , X, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Ring__and__Field_Ofield'( 't_a' ) ],
% 1.11/1.48 [ 'c_lessequals'( 'c_Suc'( 'v_y' ), 'c_Suc'( 'v_x' ), 'tc_nat' ) ],
% 1.11/1.48 [ ~( =( 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.11/1.48 'v_a', 't_a' ), 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( 'v_x' ), 'c_Suc'(
% 1.11/1.48 'v_y' ), 'tc_nat' ), 't_a' ), 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.48 'c_Power_Opower__class_Opower'( 'v_a', 'c_Suc'( 'v_y' ), 't_a' ),
% 1.11/1.48 'c_Power_Opower__class_Opower'( 'v_a', 'c_Suc'( 'v_x' ), 't_a' ), 't_a' )
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ =( 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.11/1.48 'v_a', 't_a' ), 'c_HOL_Ominus__class_Ominus'( 'v_x', 'v_y', 'tc_nat' ),
% 1.11/1.48 't_a' ), 'c_HOL_Oinverse__class_Odivide'( 'c_Power_Opower__class_Opower'(
% 1.11/1.48 'v_a', 'v_y', 't_a' ), 'c_Power_Opower__class_Opower'( 'v_a', 'v_x',
% 1.11/1.48 't_a' ), 't_a' ) ), ~( 'c_lessequals'( 'v_y', 'v_x', 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_Ring__and__Field_Ono__zero__divisors'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_OrderedGroup_Oab__semigroup__mult'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_OrderedGroup_Oab__semigroup__add'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_Ring__and__Field_Odivision__ring'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_Ring__and__Field_Ocomm__semiring'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_OrderedGroup_Ocomm__monoid__add'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_Ring__and__Field_Ozero__neq__one'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_Ring__and__Field_Ocomm__ring__1'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_Ring__and__Field_Osemiring__1'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_Ring__and__Field_Osemiring__0'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_OrderedGroup_Oab__group__add'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_Ring__and__Field_Omult__zero'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_Ring__and__Field_Ocomm__ring'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_OrderedGroup_Omonoid__mult'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_Ring__and__Field_Osemiring'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_OrderedGroup_Omonoid__add'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_OrderedGroup_Ogroup__add'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_Ring__and__Field_Oring__1'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_Ring__and__Field_Oring'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_Ring__and__Field_Oidom'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.11/1.48 'class_Ring__and__Field_Odvd'( X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), 'class_Power_Opower'( X ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.11/1.48 ],
% 1.11/1.48 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.11/1.48 ) ],
% 1.11/1.48 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.11/1.48 ],
% 1.11/1.48 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.11/1.48 [ 'class_Power_Opower'( 'tc_nat' ) ]
% 1.11/1.48 ] .
% 1.11/1.48
% 1.11/1.48
% 1.11/1.48 percentage equality = 0.212066, percentage horn = 0.845436
% 1.11/1.48 This is a problem with some equality
% 1.11/1.48
% 1.11/1.48
% 1.11/1.48
% 1.11/1.48 Options Used:
% 1.11/1.48
% 1.11/1.48 useres = 1
% 1.11/1.48 useparamod = 1
% 1.11/1.48 useeqrefl = 1
% 1.11/1.48 useeqfact = 1
% 1.11/1.48 usefactor = 1
% 1.11/1.48 usesimpsplitting = 0
% 1.11/1.48 usesimpdemod = 5
% 1.56/1.93 usesimpres = 3
% 1.56/1.93
% 1.56/1.93 resimpinuse = 1000
% 1.56/1.93 resimpclauses = 20000
% 1.56/1.93 substype = eqrewr
% 1.56/1.93 backwardsubs = 1
% 1.56/1.93 selectoldest = 5
% 1.56/1.93
% 1.56/1.93 litorderings [0] = split
% 1.56/1.93 litorderings [1] = extend the termordering, first sorting on arguments
% 1.56/1.93
% 1.56/1.93 termordering = kbo
% 1.56/1.93
% 1.56/1.93 litapriori = 0
% 1.56/1.93 termapriori = 1
% 1.56/1.93 litaposteriori = 0
% 1.56/1.93 termaposteriori = 0
% 1.56/1.93 demodaposteriori = 0
% 1.56/1.93 ordereqreflfact = 0
% 1.56/1.93
% 1.56/1.93 litselect = negord
% 1.56/1.93
% 1.56/1.93 maxweight = 15
% 1.56/1.93 maxdepth = 30000
% 1.56/1.93 maxlength = 115
% 1.56/1.93 maxnrvars = 195
% 1.56/1.93 excuselevel = 1
% 1.56/1.93 increasemaxweight = 1
% 1.56/1.93
% 1.56/1.93 maxselected = 10000000
% 1.56/1.93 maxnrclauses = 10000000
% 1.56/1.93
% 1.56/1.93 showgenerated = 0
% 1.56/1.93 showkept = 0
% 1.56/1.93 showselected = 0
% 1.56/1.93 showdeleted = 0
% 1.56/1.93 showresimp = 1
% 1.56/1.93 showstatus = 2000
% 1.56/1.93
% 1.56/1.93 prologoutput = 1
% 1.56/1.93 nrgoals = 5000000
% 1.56/1.93 totalproof = 1
% 1.56/1.93
% 1.56/1.93 Symbols occurring in the translation:
% 1.56/1.93
% 1.56/1.93 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.56/1.93 . [1, 2] (w:1, o:123, a:1, s:1, b:0),
% 1.56/1.93 ! [4, 1] (w:0, o:55, a:1, s:1, b:0),
% 1.56/1.93 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.56/1.93 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.56/1.93 'class_Divides_Osemiring__div' [40, 1] (w:1, o:61, a:1, s:1, b:0),
% 1.56/1.93 'c_Divides_Odiv__class_Omod' [44, 3] (w:1, o:150, a:1, s:1, b:0),
% 1.56/1.93 'c_Ring__and__Field_Odvd__class_Odvd' [45, 3] (w:1, o:151, a:1, s:1
% 1.56/1.93 , b:0),
% 1.56/1.93 'tc_nat' [49, 0] (w:1, o:27, a:1, s:1, b:0),
% 1.56/1.93 'c_HOL_Oplus__class_Oplus' [50, 3] (w:1, o:154, a:1, s:1, b:0),
% 1.56/1.93 'c_HOL_Oord__class_Oless' [51, 3] (w:1, o:153, a:1, s:1, b:0),
% 1.56/1.93 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [54, 1]
% 1.56/1.93 (w:1, o:63, a:1, s:1, b:0),
% 1.56/1.93 'class_OrderedGroup_Ocomm__monoid__add' [55, 1] (w:1, o:64, a:1, s:1
% 1.56/1.93 , b:0),
% 1.56/1.93 'c_lessequals' [59, 3] (w:1, o:155, a:1, s:1, b:0),
% 1.56/1.93 'c_HOL_Ozero__class_Ozero' [60, 1] (w:1, o:65, a:1, s:1, b:0),
% 1.56/1.93 'c_GCD_Ogcd__class_Ogcd' [61, 3] (w:1, o:152, a:1, s:1, b:0),
% 1.56/1.93 'c_HOL_Oone__class_Oone' [62, 1] (w:1, o:66, a:1, s:1, b:0),
% 1.56/1.93 'c_HOL_Otimes__class_Otimes' [63, 3] (w:1, o:156, a:1, s:1, b:0),
% 1.56/1.93 'c_Suc' [64, 1] (w:1, o:67, a:1, s:1, b:0),
% 1.56/1.93 'c_HOL_Ominus__class_Ominus' [66, 3] (w:1, o:157, a:1, s:1, b:0),
% 1.56/1.93 'class_Ring__and__Field_Oring' [67, 1] (w:1, o:68, a:1, s:1, b:0),
% 1.56/1.93 'class_Ring__and__Field_Oordered__semiring__strict' [70, 1] (w:1, o:
% 1.56/1.93 74, a:1, s:1, b:0),
% 1.56/1.93 'class_Ring__and__Field_Oordered__field' [71, 1] (w:1, o:75, a:1, s:1
% 1.56/1.93 , b:0),
% 1.56/1.93 'class_Ring__and__Field_Odivision__by__zero' [72, 1] (w:1, o:80, a:1
% 1.56/1.93 , s:1, b:0),
% 1.56/1.93 'c_HOL_Oinverse__class_Odivide' [73, 3] (w:1, o:158, a:1, s:1, b:0),
% 1.56/1.93
% 1.56/1.93 'class_OrderedGroup_Omonoid__mult' [74, 1] (w:1, o:82, a:1, s:1, b:0)
% 1.56/1.93 ,
% 1.56/1.93 'class_OrderedGroup_Ocomm__monoid__mult' [75, 1] (w:1, o:83, a:1, s:1
% 1.56/1.93 , b:0),
% 1.56/1.93 'class_Ring__and__Field_Ocomm__semiring__1' [76, 1] (w:1, o:78, a:1
% 1.56/1.93 , s:1, b:0),
% 1.56/1.93 'class_Ring__and__Field_Odvd' [77, 1] (w:1, o:84, a:1, s:1, b:0),
% 1.56/1.93 'class_Ring__and__Field_Oidom' [78, 1] (w:1, o:85, a:1, s:1, b:0),
% 1.56/1.93 'class_Int_Onumber__ring' [79, 1] (w:1, o:86, a:1, s:1, b:0),
% 1.56/1.93 'class_Ring__and__Field_Oordered__ring__strict' [80, 1] (w:1, o:73
% 1.56/1.93 , a:1, s:1, b:0),
% 1.56/1.93 'c_Power_Opower__class_Opower' [81, 3] (w:1, o:159, a:1, s:1, b:0),
% 1.56/1.93 'class_Nat_Osemiring__char__0' [82, 1] (w:1, o:62, a:1, s:1, b:0),
% 1.56/1.93 'c_Nat_Osemiring__1__class_Oof__nat' [83, 2] (w:1, o:148, a:1, s:1
% 1.56/1.93 , b:0),
% 1.56/1.93 'class_Ring__and__Field_Oordered__semiring' [84, 1] (w:1, o:87, a:1
% 1.56/1.93 , s:1, b:0),
% 1.56/1.93 'class_OrderedGroup_Olordered__ab__group__add' [87, 1] (w:1, o:81, a:
% 1.56/1.93 1, s:1, b:0),
% 1.56/1.93 'class_OrderedGroup_Opordered__comm__monoid__add' [88, 1] (w:1, o:88
% 1.56/1.93 , a:1, s:1, b:0),
% 1.56/1.93 'class_Ring__and__Field_Ono__zero__divisors' [89, 1] (w:1, o:72, a:1
% 1.56/1.93 , s:1, b:0),
% 1.56/1.93 'class_Ring__and__Field_Oring__no__zero__divisors' [90, 1] (w:1, o:89
% 1.56/1.93 , a:1, s:1, b:0),
% 1.56/1.93 'class_Ring__and__Field_Oordered__idom' [91, 1] (w:1, o:90, a:1, s:1
% 1.56/1.93 , b:0),
% 1.56/1.93 'class_Ring__and__Field_Ozero__neq__one' [92, 1] (w:1, o:91, a:1, s:1
% 1.56/1.93 , b:0),
% 1.56/1.93 'c_HOL_Oinverse__class_Oinverse' [97, 2] (w:1, o:149, a:1, s:1, b:0)
% 17.80/18.20 ,
% 17.80/18.20 'class_Ring__and__Field_Ofield' [98, 1] (w:1, o:92, a:1, s:1, b:0),
% 17.80/18.20 'class_Ring__and__Field_Oordered__semidom' [99, 1] (w:1, o:93, a:1
% 17.80/18.20 , s:1, b:0),
% 17.80/18.20 'class_Orderings_Olinorder' [100, 1] (w:1, o:94, a:1, s:1, b:0),
% 17.80/18.20 'class_Orderings_Oorder' [101, 1] (w:1, o:95, a:1, s:1, b:0),
% 17.80/18.20 'class_Orderings_Opreorder' [102, 1] (w:1, o:96, a:1, s:1, b:0),
% 17.80/18.20 'class_OrderedGroup_Oab__group__add' [103, 1] (w:1, o:97, a:1, s:1
% 17.80/18.20 , b:0),
% 17.80/18.20 'class_OrderedGroup_Oab__semigroup__add' [104, 1] (w:1, o:98, a:1, s:
% 17.80/18.20 1, b:0),
% 17.80/18.20 'class_Ring__and__Field_Omult__zero' [105, 1] (w:1, o:69, a:1, s:1
% 17.80/18.20 , b:0),
% 17.80/18.20 'class_Power_Opower' [106, 1] (w:1, o:108, a:1, s:1, b:0),
% 17.80/18.20 'class_RealVector_Oreal__normed__algebra' [107, 1] (w:1, o:109, a:1
% 17.80/18.20 , s:1, b:0),
% 17.80/18.20 'class_Ring__and__Field_Osemiring' [108, 1] (w:1, o:112, a:1, s:1, b:
% 17.80/18.20 0),
% 17.80/18.20 'class_Ring__and__Field_Oordered__comm__semiring__strict' [111, 1]
% 17.80/18.20 (w:1, o:113, a:1, s:1, b:0),
% 17.80/18.20 'class_OrderedGroup_Oab__semigroup__idem__mult' [112, 1] (w:1, o:99
% 17.80/18.20 , a:1, s:1, b:0),
% 17.80/18.20 'class_Ring__and__Field_Osemiring__0' [113, 1] (w:1, o:114, a:1, s:1
% 17.80/18.20 , b:0),
% 17.80/18.20 'class_Ring__and__Field_Omult__mono1' [115, 1] (w:1, o:70, a:1, s:1
% 17.80/18.20 , b:0),
% 17.80/18.20 'class_Ring__and__Field_Omult__mono' [116, 1] (w:1, o:71, a:1, s:1
% 17.80/18.20 , b:0),
% 17.80/18.20 'class_Ring__and__Field_Opordered__ring' [117, 1] (w:1, o:115, a:1
% 17.80/18.20 , s:1, b:0),
% 17.80/18.20 'class_Ring__and__Field_Odivision__ring' [118, 1] (w:1, o:116, a:1
% 17.80/18.20 , s:1, b:0),
% 17.80/18.20 'class_Ring__and__Field_Osemiring__1' [119, 1] (w:1, o:117, a:1, s:1
% 17.80/18.20 , b:0),
% 17.80/18.20 'class_Ring__and__Field_Ocomm__ring' [120, 1] (w:1, o:76, a:1, s:1
% 17.80/18.20 , b:0),
% 17.80/18.20 'class_Ring__and__Field_Opordered__cancel__semiring' [123, 1] (w:1
% 17.80/18.20 , o:118, a:1, s:1, b:0),
% 17.80/18.20 'class_OrderedGroup_Oab__semigroup__mult' [124, 1] (w:1, o:100, a:1
% 17.80/18.20 , s:1, b:0),
% 17.80/18.20 'class_Ring__and__Field_Ocomm__semiring' [127, 1] (w:1, o:79, a:1, s:
% 17.80/18.20 1, b:0),
% 17.80/18.20 'class_OrderedGroup_Omonoid__add' [128, 1] (w:1, o:101, a:1, s:1, b:0
% 17.80/18.20 ),
% 17.80/18.20 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [129, 1]
% 17.80/18.20 (w:1, o:102, a:1, s:1, b:0),
% 17.80/18.20 'class_OrderedGroup_Opordered__ab__group__add' [130, 1] (w:1, o:103
% 17.80/18.20 , a:1, s:1, b:0),
% 17.80/18.20 'class_OrderedGroup_Opordered__ab__semigroup__add' [131, 1] (w:1, o:
% 17.80/18.20 104, a:1, s:1, b:0),
% 17.80/18.20 'class_Ring__and__Field_Opordered__semiring' [133, 1] (w:1, o:119, a:
% 17.80/18.20 1, s:1, b:0),
% 17.80/18.20 'class_OrderedGroup_Ocancel__ab__semigroup__add' [134, 1] (w:1, o:105
% 17.80/18.20 , a:1, s:1, b:0),
% 17.80/18.20 'class_OrderedGroup_Ocancel__semigroup__add' [135, 1] (w:1, o:106, a:
% 17.80/18.20 1, s:1, b:0),
% 17.80/18.20 'class_Divides_Oring__div' [136, 1] (w:1, o:60, a:1, s:1, b:0),
% 17.80/18.20 'class_Ring__and__Field_Ocomm__ring__1' [139, 1] (w:1, o:77, a:1, s:1
% 17.80/18.20 , b:0),
% 17.80/18.20 'class_OrderedGroup_Ogroup__add' [140, 1] (w:1, o:107, a:1, s:1, b:0)
% 17.80/18.20 ,
% 17.80/18.20 'class_RealVector_Oreal__field' [141, 1] (w:1, o:120, a:1, s:1, b:0)
% 17.80/18.20 ,
% 17.80/18.20 'class_Ring__and__Field_Oring__1__no__zero__divisors' [143, 1] (w:1
% 17.80/18.20 , o:110, a:1, s:1, b:0),
% 17.80/18.20 'class_RealVector_Oreal__normed__field' [144, 1] (w:1, o:121, a:1, s:
% 17.80/18.20 1, b:0),
% 17.80/18.20 't_a' [148, 0] (w:1, o:47, a:1, s:1, b:0),
% 17.80/18.20 'v_a' [149, 0] (w:1, o:48, a:1, s:1, b:0),
% 17.80/18.20 'c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1' [154, 1] (w:1, o:122, a:
% 17.80/18.20 1, s:1, b:0),
% 17.80/18.20 'class_Ring__and__Field_Oring__1' [155, 1] (w:1, o:111, a:1, s:1, b:0
% 17.80/18.20 ),
% 17.80/18.20 'v_y' [157, 0] (w:1, o:53, a:1, s:1, b:0),
% 17.80/18.20 'v_x' [158, 0] (w:1, o:52, a:1, s:1, b:0).
% 17.80/18.20
% 17.80/18.20
% 17.80/18.20 Starting Search:
% 17.80/18.20
% 17.80/18.20 Resimplifying inuse:
% 17.80/18.20 Done
% 17.80/18.20
% 17.80/18.20
% 17.80/18.20 Intermediate Status:
% 17.80/18.20 Generated: 4714
% 17.80/18.20 Kept: 2027
% 17.80/18.20 Inuse: 219
% 17.80/18.20 Deleted: 7
% 17.80/18.20 Deletedinuse: 0
% 17.80/18.20
% 17.80/18.20 Resimplifying inuse:
% 17.80/18.20 Done
% 17.80/18.20
% 17.80/18.20 Resimplifying inuse:
% 17.80/18.20 Done
% 17.80/18.20
% 17.80/18.20
% 17.80/18.20 Intermediate Status:
% 17.80/18.20 Generated: 10828
% 17.80/18.20 Kept: 4125
% 17.80/18.20 Inuse: 298
% 17.80/18.20 Deleted: 14
% 17.80/18.20 Deletedinuse: 1
% 17.80/18.20
% 17.80/18.20 Resimplifying inuse:
% 17.80/18.20 Done
% 17.80/18.20
% 17.80/18.20 Resimplifying inuse:
% 17.80/18.20 Done
% 17.80/18.20
% 17.80/18.20
% 17.80/18.20 Intermediate Status:
% 17.80/18.20 Generated: 18206
% 17.80/18.20 Kept: 6163
% 17.80/18.20 Inuse: 323
% 17.80/18.20 Deleted: 14
% 17.80/18.20 Deletedinuse: 1
% 17.80/18.20
% 17.80/18.20 Resimplifying inuse:
% 17.80/18.20 Done
% 17.80/18.20
% 17.80/18.20 Resimplifying inuse:
% 17.80/18.20 Done
% 17.80/18.20
% 17.80/18.20
% 17.80/18.20 Intermediate Status:
% 62.78/63.17 Generated: 28447
% 62.78/63.17 Kept: 8206
% 62.78/63.17 Inuse: 378
% 62.78/63.17 Deleted: 15
% 62.78/63.17 Deletedinuse: 2
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 40191
% 62.78/63.17 Kept: 10516
% 62.78/63.17 Inuse: 456
% 62.78/63.17 Deleted: 22
% 62.78/63.17 Deletedinuse: 2
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 51634
% 62.78/63.17 Kept: 12649
% 62.78/63.17 Inuse: 476
% 62.78/63.17 Deleted: 22
% 62.78/63.17 Deletedinuse: 2
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 62671
% 62.78/63.17 Kept: 14664
% 62.78/63.17 Inuse: 532
% 62.78/63.17 Deleted: 26
% 62.78/63.17 Deletedinuse: 4
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 75099
% 62.78/63.17 Kept: 16696
% 62.78/63.17 Inuse: 591
% 62.78/63.17 Deleted: 29
% 62.78/63.17 Deletedinuse: 4
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 97213
% 62.78/63.17 Kept: 19656
% 62.78/63.17 Inuse: 678
% 62.78/63.17 Deleted: 33
% 62.78/63.17 Deletedinuse: 5
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying clauses:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 108795
% 62.78/63.17 Kept: 21673
% 62.78/63.17 Inuse: 699
% 62.78/63.17 Deleted: 597
% 62.78/63.17 Deletedinuse: 5
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 119533
% 62.78/63.17 Kept: 23686
% 62.78/63.17 Inuse: 753
% 62.78/63.17 Deleted: 604
% 62.78/63.17 Deletedinuse: 9
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 131490
% 62.78/63.17 Kept: 25700
% 62.78/63.17 Inuse: 794
% 62.78/63.17 Deleted: 608
% 62.78/63.17 Deletedinuse: 11
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 143350
% 62.78/63.17 Kept: 27727
% 62.78/63.17 Inuse: 832
% 62.78/63.17 Deleted: 608
% 62.78/63.17 Deletedinuse: 11
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 156142
% 62.78/63.17 Kept: 29834
% 62.78/63.17 Inuse: 857
% 62.78/63.17 Deleted: 608
% 62.78/63.17 Deletedinuse: 11
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 173725
% 62.78/63.17 Kept: 32003
% 62.78/63.17 Inuse: 892
% 62.78/63.17 Deleted: 609
% 62.78/63.17 Deletedinuse: 12
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 183514
% 62.78/63.17 Kept: 34013
% 62.78/63.17 Inuse: 931
% 62.78/63.17 Deleted: 609
% 62.78/63.17 Deletedinuse: 12
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 198418
% 62.78/63.17 Kept: 36043
% 62.78/63.17 Inuse: 957
% 62.78/63.17 Deleted: 611
% 62.78/63.17 Deletedinuse: 14
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 218695
% 62.78/63.17 Kept: 38732
% 62.78/63.17 Inuse: 1008
% 62.78/63.17 Deleted: 615
% 62.78/63.17 Deletedinuse: 14
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 228184
% 62.78/63.17 Kept: 40745
% 62.78/63.17 Inuse: 1035
% 62.78/63.17 Deleted: 620
% 62.78/63.17 Deletedinuse: 16
% 62.78/63.17
% 62.78/63.17 Resimplifying clauses:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 266257
% 62.78/63.17 Kept: 44076
% 62.78/63.17 Inuse: 1051
% 62.78/63.17 Deleted: 1886
% 62.78/63.17 Deletedinuse: 17
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 283799
% 62.78/63.17 Kept: 46786
% 62.78/63.17 Inuse: 1066
% 62.78/63.17 Deleted: 1886
% 62.78/63.17 Deletedinuse: 17
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 295353
% 62.78/63.17 Kept: 48787
% 62.78/63.17 Inuse: 1097
% 62.78/63.17 Deleted: 1887
% 62.78/63.17 Deletedinuse: 17
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 312142
% 62.78/63.17 Kept: 50916
% 62.78/63.17 Inuse: 1115
% 62.78/63.17 Deleted: 1888
% 62.78/63.17 Deletedinuse: 18
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 322011
% 62.78/63.17 Kept: 53132
% 62.78/63.17 Inuse: 1125
% 62.78/63.17 Deleted: 1889
% 62.78/63.17 Deletedinuse: 19
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 336697
% 62.78/63.17 Kept: 55277
% 62.78/63.17 Inuse: 1161
% 62.78/63.17 Deleted: 1900
% 62.78/63.17 Deletedinuse: 21
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 360335
% 62.78/63.17 Kept: 57950
% 62.78/63.17 Inuse: 1176
% 62.78/63.17 Deleted: 1900
% 62.78/63.17 Deletedinuse: 21
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 374472
% 62.78/63.17 Kept: 59956
% 62.78/63.17 Inuse: 1198
% 62.78/63.17 Deleted: 1900
% 62.78/63.17 Deletedinuse: 21
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying clauses:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17 Resimplifying inuse:
% 62.78/63.17 Done
% 62.78/63.17
% 62.78/63.17
% 62.78/63.17 Intermediate Status:
% 62.78/63.17 Generated: 392394
% 62.78/63.17 Kept: 62107
% 143.21/143.65 Inuse: 1241
% 143.21/143.65 Deleted: 2587
% 143.21/143.65 Deletedinuse: 21
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 408233
% 143.21/143.65 Kept: 64267
% 143.21/143.65 Inuse: 1276
% 143.21/143.65 Deleted: 2590
% 143.21/143.65 Deletedinuse: 24
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 424393
% 143.21/143.65 Kept: 66327
% 143.21/143.65 Inuse: 1301
% 143.21/143.65 Deleted: 2590
% 143.21/143.65 Deletedinuse: 24
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 440785
% 143.21/143.65 Kept: 68486
% 143.21/143.65 Inuse: 1311
% 143.21/143.65 Deleted: 2590
% 143.21/143.65 Deletedinuse: 24
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 462693
% 143.21/143.65 Kept: 70809
% 143.21/143.65 Inuse: 1352
% 143.21/143.65 Deleted: 2590
% 143.21/143.65 Deletedinuse: 24
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 476075
% 143.21/143.65 Kept: 72935
% 143.21/143.65 Inuse: 1366
% 143.21/143.65 Deleted: 2590
% 143.21/143.65 Deletedinuse: 24
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 489958
% 143.21/143.65 Kept: 75022
% 143.21/143.65 Inuse: 1391
% 143.21/143.65 Deleted: 2590
% 143.21/143.65 Deletedinuse: 24
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 514622
% 143.21/143.65 Kept: 78271
% 143.21/143.65 Inuse: 1416
% 143.21/143.65 Deleted: 2590
% 143.21/143.65 Deletedinuse: 24
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 530195
% 143.21/143.65 Kept: 80282
% 143.21/143.65 Inuse: 1423
% 143.21/143.65 Deleted: 2590
% 143.21/143.65 Deletedinuse: 24
% 143.21/143.65
% 143.21/143.65 Resimplifying clauses:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 541971
% 143.21/143.65 Kept: 82340
% 143.21/143.65 Inuse: 1446
% 143.21/143.65 Deleted: 3283
% 143.21/143.65 Deletedinuse: 24
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 557579
% 143.21/143.65 Kept: 84392
% 143.21/143.65 Inuse: 1476
% 143.21/143.65 Deleted: 3283
% 143.21/143.65 Deletedinuse: 24
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 569891
% 143.21/143.65 Kept: 86411
% 143.21/143.65 Inuse: 1499
% 143.21/143.65 Deleted: 3283
% 143.21/143.65 Deletedinuse: 24
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 585594
% 143.21/143.65 Kept: 88477
% 143.21/143.65 Inuse: 1521
% 143.21/143.65 Deleted: 3283
% 143.21/143.65 Deletedinuse: 24
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 603710
% 143.21/143.65 Kept: 90817
% 143.21/143.65 Inuse: 1551
% 143.21/143.65 Deleted: 3283
% 143.21/143.65 Deletedinuse: 24
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 625641
% 143.21/143.65 Kept: 93604
% 143.21/143.65 Inuse: 1576
% 143.21/143.65 Deleted: 3283
% 143.21/143.65 Deletedinuse: 24
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 646823
% 143.21/143.65 Kept: 96243
% 143.21/143.65 Inuse: 1586
% 143.21/143.65 Deleted: 3283
% 143.21/143.65 Deletedinuse: 24
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 672102
% 143.21/143.65 Kept: 100801
% 143.21/143.65 Inuse: 1605
% 143.21/143.65 Deleted: 3283
% 143.21/143.65 Deletedinuse: 24
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying clauses:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 684747
% 143.21/143.65 Kept: 105055
% 143.21/143.65 Inuse: 1615
% 143.21/143.65 Deleted: 3593
% 143.21/143.65 Deletedinuse: 25
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 697647
% 143.21/143.65 Kept: 107273
% 143.21/143.65 Inuse: 1636
% 143.21/143.65 Deleted: 3595
% 143.21/143.65 Deletedinuse: 27
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 708601
% 143.21/143.65 Kept: 109275
% 143.21/143.65 Inuse: 1644
% 143.21/143.65 Deleted: 3595
% 143.21/143.65 Deletedinuse: 27
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 719957
% 143.21/143.65 Kept: 111595
% 143.21/143.65 Inuse: 1651
% 143.21/143.65 Deleted: 3595
% 143.21/143.65 Deletedinuse: 27
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 730294
% 143.21/143.65 Kept: 113730
% 143.21/143.65 Inuse: 1671
% 143.21/143.65 Deleted: 3595
% 143.21/143.65 Deletedinuse: 27
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 768339
% 143.21/143.65 Kept: 118222
% 143.21/143.65 Inuse: 1696
% 143.21/143.65 Deleted: 3595
% 143.21/143.65 Deletedinuse: 27
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Status:
% 143.21/143.65 Generated: 784889
% 143.21/143.65 Kept: 121109
% 143.21/143.65 Inuse: 1712
% 143.21/143.65 Deleted: 3599
% 143.21/143.65 Deletedinuse: 27
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying clauses:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65 Resimplifying inuse:
% 143.21/143.65 Done
% 143.21/143.65
% 143.21/143.65
% 143.21/143.65 Intermediate Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------